Question 1

In the following letter pair analogy, PIR is related to OHQ in a particular way. Using the same pattern, which of the following letter pairs correctly completes the analogy?

Accepted Answer

Introduction / Context: This question presents a relationship between two three letter groups, PIR and OHQ, and asks you to select another pair of three letter groups that follows the same rule. Letter analogies usually involve operations on positions in the English alphabet such as shifting letters forward or backward by a fixed number, or applying different shifts to different positions. Here we must carefully examine how each letter in PIR transforms into each letter in OHQ. Given Data / Assumptions: - First group: PIR is transformed into second group: OHQ. - Each position may undergo the same or a different shift in the alphabet. - The alphabet positions are A = 1, B = 2, and so on up to Z = 26. - We must find the option whose first three letter group transforms into the second three letter group in exactly the same way that PIR transforms into OHQ. Concept / Approach: We convert letters to their alphabet positions and then compare. P is the 16th letter, O is the 15th letter, I is the 9th letter, H is the 8th letter, R is the 18th letter, and Q is the 17th letter. In each case, the second letter in the pair is one position earlier in the alphabet than the first letter. Therefore the rule is shift each letter back by one position. We must now find an option where the second group is formed by shifting every letter of the first group back by exactly one position, taking Z to mean a shift back to Y and so on, including wrap around if needed. Step-by-Step Solution: Step 1: Calculate shifts in the given pair. P to O is minus one, I to H is minus one, and R to Q is minus one in alphabet order. Step 2: Apply this rule to option C, FAX : EZW, as a candidate. Step 3: F is the 6th letter and E is the 5th, so this is a backward shift of one position. Step 4: A is the 1st letter and Z is the 26th. Moving from A back by one position wraps around to Z, again a backward shift of one. Step 5: X is the 24th letter and W is the 23rd, again a backward shift of one position. Step 6: Since each letter in FAX moves back by exactly one position to produce EZW, this pair follows the same pattern as PIR : OHQ. Verification / Alternative check: Check the other options to ensure they do not follow the same rule. In option A, KLO : MOR, K to M is plus two, not minus one. In option B, the shifts are inconsistent across letters, and in option D, KMN : LNO, again the first letters increase instead of decrease. Therefore, only option C obeys the consistent rule of each letter moving one step backward in the alphabet. This mirrors exactly how PIR transforms into OHQ. Why Other Options Are Wrong: Option A shows a forward shift rather than a backward one, which does not match the original pattern. Option B contains unequal shifts across letters, meaning there is no single step change from the first group to the second. Option D likewise fails to maintain a constant shift of minus one for each letter. Since the original analogy clearly uses a fixed backward shift of one step for each character, those options cannot be correct. Common Pitfalls: A frequent error is checking only one or two letters and ignoring the rest, which can make an inconsistent pattern appear valid. Another mistake is miscounting alphabet positions or forgetting to handle wrap around at A and Z. To avoid these issues, always verify the transformation for every letter in the group and confirm that the same operation is applied consistently. When you do this carefully, FAX : EZW stands out as the only pair that matches PIR : OHQ. Final Answer: Because each letter in FAX is shifted back by one position to form EZW, just as each letter in PIR is shifted back by one to form OHQ, the correct pair is FAX : EZW, so option C is correct.

Question 2

In the following number analogy, 563 is related to 635. Using the same rearrangement pattern, 894 will be related to which of the following numbers?

Accepted Answer

Introduction / Context: This is a number analogy involving rearrangement of digits. The pair 563 : 635 suggests that the digits of the first number have been permuted to obtain the second. The question is to identify the same pattern and apply it to 894 to determine the correct related number. Such questions test observation of position changes rather than arithmetic operations like addition or multiplication. Given Data / Assumptions: - First pair is 563 and 635, written as 563 : 635. - Second pair begins with 894 and needs to be completed as 894 : ?. - Each number has three digits, so patterns may involve rotation or rearrangement of these digits. - The correct option must be obtainable by applying the same positional change to 894 that turns 563 into 635. Concept / Approach: First, analyse how the digits move in the pair 563 to 635. The digits of 563 are 5, 6, and 3. The digits of 635 are 6, 3, and 5. The hundreds digit 5 has moved to the units place, the tens digit 6 has moved to the hundreds place, and the units digit 3 has moved to the tens place. This is equivalent to a left rotation of the digits, where each digit moves one place left and the leftmost digit wraps around to the right. Once this pattern is recognised, apply the same left rotation to 8, 9, and 4 in 894. Step-by-Step Solution: Step 1: Write down 563 as 5, 6, 3 and its partner 635 as 6, 3, 5. Step 2: Observe that 5 moves from first to third position, 6 moves from second to first, and 3 moves from third to second. Step 3: Recognise this as a left rotation: 5, 6, 3 becomes 6, 3, 5. Step 4: Now write 894 as 8, 9, 4. Step 5: Apply the same left rotation. The first digit 8 goes to the end, the second digit 9 moves to the first position, and the third digit 4 moves to the second position. Step 6: The new order is 9, 4, 8, which forms the number 948. Step 7: Check options and confirm that 948 is offered as option D. Verification / Alternative check: To verify, test the identified rule again on the original pair. Rotating 5, 6, 3 left gives 6, 3, 5, which matches 635 exactly. No arithmetic adjustment is required, so the rule is purely positional. Applying any different rearrangement to 894, such as reversing digits or rotating right, produces results like 498 or 489, which do not follow the same pattern. Therefore only 948 is consistent with the given example. Why Other Options Are Wrong: Option A, 849, corresponds to moving the last digit to the first position and shifting others right, which is a different rotation. Option B, 489, is a more complex rearrangement that does not match the original pattern. Option C, 498, appears to be a reversal of 894 with an additional change. None of these transitions reflect the simple left rotation that transforms 563 into 635. Hence they must be rejected. Common Pitfalls: Some learners immediately apply arithmetic operations such as adding or subtracting fixed values between numbers, overlooking that the digits have simply been rearranged. Others may detect a rotation but apply it in the wrong direction. To avoid these mistakes, always compare each digit position in both numbers and look for a consistent positional mapping before attempting more complex operations. This reduces confusion and leads quickly to the correct answer in this type of question. Final Answer: Following the same left rotation of digits that maps 563 to 635, the number 894 is mapped to 948, so option D is correct.

Question 3

In the following letter pair analogy, MOK is related to KLG. Using the same alphabetic shift pattern, which of the following pairs correctly completes the analogy?

Accepted Answer

Introduction / Context: This analogy involves three letter groups and checks the ability to recognise different alphabetic shifts applied to each position. The reference pair MOK : KLG suggests that each letter has been shifted by a different fixed amount. The challenge is to identify these shifts and then choose the option where the first group of three letters changes to the second group using the same pattern. Recognition of positional shifts is a common requirement in letter based logical reasoning questions. Given Data / Assumptions: - The first pair given is MOK and KLG. - The letters are all capital, and we use the English alphabet positions A = 1 to Z = 26. - Each letter in MOK may be shifted by a different constant to obtain KLG. - The correct option must apply the same set of shifts to its own first triple to produce its second triple. Concept / Approach: First, convert each letter into its numeric position. M is 13, O is 15, K is 11. K is 11, L is 12, G is 7. The shift from M to K is minus 2, from O to L is minus 3, and from K to G is minus 4. Thus the pattern is position one minus two, position two minus three, and position three minus four. We now test each option to see which first triple transforms into the second triple under this exact sequence of shifts. Only the pair that follows minus two, minus three, and minus four consistently is acceptable. Step-by-Step Solution: Step 1: Compute the shifts for MOK to KLG. M(13) to K(11) is minus two. Step 2: O(15) to L(12) is minus three. Step 3: K(11) to G(7) is minus four. Step 4: Apply the same pattern to option A, FIM : DFI. F(6) minus two equals D(4), I(9) minus three equals F(6), and M(13) minus four equals I(9). Step 5: All three letters in FIM transform perfectly into DFI under the pattern minus two, minus three, minus four. Step 6: Test the other options quickly and see that they do not follow this exact sequence of decreases, so option A uniquely matches the original rule. Verification / Alternative check: We can reconfirm by reversing the operation for option A. Adding two, three, and four to DFI should bring us back to FIM. D(4) plus two gives F(6), F(6) plus three gives I(9), and I(9) plus four gives M(13), demonstrating that the transformation is symmetric and stable. The original pair MOK and KLG also shows this behaviour, so the pattern is confirmed. Other options either use different shifts, unequal shifts, or include letters that would fall outside the alphabet if the same subtraction were applied. Why Other Options Are Wrong: Option B, TMA : UNB, involves different directional shifts and does not match the minus two, minus three, minus four pattern. Option C, KCN : JBM, and option D, FSA : IVD, also fail when checked position by position, because their letters do not reduce by the same set of values. Without a consistent transformation, they cannot represent the same relationship as MOK : KLG. Common Pitfalls: A typical mistake is to assume that every letter shifts by the same amount, leading to rejection of the correct pattern. Another pitfall is miscounting alphabet positions or forgetting that separate positions can have separate fixed shifts. To avoid errors, always record the numeric positions of the letters and calculate the differences carefully for each position. Then apply the exact same sequence of changes to each candidate pair to see which one matches the model pattern exactly. Final Answer: The only pair that follows the position wise shifts minus two, minus three, and minus four, just as MOK changes to KLG, is FIM : DFI, so option A is correct.

Question 4

Select the related letter pair that completes the analogy: GI is related to HJ in the same way as PR is related to which of the following?

Accepted Answer

Introduction / Context: This question uses a simple alphabet shift analogy. The pair GI : HJ indicates that each letter in the first pair has been shifted forward in the alphabet by the same amount to produce the second pair. We must detect that shift and apply it to the new pair PR to identify the correct completion. Such questions appear frequently in logical reasoning and test the ability to work with alphabet positions in a systematic way. Given Data / Assumptions: - First pair: GI is transformed into HJ. - Second pair: PR must transform into an unknown pair from the options. - We use standard English alphabet positions with A = 1, B = 2, and so on. - The shift is expected to be the same for each letter within the pair GI : HJ. Concept / Approach: Begin by assigning alphabet positions. G is the 7th letter, H is the 8th letter. I is the 9th letter, and J is the 10th letter. So G moves forward to H by plus one, and I moves forward to J also by plus one. This reveals a simple pattern: each letter is shifted forward by one position. Next we apply the same rule to P and R. P is the 16th letter, and moving forward one step gives Q (17th). R is the 18th letter, and moving forward one step gives S (19th). Therefore PR becomes QS under the same rule. Step-by-Step Solution: Step 1: Write the first pair GI : HJ and determine the shift from G to H. Step 2: Note that G(7) to H(8) is plus one, and I(9) to J(10) is also plus one. Step 3: Conclude that the rule is shift each letter forward by one alphabet position. Step 4: Apply this to P and R. P(16) plus one becomes Q(17). Step 5: R(18) plus one becomes S(19). Step 6: The resulting pair is QS, which appears as option C. Verification / Alternative check: We can quickly test the other options. Option A, QR, would require P to move to Q and R to remain R, which does not use the same shift on both letters. Option B, PO, involves moving backwards or staying in place, not moving forward. Option D, NO, requires decreasing both letters. None of these match the consistent plus one pattern that GI : HJ clearly demonstrates. Therefore, QS is the only option that fits. Why Other Options Are Wrong: Option A changes only the first letter but not the second in a consistent way. Option B moves P back to P and R back to O, blending different directions and magnitudes of shift. Option D also mixes shifts in a way that does not correspond to the simple plus one rule. Since analogies require the exact same operation to be applied, any option without uniform forward shifting must be rejected. Common Pitfalls: A common trap is to focus on the shapes or sound of the letters instead of their positions in the alphabet. Another mistake is to compute the shift for one letter correctly but not verify the others, leading to acceptance of inconsistent patterns. To avoid such errors, always convert letters into numeric positions and ensure the shift is the same in every position for that pair. Quick mental practice with alphabet positions makes such questions simple in timed tests. Final Answer: Since GI is transformed into HJ by adding one to each letter, PR must similarly become QS, so option C is the correct answer.

Question 5

Select the related word that completes the analogy: AIDS is related to VIRUS in the same way as MALARIA is related to which of the following?

Accepted Answer

Introduction / Context: This analogy is based on diseases and their causative agents. The pair AIDS : VIRUS indicates that AIDS is a disease caused by a virus, specifically the human immunodeficiency virus. The second part of the analogy asks for the type of organism responsible for causing malaria. Recognising which organisms cause which diseases is part of basic general science and biology knowledge frequently tested in aptitude and entrance examinations. Given Data / Assumptions: - AIDS is a disease caused by a virus. - The word VIRUS in the pair describes the causative agent type, not the specific virus name. - Malaria is another infectious disease transmitted by the bite of certain mosquitoes. - The options list different groups of microscopic organisms: Protozoa, Bacteria, Fungi, and Algae. Concept / Approach: The relation is disease to causative agent. Therefore we must identify the organism group that causes malaria. Biology tells us that malaria is caused by parasites belonging to the genus Plasmodium. Plasmodium species are protozoan organisms, not bacteria, fungi, or algae. Thus the correct completion of the analogy is MALARIA : PROTOZOA. The other organism groups are associated with other types of infections or roles in ecosystems but not with malaria specifically. Step-by-Step Solution: Step 1: Interpret the given pair. AIDS is caused by a virus, so AIDS : VIRUS follows the pattern disease to causative agent type. Step 2: Recall that malaria is caused by Plasmodium parasites. Step 3: Classify Plasmodium. It belongs to the kingdom of protozoa, a group of single celled eukaryotic organisms. Step 4: Option A, Protozoa, matches this classification directly. Step 5: Option B, Bacteria, refers to prokaryotic organisms which cause other diseases like tuberculosis but not malaria. Step 6: Option C, Fungi, includes yeasts and moulds, responsible for fungal infections, and option D, Algae, mainly describe photosynthetic aquatic organisms. Step 7: Therefore MALARIA : PROTOZOA mirrors the pattern of AIDS : VIRUS. Verification / Alternative check: As a verification step, we can rewrite both pairs explicitly. AIDS is caused by a virus is accurate, and malaria is caused by protozoa is also accurate. Malaria is not caused by bacteria, fungi, or algae, so any attempt to substitute those groups produces a false statement. This confirms that the only correct choice is Protozoa. Many biology textbooks and exam syllabi highlight this specific cause, which supports the analogy. Why Other Options Are Wrong: Bacteria are important disease causing agents but are not responsible for malaria. Fungi cause conditions like ringworm and candidiasis. Algae can cause blooms in water bodies but are not considered parasites in the same sense. Hence, choosing any of these would misrepresent the well established medical fact about malaria. Since the analogy depends on correct scientific relationships, only Protozoa satisfies the requirement. Common Pitfalls: Some learners may confuse bacteria and protozoa because both are microscopic and associated with infectious diseases. Others might simply pick any organism that sounds familiar without recalling the specific disease agent. To avoid such mistakes, it helps to remember standard examples: AIDS virus for viral disease, Plasmodium protozoa for malaria, and tubercle bacillus for a bacterial disease. Mnemonics and repeated practice with such analogies can make these associations easier to recall in exams. Final Answer: Since malaria is caused by protozoan parasites, the correct completion of the analogy is MALARIA : PROTOZOA, and option A is correct.

Question 6

Select the related letter that completes the analogy: E is related to V in the same mirror position pattern as D is related to which of the following letters?

Accepted Answer

Introduction / Context: This analogy question uses alphabet positions that are symmetric around the middle of the alphabet. The pair E : V hints that the second letter is positioned in a way that mirrors the first letter with respect to the centre of the alphabet. We need to apply the same mirror relationship to D and choose the corresponding letter from the options. Understanding opposite or complementary positions in the alphabet is useful in many coding and decoding type reasoning questions. Given Data / Assumptions: - The English alphabet has 26 letters from A to Z. - E is the 5th letter from the start, and V is the 22nd letter. - The sum of positions 5 and 22 is 27, which is one more than the total number of letters in the alphabet. - For a symmetrical or mirror relationship, the positions of the two letters should add up to 27 (for standard 26 letter alphabet indexing). Concept / Approach: In such mirror position analogies, A and Z form a pair because their positions are 1 and 26, which sum to 27. Likewise, B and Y sum to 27, C and X sum to 27, and so on. E is 5 and V is 22, and 5 plus 22 equals 27, so they are mirror letters about the centre of the alphabet. To find the corresponding partner for D, which is the 4th letter, we need a letter whose position is 27 minus 4, which is 23. The 23rd letter of the alphabet is W. Step-by-Step Solution: Step 1: Confirm the pattern. E is 5, V is 22, and 5 + 22 = 27, so they are mirror letters. Step 2: Determine the position of D in the alphabet. D is the 4th letter. Step 3: Use the mirror formula. Mirror position = 27 minus current position. Step 4: Compute 27 - 4 = 23. Step 5: Identify the 23rd letter of the alphabet, which is W. Step 6: Check options and confirm that W is given as option D. Verification / Alternative check: We can verify the pattern by listing a few mirror pairs: A with Z (1 and 26), B with Y (2 and 25), C with X (3 and 24), D with W (4 and 23), and E with V (5 and 22). The sequence is consistent and confirms that D pairs with W in the same way E pairs with V. Any different letter would break the simple sum to 27 rule. Why Other Options Are Wrong: Option A, E, is position 5, which would give a sum 4 + 5 = 9, not 27. Option B, G, is position 7, and option C, I, is position 9. Neither sum with 4 to 27. They therefore do not form mirror pairs with D. Because the analogy requires the same symmetric relationship as between E and V, only W fits the requirement. Common Pitfalls: Learners sometimes guess based on the letters seeming close in the alphabet or visually similar, rather than computing positions. Others may think in terms of simple forward or backward shifts, which do not capture the mirror idea. To avoid mistakes, remember the rule that mirror letters in a 26 letter alphabet have positions that add up to 27. Using this simple formula makes such questions straightforward and prevents confusion in exam conditions. Final Answer: Because E and V are mirror letters whose positions sum to 27, D must pair with W to maintain the same relationship, so option D is correct.

Question 7

In the following number code analogy, 58531 is related to 11 according to a specific digit sum rule. Using the same rule, 78363 will be related to which of the following numbers?

Accepted Answer

Introduction / Context: This question uses a number code based on the digits that occupy specific positions. The first pair 58531 : 11 suggests that the number 11 has been obtained from 58531 by performing a certain operation on its digits. The same operation must then be applied to 78363 in order to find the correct related number. Such coding and decoding questions are common in reasoning sections and often involve position wise sums or differences of digits. Given Data / Assumptions: - First number: 58531, composed of digits 5, 8, 5, 3, and 1. - Its code: 11, given as the second number in the pair. - Second number: 78363, composed of digits 7, 8, 3, 6, and 3. - The same coding rule must be applied to 78363 to obtain the missing number from the options 11, 13, 9, and 7. Concept / Approach: In many such codes, the sum of digits at specific positions is used. If we take the first, third, and fifth digits of 58531 and add them, we get 5 + 5 + 1 = 11, which matches the given code. This suggests that the rule is to add the digits in positions one, three, and five. To verify, we then apply the same rule to 78363 by summing its first, third, and fifth digits. This produces a new number, which we compare with the answer options to select the correct one. Step-by-Step Solution: Step 1: Break 58531 into its digits: 5 (first), 8 (second), 5 (third), 3 (fourth), and 1 (fifth). Step 2: Sum the first, third, and fifth digits: 5 + 5 + 1 = 11. Step 3: Confirm that this sum equals the given related number 11, so the rule is consistent. Step 4: Break 78363 into its digits: 7 (first), 8 (second), 3 (third), 6 (fourth), and 3 (fifth). Step 5: Sum the first, third, and fifth digits: 7 + 3 + 3 = 13. Step 6: Check options and find that 13 is present as option B, making it the correct related number. Verification / Alternative check: To ensure this is the intended rule, we can test other simple patterns such as summing all digits, summing only even position digits, or summing even digits. The total sum of digits of 58531 is 22, not 11, so that pattern does not match. The sum of second and fourth digits is 8 + 3 = 11, but applying that to 78363 would give 8 + 6 = 14, which is not an option. The first, third, and fifth digit sum rule fits cleanly for both numbers and gives an answer that appears in the option list, so it is the most logical coding rule. Why Other Options Are Wrong: Option A, 11, incorrectly repeats the first code outcome instead of applying the rule to the new number. Option C, 9, and option D, 7, do not match any natural combination of the specified position sums for 78363 under the rule derived from 58531. Selecting any of these would break the consistency of the coding scheme and hence must be rejected. Common Pitfalls: Some learners rush to sum all digits and stop when they see a familiar number, without checking that the same logic works for every example. Others may not pay attention to positions and incorrectly assume a different pattern. It is crucial to test any suspected rule on both the given example and the unknown case. Only rules that hold for all relevant numbers and produce an option present in the list should be accepted in coding type questions. Final Answer: Using the rule of summing the first, third, and fifth digits, 58531 maps to 11 and 78363 maps to 13, so option B is the correct answer.

Question 8

Select the related author that completes the analogy: Five Point Someone is related to Chetan Bhagat in the same way as Swami and Friends is related to which of the following writers?

Accepted Answer

Introduction / Context: This analogy connects famous literary works with their authors. The pair Five Point Someone : Chetan Bhagat indicates that Chetan Bhagat wrote the novel Five Point Someone. The task is to identify the author of the classic Indian novel Swami and Friends from the given options. Such questions test knowledge of literature and also the ability to recognise that the relationship is book to author. Given Data / Assumptions: - Five Point Someone is a well known Indian novel by Chetan Bhagat. - Swami and Friends is another well known novel, especially in Indian English literature. - The options list four prominent authors, some global and some Indian. - Only one of these authors wrote Swami and Friends. Concept / Approach: The relationship in the example pair is clear: it is book to author. Therefore, we must also supply the author of Swami and Friends. Swami and Friends is a classic work by R.K. Narayan, set in the fictional South Indian town of Malgudi and focused on the childhood adventures of Swaminathan. Shakespeare, Dickens, and Tagore wrote many famous works, but not this particular novel. Recognising the correct author immediately completes the analogy in a straightforward and meaningful way. Step-by-Step Solution: Step 1: Interpret the first pair. Five Point Someone is a novel, and Chetan Bhagat is its author. Step 2: Identify the role of the second term in the pair. It is the creator of the literary work. Step 3: Recall that Swami and Friends is an early novel written by Indian author R.K. Narayan. Step 4: Evaluate option B, R.K. Narayan, and note that it matches the known author of Swami and Friends. Step 5: Confirm that Shakespeare, Dickens, and Tagore did not write this novel. Step 6: Conclude that the only correct completion for the analogy Swami and Friends : ? is R.K. Narayan. Verification / Alternative check: We can check each author against their famous works. William Shakespeare is known for plays such as Hamlet, Macbeth, and Othello. Charles Dickens is known for novels like Oliver Twist and Great Expectations. Rabindra Nath Tagore is known for works like Gitanjali and various Bengali stories and poems. None of these are connected to Swami and Friends. R.K. Narayan, however, is universally associated with the Malgudi series and Swami and Friends specifically, so option B is confirmed as correct. Why Other Options Are Wrong: Option A, William Shakespeare, was an English playwright and poet who wrote mainly plays and sonnets. Option C, Charles Dickens, wrote nineteenth century English novels with social themes. Option D, Rabindra Nath Tagore, was a Bengali poet and writer, but Swami and Friends is not among his works. Choosing any of these would violate the simple book to author relationship established in the question pair. Common Pitfalls: Some learners may be tempted to choose Tagore because he is also an Indian writer, or Shakespeare or Dickens because they are very famous names. This shows the risk of guessing based on familiarity rather than knowledge. To avoid such mistakes, it is important to learn a few key associations between famous books and their authors, especially for popular examination syllabi. Such knowledge can then be recalled quickly in analogy questions like this one. Final Answer: Five Point Someone is written by Chetan Bhagat, and Swami and Friends is written by R.K. Narayan, so option B is the correct completion of the analogy.

Question 9

Select the related group of letters that completes the analogy: EFG is related to OPQ in the same way as which of the following letter groups is related to STU?

Accepted Answer

Introduction / Context: This analogy involves three letter sequences and a fixed shift in alphabet positions. The pair EFG : OPQ suggests that each letter in EFG has been moved forward by the same number of positions to form OPQ. The task is to find the letter group that would need the same shift to reach STU. It is a standard coding style question where a consistent numerical shift in the alphabet is used across all letters. Given Data / Assumptions: - First triple: EFG, second triple: OPQ. - The alphabet positions are A = 1 to Z = 26. - We must determine the shift applied to E, F, and G to obtain O, P, and Q respectively. - STU is the target triple in the second pair, and we must find the triple that transforms into STU under the same shift. Concept / Approach: Convert letters to numeric positions. E is 5, F is 6, G is 7. O is 15, P is 16, Q is 17. The shift from E to O is plus ten. From F to P is also plus ten, and from G to Q is plus ten. This gives a consistent pattern: add ten to the position of each letter. Now we work backwards for the second pair. For STU, S is 19, T is 20, and U is 21. To find their original letters, subtract ten from each: 19 minus ten is 9, 20 minus ten is 10, and 21 minus ten is 11. The 9th, 10th, and 11th letters are I, J, and K, so the required triple is IJK. Step-by-Step Solution: Step 1: Note the positions of E, F, G as 5, 6, and 7. Step 2: Note the positions of O, P, Q as 15, 16, and 17. Step 3: Compute the differences. 15 minus 5, 16 minus 6, and 17 minus 7 all equal ten. Step 4: Conclude that each letter in the first triple is shifted forward by ten positions to get the second triple. Step 5: Apply the reverse operation to STU. S(19) minus ten is 9, T(20) minus ten is 10, U(21) minus ten is 11. Step 6: Convert 9, 10, and 11 back to letters. They are I, J, and K. Step 7: Check options and find that IJK is given as option D, which must be the correct answer. Verification / Alternative check: To verify, we can also apply the forward shift of plus ten to IJK and see if it produces STU. I(9) plus ten is S(19), J(10) plus ten is T(20), and K(11) plus ten is U(21). This confirms that IJK : STU follows exactly the same transformation as EFG : OPQ. None of the other options, when shifted by ten, yields STU, so they cannot complete the analogy. Why Other Options Are Wrong: Option A, GHI, shifted by ten gives QRS, not STU. Option B, LMN, yields VWX, and option C, JKL, yields TUV. These do not match the required second triple. Since the core of the analogy is the fixed plus ten shift, only the triple that maps to STU under this operation is acceptable. Common Pitfalls: Common errors include miscounting alphabet positions or failing to notice that the same shift is applied to every letter. Some test takers may try to guess based on how the sequences look or sound, without checking numeric positions. To avoid such mistakes, always convert letters to numbers and calculate differences for each position. Once you see a consistent shift, use it strictly on all letters involved in the analogy. Final Answer: Applying a constant shift of ten letters, EFG becomes OPQ and IJK becomes STU. Thus, the correct related group of letters is IJK, and option D is correct.

Question 10

In the following number analogy, 14 is related to 30 according to a simple arithmetic rule. Using the same rule, 16 will be related to which of the following numbers?

Accepted Answer

Introduction / Context: This is a basic numerical analogy problem where the first pair 14 : 30 suggests a specific arithmetic transformation applied to 14 to produce 30. The same operation then needs to be applied to 16 to identify the correct related number from the options. Such questions test the ability to recognise simple functional relationships like doubling, scaling, and adding or subtracting fixed constants. Given Data / Assumptions: - First number pair: 14 and 30, written as 14 : 30. - Second number pair: 16 : ? must follow exactly the same rule. - Answer options are 68, 36, 34, and 56. - The rule should be simple enough for quick mental calculation in an aptitude test environment. Concept / Approach: We test common transformations on 14 to obtain 30. If we double 14, we obtain 28. Adding 2 more gives 30. This suggests the rule Result = 2 * Number + 2. To confirm that this rule is likely intended, we check that no other simple transformation, such as adding a constant or using squares, yields 30 in a similarly neat way. Once we accept 2 * n + 2 as the rule, we apply it to 16 and see whether the resulting number appears among the options. Step-by-Step Solution: Step 1: Compute 2 * 14 = 28. Step 2: Add 2 to 28, giving 28 + 2 = 30, which matches the second number in the first pair. Step 3: Assume that the general rule is Result = 2 * Number + 2. Step 4: Apply this rule to 16. Compute 2 * 16 = 32. Step 5: Add 2 to obtain 32 + 2 = 34. Step 6: Check options and note that 34 appears as option C, so 16 : 34 matches the required pattern. Verification / Alternative check: To verify, test alternative patterns quickly. A simple constant difference would mean 30 minus 14 equals 16, and if applied to 16 would give 16 plus 16 equals 32, which is not an option. Using squares, 14 squared is 196 and does not relate to 30 in an obvious way. Therefore, the double plus two rule is much more reasonable. It is also linear and easy to compute, which is typical in exam style analogies. Why Other Options Are Wrong: Option A, 68, would imply applying a factor of more than four to 16, which does not align with the relationship between 14 and 30. Option B, 36, and option D, 56, also cannot be generated from 16 using the consistent rule 2 * n + 2, and they require different operations that do not work for 14. Because the same rule must hold across all pairs, any value that fails this test must be eliminated. Common Pitfalls: Some learners may spot that 14 plus 16 equals 30 and try to apply a similar sum to 16, without noticing that 16 is fixed and no second number is provided. Others might attempt to use trial and error on the options without identifying a rule first, leading to confusion. The better strategy is to derive a clear arithmetic formula from the first pair and then apply it systematically to the second, ensuring consistency throughout. Final Answer: Using the rule Result = 2 * Number + 2, the number corresponding to 16 is 34, so the completed analogy is 14 : 30 :: 16 : 34 and option C is correct.

Question 11

In the river and country analogy "Ganga : India :: Nile : ____", which country correctly completes the pair?

Accepted Answer

Introduction / Context: This analogy question tests basic world geography, specifically your knowledge of important rivers and the countries through which they primarily flow or with which they are most strongly associated. The pair "Ganga : India" represents a relationship between a famous river and the country that is most closely linked with it in examinations and general studies. You must extend the same type of relationship to the river Nile and select the correct country from the options. Given Data / Assumptions: The first pair given is "Ganga : India". The second incomplete pair is "Nile : ____". Options include several different countries. We use standard school level geography where each major river is linked with one key country. Concept / Approach: The Ganga, also called the Ganges, is the most famous and sacred river of India. In many general knowledge questions, Ganga is directly associated with India, even though it also flows through Bangladesh. In the same way, the Nile is one of the longest rivers in the world and is historically associated with the civilisation of ancient Egypt and with modern Egypt. Therefore, we look for the country most classically linked with the Nile, which is Egypt. Step-by-Step Solution: Step 1: Understand the first pair. The river Ganga is primarily associated with India in exam questions. Step 2: Recognise the pattern as "important river : country most strongly associated with that river". Step 3: Recall the Nile. It flows through several African countries but has a deep historical link with Egypt. Step 4: Among the options, identify Egypt as the country where the Nile delta and many famous Nile related sites exist. Step 5: Conclude that the correct completion is "Nile : Egypt". Verification / Alternative check: Pakistan is mainly associated with rivers like Indus and Jhelum. The United States of America is known for rivers such as Mississippi and Missouri. The United Kingdom has rivers like Thames and Severn. Sudan also lies along the Nile, but in standard exam level analogies, the name most strongly tied to Nile is Egypt due to the long standing historical and cultural connection. Hence, Egypt fits the pattern exactly in the same way that India fits with Ganga. Why Other Options Are Wrong: Pakistan, United States of America and United Kingdom are not classically introduced in textbooks as the home of the Nile. Sudan does share the Nile, but when one hears the phrase "River Nile", the first country that comes to mind in history and geography is Egypt. Therefore, only Egypt mirrors the strong link that India has with the Ganga in the first pair. Common Pitfalls: A common mistake is to overthink the fact that Nile flows through multiple countries and become confused between them. In reasoning questions, you should focus on the most standard and widely taught association. Another pitfall is not identifying that the first pair already uses that same idea of a single strong association rather than a complete list of river basin countries. Final Answer: The analogy is completed as "Ganga : India :: Nile : Egypt".

Question 12

In the letter analogy "RM : XG :: ER : ____", which pair of letters correctly completes the pattern?

Accepted Answer

Introduction / Context: This question is a letter based analogy where two letters are transformed into another pair of letters using a hidden rule. You are given the pair "RM : XG" and asked to apply the same rule to the pair "ER" to find the missing letters. Such questions test your ability to work with the numerical positions of letters in the English alphabet and to recognise consistent shifts. Given Data / Assumptions: First example pair: RM becomes XG. Second incomplete pair: ER becomes an unknown pair. Alphabet positions: A = 1, B = 2, ..., Z = 26. Exactly the same transformation must be applied to both pairs. Concept / Approach: To solve this, convert letters to their numerical positions and see how they are shifted. R is the 18th letter and M is the 13th letter. X is the 24th letter and G is the 7th letter. From R to X, the position increases by 6. From M to G, the position decreases by 6, since 13 minus 6 equals 7. So the rule for the pair seems to be: first letter moves forward by 6 positions, second letter moves backward by 6 positions. We then apply the same pattern to E and R. Step-by-Step Solution: Step 1: Write numerical positions for RM. R = 18, M = 13. Step 2: Write positions for XG. X = 24, G = 7. Step 3: Compare positions. For the first letter: 18 + 6 = 24, so R moves forward 6 places to X. For the second letter: 13 minus 6 = 7, so M moves backward 6 places to G. Step 4: Write positions for ER. E = 5, R = 18. Step 5: Apply the rule. First letter: 5 + 6 = 11, which is K. Second letter: 18 minus 6 = 12, which is L. Step 6: Combine these to get KL as the answer. Verification / Alternative check: Quickly check all options. PK would mean 5 becomes P (position 16) which is a shift of +11, not +6. LK would place letters in the wrong order. PL and KM also do not correspond to the exact shifts of +6 for the first letter and minus 6 for the second letter. Only KL is consistent with the transformation discovered from the example pair RM : XG. Why Other Options Are Wrong: PK, LK, PL and KM all involve different numeric shifts that are not equal in magnitude to +6 for the first position and minus 6 for the second position. Since analogy questions demand that exactly the same rule be applied to both pairs, any option that breaks that rule must be rejected. The reasoning shows that KL alone preserves the pattern. Common Pitfalls: Many students try to guess based on how similar pairs look, instead of converting letters into numbers. Another common mistake is to apply the shift in only one direction (for example, moving both letters forward) without checking both letters carefully. Writing out the positions and performing clear additions and subtractions helps avoid confusion. Final Answer: The correct completion of the analogy is "RM : XG :: ER : KL".

Question 13

In the letter analogy "ET : VG :: NO : ____", which pair of letters correctly completes the pattern?

Accepted Answer

Introduction / Context: This question is based on an alphabet complement pattern. The pair "ET : VG" suggests that the letters E and T have been transformed into V and G using a consistent rule. You must detect this rule and apply it to the pair "NO" to find the correct pair of letters that completes the analogy. The problem tests your ability to think in terms of positions in the alphabet and symmetric relationships. Given Data / Assumptions: First pair: ET becomes VG. Second incomplete pair: NO becomes an unknown pair. We use the standard English alphabet: A = 1, B = 2, ..., Z = 26. We assume the same pattern is applied to both letters of each pair. Concept / Approach: A very common pattern for such questions is alphabetic complement, where letters are paired so that their positions sum to 27 (for example A with Z, B with Y, and so on). E is the 5th letter and V is the 22nd, and 5 + 22 = 27. T is the 20th letter and G is the 7th, and 20 + 7 = 27. So in the pair ET : VG, each letter of the first pair has been replaced with its complement to 27. To find the corresponding pair for NO, we must again replace each letter with its complement. Step-by-Step Solution: Step 1: Find positions of E and T. E = 5, T = 20. Step 2: Check positions of V and G. V = 22, G = 7. Step 3: Add the positions: 5 + 22 = 27 and 20 + 7 = 27. This shows that each pair sums to 27, so each output letter is the complement of the input letter. Step 4: Now find positions of N and O. N = 14, O = 15. Step 5: Find the complements to 27. For N, 27 minus 14 = 13, which is M. For O, 27 minus 15 = 12, which is L. Step 6: Combine these letters into the pair ML. Verification / Alternative check: Check the options one by one. IM, MI, and LM do not use both complements correctly. Only ML has the first letter M (position 13) and the second letter L (position 12), which satisfy the equations 14 + 13 = 27 and 15 + 12 = 27. Therefore, ML is the only answer that perfectly follows the complement to 27 rule observed in the example pair ET : VG. Why Other Options Are Wrong: Options IM, MI and LM all break the 27 sum property for at least one of the letters. If you add the positions of N or O with these letters, you do not consistently get 27. Option NL simply repeats one of the original letters and is not a transformed complement. Because the problem is purely about symmetric complements in the alphabet, any pair that fails this check must be rejected. Common Pitfalls: A frequent mistake is to apply a fixed forward or backward shift to the letters, such as plus two or minus two, without verifying that the same rule explains the example pair. Another pitfall is to overlook the idea of complements entirely and attempt more complicated patterns. Whenever you see pairs like A with Z or E with V in analogies, you should always test for the complement to 27 pattern. Final Answer: The correct completion of the analogy is "ET : VG :: NO : ML".

Question 14

In the number analogy "97 : 63 :: 67 : ____", which number correctly completes the pattern using a product of digits?

Accepted Answer

Introduction / Context: This is a numerical analogy where the second number in each pair is formed by using the digits of the first number in a particular way. The pair "97 : 63" suggests that 63 has been derived from 97 by applying some digit based operation. You must uncover that operation and then apply it to 67 in order to find the correct answer from the options. Such questions test your ability to experiment with sums, differences, and products of digits. Given Data / Assumptions: First pair: 97 corresponds to 63. Second pair: 67 corresponds to an unknown value. Options: 38, 56, 42, 45, 36. We assume the relationship uses simple operations on individual digits. Concept / Approach: One common approach is to multiply the digits of the first number. For 97, the digits are 9 and 7, and their product is 9 * 7 = 63, which matches the second number in the pair. Therefore, the rule is that the second number is the product of the two digits of the first number. To complete the analogy, we apply the same pattern to 67. The digits 6 and 7 give 6 * 7 = 42, so 42 must be the missing term. Step-by-Step Solution: Step 1: Take the number 97 and separate its digits: 9 and 7. Step 2: Compute the product of the digits: 9 * 7 = 63. Step 3: Confirm that the result 63 matches the given pair, so the rule is consistent. Step 4: Now take the number 67 and separate its digits: 6 and 7. Step 5: Compute the product of these digits: 6 * 7 = 42. Step 6: Select 42 from the options as the number that fits the pattern. Verification / Alternative check: Check the other options quickly. 38 would require 6 and 7 to combine in a more complex way, such as 6 * 7 plus or minus something, which is not supported by the first pair. 56, 45, and 36 are also not equal to 6 * 7. Because the pattern 9 * 7 = 63 is clean and directly mirrored by 6 * 7 = 42, no other candidate fits as well as 42. This confirms that we have identified the intended rule. Why Other Options Are Wrong: The values 38, 56, 45, and 36 do not equal the product of the digits 6 and 7. Any rule that would generate these numbers from 67 would fail to produce 63 from 97, so it would not be a valid analogy rule. Since analogies require a single consistent relationship across pairs, these alternatives must be rejected. Common Pitfalls: Students sometimes attempt to use the sum of digits, difference of digits, or even reverse the digits without checking whether these operations reproduce the second number in the first pair. The simplest habit is always to start by trying sums and products of digits and see whether they match. Here, the product of digits instantly gives the correct mapping, making the problem straightforward once that is tried. Final Answer: Using the product of digits rule, 97 maps to 9 * 7 = 63 and 67 maps to 6 * 7 = 42. So the completed analogy is "97 : 63 :: 67 : 42".

Question 15

From the following numbers, which one is the odd one out based on being a perfect cube or not?

Accepted Answer

Introduction / Context: This is an odd one out question that focuses on the concept of perfect cubes. Three of the given numbers are exact cubes of integers, while one number does not represent a perfect cube. Your task is to identify the number that breaks this pattern. Such questions test your familiarity with the cubes of common natural numbers and your ability to quickly recognise standard cube values. Given Data / Assumptions: Given numbers: 1728, 2197, 3266, 2744, 3375. We consider perfect cubes of small integers such as 10, 11, 12, 13, 14 and 15. Three or more numbers will match these cubes and one will not. Concept / Approach: A perfect cube is a number that can be written as n^3 for some integer n. We recall that 12^3 = 1728, 13^3 = 2197, and 14^3 = 2744. Also, 15^3 = 3375. These values are standard and often memorised for examinations. The number 3266 does not appear in this list and is not the cube of any integer close to these. Therefore, 3266 is the odd one out because it fails the perfect cube property. Step-by-Step Solution: Step 1: Check 1728. Compute 12^3 = 12 * 12 * 12 = 144 * 12 = 1728, so this is a perfect cube. Step 2: Check 2197. Compute 13^3 = 13 * 13 * 13 = 169 * 13 = 2197, so this is also a perfect cube. Step 3: Check 2744. Compute 14^3 = 14 * 14 * 14 = 196 * 14 = 2744, confirming that this is a perfect cube. Step 4: Check 3375. Compute 15^3 = 15 * 15 * 15 = 225 * 15 = 3375, so this is a perfect cube. Step 5: Examine 3266. It lies between 14^3 and 15^3 but is not equal to either of them or to any nearby integer cube. Step 6: Conclude that 3266 is not a perfect cube and therefore is the odd one out. Verification / Alternative check: If you approximate cube roots, the cube root of 3266 would lie between 14 and 15 but will not be an integer. Since 14^3 is 2744 and 15^3 is 3375, there is no integer between 14 and 15 that can have a cube equal to 3266. This confirms that 3266 is not of the form n^3 and so does not share the important property that the other numbers share. Why Other Options Are Wrong: 1728, 2197, 2744, and 3375 are all exact cubes of consecutive integers 12, 13, 14, and 15. They clearly fit into a neat sequence of perfect cubes and therefore cannot be the odd one out. The purpose of the question is to identify the number that does not belong to this group, which is 3266. Common Pitfalls: A common error is to misremember cube values or to assume that any number close to a known cube is also a cube. Another pitfall is not checking all numbers systematically and guessing too early. It is helpful to memorise the cubes of integers at least up to 15 for aptitude exams, because such patterns appear frequently. Final Answer: The number that does not represent a perfect cube and is therefore the odd one out is 3266.

Question 16

In the analogy "Goose : geese :: ______", which option shows a similar singular to plural relationship with an irregular change?

Accepted Answer

Introduction / Context: This analogy question examines your understanding of singular and plural forms in English, especially where the plural is not formed by a simple addition of the letter s to the end of the word. In the pair "Goose : geese", the singular noun goose changes its internal vowel to form the plural geese, instead of just adding s or es. You must find a similar relationship in the options, focusing on how the form changes from singular to plural. Given Data / Assumptions: Given pair: goose (singular) and geese (plural). We need an option that mirrors this singular to plural relationship. Options include different noun pairs, some in correct order and some reversed. The analogy demands the same direction: singular on the left, plural on the right. Concept / Approach: In the original pair, the first word is singular and the second is its plural form. We look for an option where the first word is singular and the second word is the grammatically correct plural for that singular. Jacket : jacket has no change at all. Shirts : shirt reverses the logical order, since shirts is plural and shirt is singular. Socks : sock is also in reverse order. Pant : pants is the pair where the first form is singular and the second form is the usual plural, matching the pattern of goose and geese. Step-by-Step Solution: Step 1: Identify the pattern in the given pair. Goose is singular; geese is its plural. Step 2: Require the same pattern: first word singular, second word plural. Step 3: Check "Jacket : jacket". Both words are identical, so the second is not the normal plural jacket is jackets. Step 4: Check "Shirts : shirt". Here the first is plural and the second is singular, which is the reverse of the needed pattern. Step 5: Check "Pant : pants". Pant can be considered singular, and pants is the normal plural form for the garment. Step 6: Check "Socks : sock". Again, the first is plural and the second is singular, the wrong order. Verification / Alternative check: Among the provided options, only "Pant : pants" has the singular form first and the plural form second. Although child : children is a classic example of an irregular plural similar to goose : geese, it appears here as a separate distractor option and would be correct only if the first word were child and the second children. Since the prepared option list focuses on the clothing examples, Pant : pants is the logical match for the structure. Why Other Options Are Wrong: Jacket : jacket does not show any pluralisation, so it does not represent a singular to plural relation at all. Shirts : shirt and Socks : sock both reverse the expected order, starting with a plural and ending with a singular. These do not match the order goose : geese, where the singular comes first. Therefore, they break the analogy pattern. Common Pitfalls: A common mistake is to look only at whether words are related without checking word order. In analogy questions, the direction of the relationship is important. Another pitfall is to focus on irregular change only and overlook that the exam setter may be emphasising the basic singular to plural mapping even if the irregularity is weaker compared with goose : geese. Final Answer: The pair that properly mirrors the singular to plural relationship in "Goose : geese" is Pant : pants.

Question 17

In the river and city analogy "Agra : Yamuna :: Varanasi : ____", which river correctly completes the pair?

Accepted Answer

Introduction / Context: This question tests your knowledge of important Indian cities and the rivers that flow through them. The analogy "Agra : Yamuna" shows a relationship between a city and the major river on whose banks it lies. You need to continue the same relationship for the holy city of Varanasi. Such questions are very common in general knowledge and competitive exams. Given Data / Assumptions: The first pair is "Agra : Yamuna". The second pair is "Varanasi : ____". Options include several Indian rivers: Damodar, Betwa, Ganga, Son, Narmada. We assume standard geographical facts taught in school level textbooks. Concept / Approach: Agra is a famous city in Uttar Pradesh, and the river flowing by it is the Yamuna. This tells us the pattern is "city : river". Varanasi, also known as Kashi or Banaras, is one of the oldest and most sacred cities of India. It is famously situated on the banks of the river Ganga. Therefore, we must pair Varanasi with Ganga to maintain the same type of relationship that exists in the first pair. Step-by-Step Solution: Step 1: Recognise that Agra is located on the banks of the Yamuna, giving the pattern "city : its main river". Step 2: Identify Varanasi as a major religious city in Uttar Pradesh. Step 3: Recall that Varanasi is situated on the banks of the river Ganga. Step 4: Check each option to see which river flows by Varanasi. Step 5: Confirm that Ganga is the correct river associated with Varanasi. Verification / Alternative check: Damodar flows mainly through Jharkhand and West Bengal. Betwa flows through Madhya Pradesh and Uttar Pradesh but is not primarily associated with Varanasi. The river Son is also not the main river of Varanasi. Narmada flows through central India but is associated with cities like Jabalpur. Only the Ganga is directly connected in textbooks and general knowledge with the ghats of Varanasi where pilgrims bathe and perform rituals. Why Other Options Are Wrong: Damodar, Betwa, Son and Narmada all flow in different regions and are associated with other towns and cities. They do not form the classic and well known pair with Varanasi that Ganga does. Selecting any of them would break the consistent "city : correct river" pattern that is established by the first pair. Common Pitfalls: Some aspirants may confuse rivers in Uttar Pradesh or pick Betwa or Son because they also lie in North India. Others might not clearly remember the precise river for each city. Regular revision of important river city pairs is essential, as they form a common part of general awareness sections in many exams. Final Answer: The correct completion of the analogy is "Agra : Yamuna :: Varanasi : Ganga".

Question 18

In the letter analogy "IJ : PR :: ____ : SU", which pair of letters correctly completes the pattern?

Accepted Answer

Introduction / Context: This analogy involves a fixed shift in the positions of letters in the alphabet. The pair "IJ : PR" indicates that the letters I and J are transformed into P and R using a consistent rule. You must detect this rule and then apply it to an unknown pair so that the result is SU. This type of question checks your ability to handle forward shifts and to work backward from an output to an input. Given Data / Assumptions: First pair: IJ is mapped to PR. Second pair: unknown pair is mapped to SU. Alphabet positions: A = 1, B = 2, ..., Z = 26. The same shift rule must work for both letters of each pair. Concept / Approach: First, convert letters in IJ and PR into numbers. I is the 9th letter, J the 10th, P the 16th, and R the 18th. From I to P the position increases by 7 (9 + 7 = 16). From J to R the position increases by 8 (10 + 8 = 18). So the transformation uses two different shifts: +7 applied to the first letter and +8 applied to the second letter. For the pair that must become SU, we reverse the process and subtract these amounts to get the original letters. Step-by-Step Solution: Step 1: Find numerical positions. I = 9, J = 10, P = 16, R = 18. Step 2: Compute shifts. 9 + 7 = 16, so the first letter moves forward by 7. 10 + 8 = 18, so the second letter moves forward by 8. Step 3: For SU, write the positions: S = 19, U = 21. Step 4: Reverse the transformation for the first letter. 19 minus 7 = 12, which is L. Step 5: Reverse the transformation for the second letter. 21 minus 8 = 13, which is M. Step 6: Combine them to get LM, so the missing pair is LM. Verification / Alternative check: Check that if we now apply the original shifts to LM we really get SU. L is the 12th letter. 12 + 7 = 19, which is S. M is the 13th letter. 13 + 8 = 21, which is U. This confirms that LM transforms to SU under the same rule that converts IJ to PR. None of the other options, when shifted by +7 and +8 in this way, yield SU. Why Other Options Are Wrong: If you try IJ again, adding 7 and 8 gives PR, not SU. EF and LI similarly do not produce SU under the same shift pattern. MN would become T V when shifted (+7 and +8), not S U. Therefore, all options except LM break the required transformation rule and cannot be correct in the analogy. Common Pitfalls: Many students expect the same shift to be applied to both letters and miss patterns where the first and second letters use different shifts. Another common mistake is to only work forward from the given input instead of working backward from the known output. In such cases, working in reverse often makes the structure more obvious. Final Answer: The correct completion is "IJ : PR :: LM : SU".

Question 19

In the letter number analogy "CD : IP :: EB : ____", which pair of letters correctly completes the pattern?

Accepted Answer

Introduction / Context: This analogy involves a fixed forward shift in the positions of letters in the English alphabet. The pair "CD : IP" shows that the letters C and D are changed into I and P according to a hidden numerical rule. You must identify this rule and then apply it to EB to find the correct resulting pair. This checks your comfort with alphabet positions and simple arithmetic on those positions. Given Data / Assumptions: First pair: CD is mapped to IP. Second pair: EB is mapped to an unknown pair. Alphabet positions: A = 1, B = 2, C = 3, D = 4, ..., Z = 26. The same transformation must apply to both letters within each pair. Concept / Approach: Write the letters as numbers. C is position 3, D is position 4. I is position 9, P is position 16. From 3 to 9, the shift is +6. From 4 to 16, the shift is +12. So the pattern is: first letter moves forward by 6 positions, second letter moves forward by 12 positions. We then apply this same rule to E and B to generate the new letters. Step-by-Step Solution: Step 1: Convert the letters in CD to positions. C = 3 and D = 4. Step 2: Convert the letters in IP to positions. I = 9 and P = 16. Step 3: Calculate the shift for the first letter. 3 + 6 = 9, so the first letter is shifted forward by 6 positions. Step 4: Calculate the shift for the second letter. 4 + 12 = 16, so the second letter is shifted forward by 12 positions. Step 5: Now consider EB. E = 5 and B = 2. Step 6: Apply the same shifts. First letter: 5 + 6 = 11, which is K. Second letter: 2 + 12 = 14, which is N. Step 7: Combine these letters to obtain KN as the answer. Verification / Alternative check: If we test the other options using the reverse transformation, they do not match EB. For example, for HI, H is 8 and I is 9. Shifting H backward by 6 gives 2 (B), and shifting I backward by 12 gives a negative position, which does not correspond cleanly to E. Similarly, YA and XY require very different shifts that do not match the consistent pattern derived from CD : IP. Only KN follows the exact plus 6 and plus 12 rule when traced back. Why Other Options Are Wrong: HI, YA, XY, and KP all fail when you try to apply the same shift pattern in reverse. They either give positions outside the valid range or give letters that do not correspond to E and B. Since the analogy is based on fixed numerical shifts, any deviation from this pattern means that the option is not correct. Common Pitfalls: One pitfall is to assume the same amount of shift for both letters and look for a simple constant, which does not work here. Another common error is to guess visually similar letter pairs without doing the numeric checks. Converting letters to their numerical positions and writing out the arithmetic makes these patterns far easier to see and greatly reduces guesswork. Final Answer: The analogy is completed as "CD : IP :: EB : KN".

Question 20

In the number analogy "12 : 72 :: 14 : ____", which number correctly completes the pattern using a square and division rule?

Accepted Answer

Introduction / Context: This numerical analogy asks you to identify the mathematical operation that converts the first number of a pair into the second number. In the example "12 : 72", the number 72 is obtained from 12 by some rule. You must discover that rule and apply it to 14 to determine the missing number. Such questions often involve squaring, cubing, or combining operations like multiplication and division. Given Data / Assumptions: First pair: 12 is related to 72. Second pair: 14 is related to an unknown number. Options: 98, 91, 42, 60, 84. We look for a clean arithmetic rule that works for both pairs. Concept / Approach: A helpful strategy is to try operations involving the square of the number. 12^2 equals 144. If we then divide this by 2, we get 144 / 2 = 72, which matches the second number in the first pair. So the rule appears to be: second number equals (first number squared) divided by 2. Applying this to 14, we get 14^2 = 196, and 196 / 2 = 98. Therefore, 98 is the number that completes the analogy correctly. Step-by-Step Solution: Step 1: Square 12 to see if that is related to 72. Compute 12^2 = 144. Step 2: Try dividing 144 by 2. 144 / 2 = 72, which matches the given second number. Step 3: Conclude that the transformation is "square the number and then divide by 2". Step 4: Apply this rule to 14. First compute 14^2 = 196. Step 5: Divide 196 by 2 to obtain 196 / 2 = 98. Step 6: Choose 98 from the options as the correct corresponding number for 14. Verification / Alternative check: Check that none of the other options can be reached from 14 by the same rule. If we try 14 * 7, we get 98 again, but that does not explain the original pair. 91 would be 14 * 6.5, and 42 would be 14 * 3, neither of which match the squared and halved pattern. 60 and 84 also cannot be obtained from 14 using the "square and divide by 2" rule. Thus, 98 is consistent with the pattern and the only valid choice. Why Other Options Are Wrong: All other numbers in the options require a different, more complicated, or arbitrary rule when starting from 14. Because analogies demand one simple rule that fits every pair involved, any option that needs a new rule is automatically incorrect. Only 98 satisfies the same transformation that takes 12 to 72. Common Pitfalls: A common error is to try direct multiplication factors first, such as 12 * 6, and become stuck when the same factor does not work with 14. Another pitfall is to ignore squaring because it seems too large at first glance. In many exam questions, squaring and then scaling up or down is exactly the intended pattern, so it should always be checked early. Final Answer: Using the rule "square the number and divide by 2", 12 maps to 72 and 14 maps to 98, completing the analogy as "12 : 72 :: 14 : 98".

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