Question 1

In a certain code, the operation "#" between two numbers is defined so that 6 # 30 = 5, 8 # 24 = 3 and 7 # 28 = 4. Using the same pattern, what is the value of 8 # 40?

Accepted Answer

Introduction / Context:This is a typical coded operation question where an artificial symbol "#" connects two numbers. A few examples are given, and your task is to uncover the rule that links the input pair to the output. These questions test your number sense and your ability to detect simple arithmetic patterns quickly and accurately. Given Data / Assumptions: 6 # 30 = 5. 8 # 24 = 3. 7 # 28 = 4. We must find 8 # 40 following the same rule. The rule is assumed to be consistent for all examples. Concept / Approach:Look at the relationship between each pair of input numbers and the result. A natural first attempt is to check whether the result is a ratio like second number divided by first number, or some simple linear combination. Notice that in each example, the second number is divisible by the first, and the quotient looks promisingly equal to the result. This suggests that a # b might simply be b / a. Step-by-Step Solution:Step 1: For 6 # 30, compute 30 / 6 = 5, which matches the given result 5.Step 2: For 8 # 24, compute 24 / 8 = 3, which again matches the given result 3.Step 3: For 7 # 28, compute 28 / 7 = 4, consistent with the provided result 4.Step 4: The rule is therefore a # b = b / a.Step 5: Apply this to 8 # 40: we have 40 / 8 = 5. Verification / Alternative check:We should quickly check that there is no other simpler pattern that fits all three examples. If we tried a # b = a * b or a + b or a - b, they would not match the given results. Since b / a works perfectly in every case, it is the only simple consistent rule. Therefore 8 # 40 must equal 5, not any of the other distractor values. Why Other Options Are Wrong: 4 and 3 correspond to quotients from other pairs and do not match 40 / 8. 8 and 10 could come from misreading or guessing a different arithmetic pattern, such as b / 5 or a + b / 4, which do not hold for all examples. Common Pitfalls:Sometimes students try overly complicated formulas involving addition and subtraction, or they use only one example to guess a pattern. Always verify your hypothesis against every given case. Here, the simple ratio b / a works cleanly and consistently, which is a strong indicator that it is the intended rule. Final Answer:Using the rule a # b = b / a, we get 8 # 40 = 5.

Question 2

In a certain code language, the word "PRICE" is written as "GEKTR". Using the same coding pattern, how is the word "VALUE" written in that code language?

Accepted Answer

Introduction / Context:This question is from the coding decoding topic, where one English word is converted into a coded form using a hidden rule. You are given the mapping PRICE → GEKTR and asked to apply the same logic to a new word, VALUE. To succeed, you must understand how letters are transformed, including any reversal and shifting in the alphabet. Given Data / Assumptions: PRICE is written as GEKTR in the code language. The same rule must be applied to VALUE. Only capital English letters are involved. Each letter of the original word maps to exactly one coded letter. Concept / Approach:We first compare PRICE and GEKTR letter by letter to detect any pattern. A direct position wise comparison is confusing, so an effective trick is to check whether the original word was reversed before encoding. If we reverse PRICE, we get ECIRP. Comparing ECIRP with GEKTR may reveal a consistent shift in alphabetical positions. Step-by-Step Solution:Step 1: Reverse PRICE to get ECIRP.Step 2: Compare letters: E → G, C → E, I → K, R → T, P → R.Step 3: Check shifts in the alphabet: E(5) to G(7) is +2, C(3) to E(5) is +2, I(9) to K(11) is +2, R(18) to T(20) is +2, P(16) to R(18) is also +2.Step 4: So the rule is: reverse the word, then shift every letter two positions forward in the alphabet.Step 5: Apply this to VALUE: reverse VALUE to get EULAV.Step 6: Shift each letter +2: E → G, U → W, L → N, A → C, V → X.Step 7: The coded form of VALUE is therefore GWNCX. Verification / Alternative check:If we tried only a plain shift without reversing, the mapping from PRICE to GEKTR would break at some position. Similarly, reversing without shifting would give ECIRP instead of GEKTR. Reversing followed by a +2 shift matches every single letter for the given example and therefore is the correct coding rule to apply to VALUE. Why Other Options Are Wrong: FWNCX and FNWDY change some letters correctly but not all, indicating an incorrect or incomplete shift. DWNCY does not follow the precise +2 shift from the reversed word. GWNXY alters the final letter incorrectly and does not match the derived pattern. Common Pitfalls:Many students look only for direct shifts and ignore the possibility that the word might be reversed. Another error is miscounting positions when shifting letters in the alphabet. Always check the transformation on every letter, not just the first and last, to be confident in the rule you deduce. Final Answer:Using the rule "reverse the word and then shift each letter two places forward", VALUE is coded as GWNCX.

Question 3

In a certain code language, the symbols are redefined so that "-" represents "+", "+" represents "x", "x" represents "÷" and "÷" represents "-". Using these rules, what is the value of 9 - 18 + 35 x 10 ÷ 30?

Accepted Answer

Introduction / Context:This coding decoding problem changes the meanings of the arithmetic operators. You must carefully translate each symbol into its true arithmetic role and then evaluate the resulting expression. The challenge lies in not confusing the original printed symbol with the operation it actually represents under the coding scheme. Given Data / Assumptions: "-" represents "+". "+" represents "x" (multiplication). "x" represents "÷" (division). "÷" represents "-". Coded expression: 9 - 18 + 35 x 10 ÷ 30. Standard arithmetic precedence applies after decoding. Concept / Approach:First decode the expression by replacing every coded symbol with the real operation it stands for. Second, evaluate the new expression using normal rules: perform all multiplication and division operations before addition and subtraction. Writing the decoded expression separately helps avoid mistakes caused by mentally juggling the meanings. Step-by-Step Solution:Step 1: Start with 9 - 18 + 35 x 10 ÷ 30.Step 2: Replace each symbol: "-" becomes "+", "+" becomes "x", "x" becomes "÷", and "÷" becomes "-".Step 3: The decoded expression becomes: 9 + 18 x 35 ÷ 10 - 30.Step 4: Evaluate multiplication and division from left to right: 18 x 35 = 630, then 630 ÷ 10 = 63.Step 5: Substitute back: 9 + 63 - 30.Step 6: Now handle addition and subtraction: 9 + 63 = 72 and 72 - 30 = 42. Verification / Alternative check:Re check the substitution: no "+" or "-" remains undecoded, and there is exactly one multiplication and one division inside the middle part 18 x 35 ÷ 10. Repeating the calculations confirms that the middle block evaluates to 63 and the overall expression to 42. So our answer is consistent and does not depend on any unusual convention. Why Other Options Are Wrong: 40, 44, 39 and 41 arise from common errors such as decoding only some symbols or doing operations strictly left to right. Any option different from 42 indicates at least one mistake either in the substitution step or in handling precedence. Common Pitfalls:Many candidates accidentally treat the symbols according to their usual meaning rather than their coded meaning. Others forget that after decoding, multiplication and division must be evaluated before addition and subtraction. Writing down the decoded expression clearly is the simplest way to keep the operations straight in your mind. Final Answer:After decoding the operators and simplifying, the value of the expression is 42.

Question 4

In a certain operator puzzle, the operation "α" is defined so that 16 α 1 = 8, 14 α 6 = 42 and 12 α 5 = 30. Using the same pattern, what is the value of 2 α 6?

Accepted Answer

Introduction / Context:This question introduces a special operator "α" defined by examples. Your task is to deduce the hidden rule that links the pair of numbers on the left to the result on the right and then apply this rule to a new pair. Such problems check pattern recognition skills and speed in working with basic arithmetic operations. Given Data / Assumptions: 16 α 1 = 8. 14 α 6 = 42. 12 α 5 = 30. We must compute 2 α 6. The same rule is used in all three examples. Concept / Approach:Look for a simple arithmetic relation involving the two numbers. Because the result in each case seems smaller than the product but larger than either number alone, dividing the product by a fixed constant is a strong possibility. Testing a formula like a α b = a * b / 2 is very natural here because products such as 16 * 1, 14 * 6 and 12 * 5 all give even numbers that are divisible by 2. Step-by-Step Solution:Step 1: For 16 α 1, compute (16 * 1) / 2 = 16 / 2 = 8, which matches the given result.Step 2: For 14 α 6, compute (14 * 6) / 2 = 84 / 2 = 42, again matching the given value.Step 3: For 12 α 5, compute (12 * 5) / 2 = 60 / 2 = 30, which also matches the given result.Step 4: Therefore the rule is a α b = (a * b) / 2.Step 5: Apply this rule to 2 α 6: (2 * 6) / 2 = 12 / 2 = 6. Verification / Alternative check:If we had tried a α b = a + b or a - b or a * b, one of the given examples would not match. The fact that (a * b) / 2 fits all three examples perfectly shows that it is the intended definition of α. Computing 2 α 6 with this rule gives 6, and no other simple consistent rule would produce a different result without breaking an earlier equality. Why Other Options Are Wrong: 18 would come from using a * b / (some other divisor), which would not fit all examples. 4, 8 and 10 correspond to incorrect formulas such as a + b, b - a or half of the sum, none of which match the given three equations. Common Pitfalls:Candidates sometimes try to force elaborate expressions instead of testing simple possibilities like half the product. Another risk is using a different rule for each example. In these questions, there is always a single consistent pattern, so every guessed rule must be validated across all given equalities. Final Answer:Using the rule a α b = (a * b) / 2, we get 2 α 6 = 6.

Question 5

In a certain code language, the word "ETHANOL" is written as "HWKDQRO". Using the same coding rule, how will the word "MIX" be written in that code language?

Accepted Answer

Introduction / Context:This coding decoding problem deals with letter shifts in the English alphabet. One word, ETHANOL, is converted to HWKDQRO. Your goal is to identify the transformation applied to each letter and then use the same rule to encode another word, MIX. These questions are classic examples of alphabet shifting, similar to Caesar ciphers. Given Data / Assumptions: ETHANOL is coded as HWKDQRO. The same rule applies to coding MIX. All letters are in uppercase and follow standard A to Z ordering. Concept / Approach:We compare each letter of ETHANOL with the corresponding letter of HWKDQRO and calculate the shift in alphabetical position. If the shift is constant, we can confidently apply it to other words. In many exam questions, the shift is a small positive number, and letters beyond Z wrap around to the beginning of the alphabet. Step-by-Step Solution:Step 1: Write positions: E(5), T(20), H(8), A(1), N(14), O(15), L(12).Step 2: Code positions: H(8), W(23), K(11), D(4), Q(17), R(18), O(15).Step 3: Compute differences: 5 → 8 is +3, 20 → 23 is +3, 8 → 11 is +3, 1 → 4 is +3, 14 → 17 is +3, 15 → 18 is +3, 12 → 15 is +3.Step 4: So the rule is "shift every letter three places forward in the alphabet".Step 5: Apply this to MIX. Positions: M(13), I(9), X(24).Step 6: Add 3: M → P(16), I → L(12), X → 27, which wraps around to A(1).Step 7: Therefore MIX is coded as PLA. Verification / Alternative check:We can quickly check that a different constant shift such as +2 or +4 would break at least one letter mapping between ETHANOL and HWKDQRO. The fact that +3 works exactly for every position confirms that we have the correct rule. Applying this rule to MIX gives us PLA without any inconsistencies. Why Other Options Are Wrong: RFV, BGT and NHY would require different non uniform shifts and therefore do not preserve the simple +3 pattern. QLA is close but shifts only some letters correctly, meaning the pattern does not match the given example. Common Pitfalls:Students sometimes forget to wrap around after Z when shifting forward or mix up the direction of the shift. Another common mistake is checking the rule for only one or two letters instead of confirming it across the entire word. Always verify the pattern for every letter, especially in a code that is supposed to be consistent. Final Answer:Using a uniform +3 alphabet shift, MIX is written as PLA in the code language.

Question 6

In a certain code language, "+" represents "x", "-" represents "+", "x" represents "÷" and "÷" represents "-". Using these definitions, what is the value of the coded expression 24 x 6 - 8 + 2?

Accepted Answer

Introduction / Context:This is another operator coding problem where every arithmetic symbol is reassigned a new meaning. You must first decode the expression by replacing each symbol with its true operation and then evaluate the resulting normal arithmetic expression. Questions like this test attention to detail and understanding of operator precedence. Given Data / Assumptions: "+" represents "x" (multiplication). "-" represents "+". "x" represents "÷" (division). "÷" represents "-". Coded expression: 24 x 6 - 8 + 2. Standard precedence rules apply after decoding. Concept / Approach:The strategy is to translate the coded expression symbol by symbol. It is safer to write the decoded expression clearly on paper instead of doing mental substitution. Once decoding is done, you evaluate using the familiar rules: perform division and multiplication before resolving addition and subtraction from left to right. Step-by-Step Solution:Step 1: Start with 24 x 6 - 8 + 2.Step 2: Decode each symbol: "x" means "÷", "-" means "+", and "+" means "x". There is no "÷" in this particular expression.Step 3: The decoded expression is: 24 ÷ 6 + 8 x 2.Step 4: Apply precedence: 24 ÷ 6 = 4 and 8 x 2 = 16.Step 5: Now add the results: 4 + 16 = 20. Verification / Alternative check:Double check that the symbols were not misread. The original expression has one "x", one "-" and one "+", so after decoding we must have one division, one addition and one multiplication. No subtraction remains. Recomputing 24 ÷ 6 = 4 and 8 x 2 = 16 again gives the sum 20, confirming the result. Why Other Options Are Wrong: 25 and 24 could arise from doing operations strictly left to right without applying precedence. 50 and 40 would come from incorrectly treating "+" as addition instead of multiplication or misplacing the division. Common Pitfalls:Typical errors include forgetting the new meanings of the symbols mid way through the calculation and ignoring operator precedence after decoding. Some candidates also decode only one symbol and then start calculating, which is risky. Always translate the entire expression first, then evaluate systematically. Final Answer:After decoding and simplifying, the value of the expression is 20.

Question 7

In a certain operator puzzle, the symbol "$" is defined so that 10 $ 25 = 8 and 12 $ 25 = 10. Using the same rule, what is the value of 14 $ 53?

Accepted Answer

Introduction / Context:This question defines a special operation "$" using examples and asks you to extend the pattern to a new pair of numbers. The mapping involves the numbers 10, 25, 12, 25 and the results 8 and 10. Since the operation seems small relative to the inputs, it suggests that the rule might involve the digits of the numbers rather than the numbers themselves directly. Given Data / Assumptions: 10 $ 25 = 8. 12 $ 25 = 10. The same rule must be applied to 14 $ 53. We assume a single consistent operation for all examples. Concept / Approach:Check the digits of the numbers rather than their full values. For 10 and 25, the digits are 1, 0, 2 and 5. The result 8 can be obtained by adding these digits: 1 + 0 + 2 + 5 = 8. For 12 and 25, the digits are 1, 2, 2 and 5. Their sum is 1 + 2 + 2 + 5 = 10, which matches the given result. So a natural rule is that a $ b equals the sum of all decimal digits in a and b together. Step-by-Step Solution:Step 1: Verify the rule with 10 $ 25: digits 1, 0, 2 and 5 give 1 + 0 + 2 + 5 = 8.Step 2: Verify the rule with 12 $ 25: digits 1, 2, 2 and 5 give 1 + 2 + 2 + 5 = 10.Step 3: The rule is therefore "sum of all digits in both numbers".Step 4: For 14 $ 53, the digits are 1, 4, 5 and 3.Step 5: Add them: 1 + 4 + 5 + 3 = 13. Verification / Alternative check:Try alternative rules like absolute differences, ratios or simple algebraic combinations. None of them produce both 8 from (10, 25) and 10 from (12, 25) in a consistent way, while the digit sum rule works cleanly for both. Because 14 and 53 are similar two digit numbers, it is natural to apply the same digit sum rule to them as well. Why Other Options Are Wrong: 15, 11, 9 and 12 do not equal the sum of the digits 1, 4, 5 and 3. They could only arise from incorrect partial addition or from using a different inconsistent formula. Common Pitfalls:Some examinees immediately look for a formula involving the full numbers, such as (a + b) / something or a * b. Those approaches quickly fail when checked against both given examples. When dealing with two digit numbers, always consider digit level patterns like sums and differences, since they are very popular in reasoning exams. Final Answer:Using the digit sum rule, 14 $ 53 equals 1 + 4 + 5 + 3 = 13.

Question 8

In a certain code language, the eight-letter word "STUBBORN" is written as "TUVCANQM". Using the same coding rule, how is the eight-letter word "TRAINING" written in that code language?

Accepted Answer

Introduction / Context:This coding decoding question involves both positional shifts and different treatment of the first and second halves of an eight letter word. You are given the mapping STUBBORN → TUVCANQM and must apply the same pattern to TRAINING. The difficulty lies in spotting that the shift applied to the first four letters is different from the shift applied to the last four letters. Given Data / Assumptions: STUBBORN is coded as TUVCANQM. The word TRAINING also has eight letters. The same transformation rule applies positionwise. Letter positions in the alphabet follow A = 1, B = 2, …, Z = 26. Concept / Approach:Write the original and coded words in parallel to see how each letter changes. For STUBBORN, we line up S T U B B O R N with T U V C A N Q M. Then, we compute the alphabetic shift for each position. A careful observation reveals that the first four letters are all shifted forward by one position, whereas the last four letters are all shifted backward by one position. This split rule must then be applied to TRAINING. Step-by-Step Solution:Step 1: For STUBBORN → TUVCANQM, check the first four letters: S → T, T → U, U → V, B → C. Each is a +1 shift.Step 2: Check the last four letters: B → A, O → N, R → Q, N → M. Each is a -1 shift.Step 3: Therefore, for any eight letter word, positions 1 to 4 are shifted +1 and positions 5 to 8 are shifted -1.Step 4: Write TRAINING: T(20), R(18), A(1), I(9), N(14), I(9), N(14), G(7).Step 5: Apply +1 to the first four positions: T → U(21), R → S(19), A → B(2), I → J(10).Step 6: Apply -1 to the last four positions: N → M(13), I → H(8), N → M(13), G → F(6).Step 7: The coded word is USBJMHMF. Verification / Alternative check:Rechecking for STUBBORN confirms the pattern for all eight positions, so there is no inconsistency in the rule. Applying the split shift (+1 for the first half and -1 for the second half) to TRAINING produces a unique result. None of the other answer choices matches this precise combination of shifts at each position, which confirms our answer is correct. Why Other Options Are Wrong: USBJMHFM has the last two letters swapped and does not follow the consistent -1 rule for every one of the last four positions. JBSUFMHM and USBJMHME show incorrect shifts in several positions. USBNMHMF breaks the required pattern at the sixth position. Common Pitfalls:Students often assume a constant shift across all letters and miss the fact that the word is split into two halves with different operations. Others correctly see the shift but accidentally apply +1 or -1 in the wrong direction for some letters. Always check the transformation letter by letter against the example before applying the rule to a new word. Final Answer:Following the pattern, TRAINING is coded as USBJMHMF.

Question 9

In a certain code language, the symbols are redefined so that "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by". Using these rules, evaluate the expression 300 x 10 - 5 + 36 ÷ 57.

Accepted Answer

Introduction / Context:This operator coding question reassigns meanings to the standard arithmetic symbols. You must decode each symbol carefully and then evaluate the resulting expression. These problems are designed to test whether you can switch between symbol meanings and still respect the normal precedence of operations. Given Data / Assumptions: "+" means minus. "x" means divided by. "÷" means plus. "-" means multiplied by. Expression: 300 x 10 - 5 + 36 ÷ 57. After decoding, we apply usual arithmetic rules. Concept / Approach:The solution has two main steps. First, translate the coded expression into a standard arithmetic expression by replacing each symbol with its real meaning. Second, evaluate the translated expression using the familiar precedence, performing division and multiplication before addition and subtraction. Keeping the decoding step and the evaluation step separate helps prevent confusion. Step-by-Step Solution:Step 1: Start with 300 x 10 - 5 + 36 ÷ 57.Step 2: Replace "x" with "÷", "-" with "multiplied by", "+" with "minus" and "÷" with "plus".Step 3: The decoded expression becomes: 300 ÷ 10 * 5 - 36 + 57.Step 4: Evaluate division and multiplication first: 300 ÷ 10 = 30, and 30 * 5 = 150.Step 5: Substitute back: 150 - 36 + 57.Step 6: Now handle subtraction and addition from left to right: 150 - 36 = 114, and 114 + 57 = 171. Verification / Alternative check:We can quickly verify that no symbol was misinterpreted by re reading the definitions and ensuring that each occurrence in the original expression has been decoded. Re computing 300 ÷ 10 * 5 confirms the intermediate total 150. Adding and subtracting 36 and 57 again gives 171. Since the operations are straightforward, the chance of arithmetic error is low once decoding is correct. Why Other Options Are Wrong: 150 would be the result if we stopped after multiplication and division. 230 and 234 imply incorrect ordering or mis decoding of plus and minus. 180 could arise from replacing one symbol incorrectly or ignoring part of the expression. Common Pitfalls:A major pitfall is inadvertently mixing the original symbol meanings with their coded definitions. Another common error is to calculate from left to right without prioritising multiplication and division after decoding. Always verify the decoded expression before doing any arithmetic to avoid compounding mistakes. Final Answer:After decoding and evaluating, the expression 300 x 10 - 5 + 36 ÷ 57 equals 171.

Question 10

In a certain code language, "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by". Using these rules, what is the value of 76 x 4 + 4 - 12 ÷ 37?

Accepted Answer

Introduction / Context:This problem again redefines the standard arithmetic symbols. The challenge is to decode the expression properly and then evaluate it using standard operator precedence. It checks your ability to apply a coding key consistently and to handle mixed operations correctly. Given Data / Assumptions: "+" means minus. "x" means divided by. "÷" means plus. "-" means multiplied by. Expression: 76 x 4 + 4 - 12 ÷ 37. Usual arithmetic precedence applies after decoding. Concept / Approach:As before, we begin by translating the coded expression into a normal arithmetic form. Once we have a standard expression with the usual symbols, we perform division and multiplication first, followed by addition and subtraction from left to right. Careful substitution is crucial, because a single incorrect replacement changes the whole result. Step-by-Step Solution:Step 1: Start with 76 x 4 + 4 - 12 ÷ 37.Step 2: Decode symbols: "x" means "÷", "+" means "minus", "-" means "multiplied by", and "÷" means "plus".Step 3: The decoded expression becomes: 76 ÷ 4 - 4 * 12 + 37.Step 4: Perform division and multiplication first: 76 ÷ 4 = 19, and 4 * 12 = 48.Step 5: Substitute into the expression: 19 - 48 + 37.Step 6: Now handle subtraction and addition from left to right: 19 - 48 = -29, then -29 + 37 = 8. Verification / Alternative check:Re reading the problem confirms that the coding scheme is identical to the one in the previous question, and the decoding step is applied consistently. Re computing each operation yields the same intermediate values 19 and 48 and the final result 8, so the answer is stable under re calculation. Why Other Options Are Wrong: 9, 7, 3 and 11 would arise only if one or more symbols were mis decoded or if precedence was ignored. For example, treating "x" as multiplication instead of division or "+" as addition instead of minus would completely change the result. Common Pitfalls:The main traps are mixing up the substituted meanings of "+" and "-", and forgetting to apply precedence to the decoded expression. Another error is to treat the original sequence as if it were already in standard arithmetic, which it is not. Always write down the fully decoded expression and then compute carefully. Final Answer:After decoding and simplifying, the value of 76 x 4 + 4 - 12 ÷ 37 is 8.

Question 11

In the following coded arithmetic expression, "S" denotes "multiplied by", "V" denotes "subtracted from", "M" denotes "added to" and "L" denotes "divided by". What is the value of 96 L 8 S 4 V 16 M 9?

Accepted Answer

Introduction / Context:This question uses letters to represent arithmetic operations. You are told what each letter stands for and must evaluate the expression accordingly. These problems test basic arithmetic skill and the ability to translate between symbolic and verbal descriptions of operations. Given Data / Assumptions: "S" denotes "multiplied by". "V" denotes "subtracted from". "M" denotes "added to". "L" denotes "divided by". Expression: 96 L 8 S 4 V 16 M 9. We will treat "subtracted from" as a standard subtraction in left to right evaluation, as is common in such exam questions. Concept / Approach:First replace each letter with its corresponding arithmetic symbol to form a standard expression. Then evaluate using the usual precedence rules: perform division and multiplication first, followed by addition and subtraction from left to right. Although the phrase "subtracted from" normally reverses order in English, in many reasoning questions it is simply used to indicate subtraction between terms of the expression. Step-by-Step Solution:Step 1: Decode the expression: 96 L 8 S 4 V 16 M 9 becomes 96 ÷ 8 × 4 - 16 + 9.Step 2: Perform division and multiplication: 96 ÷ 8 = 12 and 12 × 4 = 48.Step 3: Substitute back: 48 - 16 + 9.Step 4: Now calculate from left to right: 48 - 16 = 32.Step 5: Then 32 + 9 = 41. Verification / Alternative check:If we had interpreted "subtracted from" as reversing the order of subtraction, we would effectively compute 16 - 48, leading to a negative value which does not match any of the answer choices given. The exam pattern therefore clearly expects the simpler interpretation where "V" is treated as a normal minus sign between adjacent terms. Under this assumption, the result 41 is obtained consistently. Why Other Options Are Wrong: 32 and 48 correspond to stopping midway through the calculation or omitting the final addition. 37 and 39 would require different arithmetic such as mis dividing or mis subtracting. Common Pitfalls:The main confusion here is linguistic: "subtracted from" in pure English implies a reversal of order. In such coding questions though, letters are used more mechanically. Another common error is forgetting to carry out division and multiplication before subtraction and addition, which leads to incorrect intermediate values. Final Answer:After decoding and evaluating, 96 L 8 S 4 V 16 M 9 equals 41.

Question 12

In the following letter series c_e_cd_f_d_f, which one set of letters, when sequentially placed in the blanks, will complete the series in a consistent alphabetical pattern?

Accepted Answer

Introduction / Context:This verbal reasoning question is about completing a letter series by inserting the correct sequence of letters into blanks. The goal is to identify the underlying pattern and choose the option that makes the entire sequence consistent. Such questions are common in aptitude tests and measure pattern recognition and attention to order in alphabets. Given Data / Assumptions: Given series with blanks: c_e_cd_f_d_f. There are five blanks to be filled. Each option gives a five letter sequence to place in the blanks from left to right. Exactly one option should make the complete sequence follow a simple pattern. Concept / Approach:First, mark the positions of the blanks and then test each candidate option by inserting its letters sequentially. After filling the blanks, inspect the resulting sequence for a simple, repeating alphabetic pattern. A neat repetition is a strong indicator of the correct choice, especially in letter series where consecutive letters such as c, d, e and f frequently appear. Step-by-Step Solution:Step 1: The pattern is c _ e _ c d _ f _ d _ f, with blanks at positions 2, 4, 7, 9 and 11.Step 2: Insert the option "dfece" in order: position 2 = d, 4 = f, 7 = e, 9 = c, 11 = e.Step 3: The completed series becomes: c d e f c d e f c d e f.Step 4: Now we clearly see a perfectly repeating pattern: c d e f repeated three times in succession.Step 5: None of the other options produce such a clean and regular repetition. Verification / Alternative check:If we try the other answer choices, they create irregular strings that do not follow a simple repetition of four consecutive letters. Only with "dfece" do we get c d e f c d e f c d e f, which is a very natural and symmetric pattern in the alphabet. This strongly confirms that option "dfece" is the intended completion. Why Other Options Are Wrong: "dfcec", "cfede", "cdfed" and "cedfd" all break the c d e f repetition at some point. They produce sequences where letters do not progress uniformly through the alphabet. Common Pitfalls:Some candidates focus only on local segments and miss the global pattern of repetition. Others may try to force a complex rule when a simple cyclic pattern is present. In letter series questions, always look for repeated blocks and natural alphabet sequences first, as they are usually the intended structure. Final Answer:The sequence is completed as c d e f c d e f c d e f, so the correct set of letters is "dfece".

Question 13

In a certain code language, the word "INSTANT" is written as "IOUWESZ". Using the same coding rule, how is the word "FORGET" written in that code language?

Accepted Answer

Introduction / Context:This coding decoding question involves position dependent shifts in the alphabet. The word INSTANT is coded as IOUWESZ. Unlike simple Caesar ciphers with a constant shift, here the amount of shift changes with the position of each letter. You must discover this pattern and then apply it to the new word FORGET. Given Data / Assumptions: INSTANT is written as IOUWESZ. We must encode FORGET using the same rule. Letters follow the standard A to Z order. Concept / Approach:We compare each letter of INSTANT with its coded counterpart in IOUWESZ and compute the shift. This reveals how the shift increases step by step. Once we know the shift for each position (first, second, third, etc.), we use the same set of shifts for the letters of FORGET, which also has six letters like the first six positions of INSTANT. Step-by-Step Solution:Step 1: Write INSTANT and IOUWESZ aligned: I → I, N → O, S → U, T → W, A → E, N → S, T → Z.Step 2: Compute shifts: I(9) → I(9) is +0, N(14) → O(15) is +1, S(19) → U(21) is +2, T(20) → W(23) is +3, A(1) → E(5) is +4, N(14) → S(19) is +5, T(20) → Z(26) is +6.Step 3: So the pattern is: first letter +0, second +1, third +2, fourth +3, fifth +4, sixth +5, seventh +6.Step 4: Apply the same incremental shifts to FORGET: letters F, O, R, G, E, T.Step 5: F(6) + 0 = F(6); O(15) + 1 = P(16); R(18) + 2 = T(20); G(7) + 3 = J(10); E(5) + 4 = I(9); T(20) + 5 = Y(25).Step 6: Thus, FORGET is coded as FPTJIY. Verification / Alternative check:The increasing shift rule matches every letter of INSTANT exactly, so it is highly reliable. Applying the same set of shifts to any six-letter word must give a unique code. When we encode FORGET using +0, +1, +2, +3, +4 and +5, the resulting word FPTJIY matches one of the answer choices exactly, confirming the correctness of the method. Why Other Options Are Wrong: FPOGXI, FOSIGX and FPSKHW show incorrect shifts on multiple letters and do not follow the steadily increasing pattern. FQSJHZ would require different, non uniform shifts and cannot be derived from the INSTANT example. Common Pitfalls:Students sometimes assume a constant shift for all letters or fail to observe that the amount of shift is increasing position wise. Another mistake is to miscalculate one or two letter positions, which leads to a completely different code word. Always compute the shift carefully for each position using numeric letter values. Final Answer:Following the position dependent shifts, FORGET is coded as FPTJIY.

Question 14

In a certain code language, "A" means "plus", "B" means "divide", "C" means "multiply" and "D" means "minus". Using these meanings, what is the value of 187 B 17 C 4 A 7 D 17?

Accepted Answer

Introduction / Context:This operator coding problem uses the letters A, B, C and D as stand ins for the four basic arithmetic operations. You must interpret the expression 187 B 17 C 4 A 7 D 17 correctly and then simplify it. These questions test translation skills and correct application of operator precedence. Given Data / Assumptions: "A" means plus (+). "B" means divide (÷). "C" means multiply (*). "D" means minus (-). Expression: 187 B 17 C 4 A 7 D 17. Normal arithmetic precedence applies after decoding. Concept / Approach:First decode the expression by replacing each letter with the correct arithmetic symbol. Once you have a standard expression, use the order of operations: division and multiplication first, then addition and subtraction. It is helpful to write the decoded expression clearly to avoid mental confusion between letters and true operators. Step-by-Step Solution:Step 1: Decode the expression: 187 B 17 C 4 A 7 D 17 becomes 187 ÷ 17 * 4 + 7 - 17.Step 2: Perform division first: 187 ÷ 17 = 11.Step 3: Multiply the result by 4: 11 * 4 = 44.Step 4: Now the expression is 44 + 7 - 17.Step 5: Carry out addition and subtraction from left to right: 44 + 7 = 51.Step 6: Then 51 - 17 = 34. Verification / Alternative check:Because 187 and 17 divide exactly to give 11, any error in this early step would quickly show up as a fractional or inconsistent result. Re performing the arithmetic confirms that 11 * 4 is 44, and 44 + 7 - 17 equals 34. The decoded expression and the computed value both check out, so the answer is reliable. Why Other Options Are Wrong: 30 and 33 could result from incorrect subtraction at the final stage. 44 would be obtained if we forgot to add 7 and subtract 17. 39 corresponds to miscalculating 44 + 7 or 51 - 17. Common Pitfalls:Students often decode some but not all letters correctly, especially when there are four different operators. Another common error is to ignore the precedence of division and multiplication and work from left to right only. Writing down the decoded form and then doing the arithmetic step by step prevents these mistakes. Final Answer:After decoding and simplifying, the value of 187 B 17 C 4 A 7 D 17 is 34.

Question 15

In a certain code language, the word "BISLERI" is written as "IREBISL". Using the same coding rule, how is the word "PANTHER" written in that code language?

Accepted Answer

Introduction / Context:This coding decoding problem involves rearranging letters in a specific pattern. You are told that BISLERI becomes IREBISL in the code language and must use the same rearrangement to encode PANTHER. The trick is to understand the positional rearrangement rather than a simple alphabet shift. Given Data / Assumptions: BISLERI is written as IREBISL. We must encode PANTHER using the same positional pattern. All letters remain the same; only their order changes. Concept / Approach:Write down the original and coded words, align them and track which original letter ends up in which coded position. That mapping of indices can then be applied to a new word with the same length. BISLERI and PANTHER both have seven letters, so the same index mapping should work perfectly for both. Step-by-Step Solution:Step 1: List BISLERI as positions: 1 B, 2 I, 3 S, 4 L, 5 E, 6 R, 7 I.Step 2: List the coded word IREBISL: positions: 1 I, 2 R, 3 E, 4 B, 5 I, 6 S, 7 L.Step 3: Map coded positions back to original: coded1 (I) comes from original7, coded2 (R) from original6, coded3 (E) from original5, coded4 (B) from original1, coded5 (I) from original2, coded6 (S) from original3, coded7 (L) from original4.Step 4: So the pattern is: [7, 6, 5, 1, 2, 3, 4]. The coded word takes letters in the order 7th, 6th, 5th, 1st, 2nd, 3rd, 4th.Step 5: Now write PANTHER as positions: 1 P, 2 A, 3 N, 4 T, 5 H, 6 E, 7 R.Step 6: Apply the same index order: 7th → R, 6th → E, 5th → H, 1st → P, 2nd → A, 3rd → N, 4th → T.Step 7: Therefore PANTHER is coded as REHPANT. Verification / Alternative check:Re applying the pattern to BISLERI verifies that we reconstruct IREBISL correctly, so the index mapping is accurate. Because PANTHER has the same length, using the identical sequence of positions must produce the correct coded form. The result REHPANT matches exactly one of the answer choices, which confirms that the pattern has been applied correctly. Why Other Options Are Wrong: REPHANT, REHTNAP and REHNAPT correspond to other permutations of the letters that do not follow the [7, 6, 5, 1, 2, 3, 4] index order. RPEHANT also breaks the strict mapping derived from BISLERI. Common Pitfalls:Students sometimes try to guess a visual pattern without explicitly mapping positions, which easily leads to mistakes. Another trap is to assume the word was simply reversed, but BISLERI reversed would be IRELSIB, not IREBISL. Hence precise index mapping is essential for a correct solution. Final Answer:Using the same positional rearrangement, PANTHER is written as REHPANT.

Question 16

In the coded arithmetic expression, "S" denotes "multiplied by", "V" denotes "subtracted from", "M" denotes "added to" and "L" denotes "divided by". What is the value of 7 V 42 M 56 L 8 S 5?

Accepted Answer

Introduction / Context:This question continues the pattern of using letters to represent arithmetic operations. With the given meanings of S, V, M and L, you must decode the expression 7 V 42 M 56 L 8 S 5 and then simplify it. It tests translation skill and correct application of division and multiplication before addition and subtraction. Given Data / Assumptions: "S" denotes "multiplied by". "V" denotes "subtracted from". "M" denotes "added to". "L" denotes "divided by". Expression: 7 V 42 M 56 L 8 S 5. We treat V as a subtraction operator between terms for evaluation purposes. Concept / Approach:First convert the coded expression into a standard arithmetic expression. Then apply arithmetic precedence: handle division and multiplication first, followed by addition and subtraction from left to right. As in many reasoning questions, the phrase "subtracted from" is interpreted as a simple minus sign between adjacent terms within the overall expression. Step-by-Step Solution:Step 1: Decode each letter: L → ÷, S → *, V → -, M → +.Step 2: The expression 7 V 42 M 56 L 8 S 5 becomes 7 - 42 + 56 ÷ 8 * 5.Step 3: Evaluate division and multiplication first: 56 ÷ 8 = 7, then 7 * 5 = 35.Step 4: Substitute back: 7 - 42 + 35.Step 5: Simplify from left to right: 7 - 42 = -35.Step 6: Finally, -35 + 35 = 0. Verification / Alternative check:The intermediate computations are straightforward. Re evaluating 56 ÷ 8 = 7 and 7 * 5 = 35 leaves little room for error. Re performing the subtraction and addition confirms the final result 0. Because the calculation is simple, the most likely source of mistakes would be mis decoding a symbol, not the arithmetic itself. Why Other Options Are Wrong: 8, 12, 16 and 20 would result only if either division or multiplication were mis handled or if the order of operations was ignored. They do not match the correctly decoded and evaluated expression. Common Pitfalls:One frequent mistake is interpreting "subtracted from" as reversing the order of subtraction in complex expressions. Another is forgetting to do division and multiplication before addition and subtraction. Clearly decoding each operator and writing the standard expression is the safest way to avoid these issues. Final Answer:After decoding and simplifying, 7 V 42 M 56 L 8 S 5 evaluates to 0.

Question 17

In this equation based pattern, 8 x 5 x 0 = 805 and 7 x 4 x 6 = 764. Following the same pattern, what is the value of 6 x 8 x 9 = ?

Accepted Answer

Introduction / Context:This is a number pattern question where the usual multiplication sign "x" is not used in its arithmetic sense. Instead, the expressions 8 x 5 x 0 and 7 x 4 x 6 are mapped to three digit numbers 805 and 764. You must infer the pattern and apply it to 6 x 8 x 9 to determine the corresponding three digit value. Such questions test pattern spotting and handling of digits rather than actual multiplication. Given Data / Assumptions: 8 x 5 x 0 = 805. 7 x 4 x 6 = 764. We must find 6 x 8 x 9 = ? The symbol "x" is treated as a separator, not the multiplication operator. Concept / Approach:Observe how the digits on the left relate to the digits on the right. In 8 x 5 x 0 = 805, the right side digits are 8, 0 and 5, which are exactly the first, third and second numbers in order. In 7 x 4 x 6 = 764, the right side digits are 7, 6 and 4, again the first, third and second numbers from the left. Therefore the pattern is that a x b x c is converted into the three digit number with digits a, c and b in that order. Step-by-Step Solution:Step 1: Check the first example: (8, 5, 0) on the left gives 8, 0, 5 on the right.Step 2: The order is first number, third number, then second number.Step 3: Check the second example: (7, 4, 6) on the left gives 7, 6, 4 on the right, again first, third and second.Step 4: Therefore, for (6, 8, 9), we must write digits in the order: first (6), third (9), second (8).Step 5: So 6 x 8 x 9 corresponds to the three digit number 698. Verification / Alternative check:There is no multiplication or addition that naturally produces 805 or 764 from the left hand triples, so a digit rearrangement rule is clearly intended. Because both given examples fit the "first, third, second" ordering perfectly and there is no contradictory example, applying the same arrangement to 6, 8 and 9 is the only reasonable approach. It yields 698, which matches one of the answer options exactly. Why Other Options Are Wrong: 689, 968, 986 and 896 correspond to other permutations of the digits 6, 8 and 9 but do not follow the specific "first, third, second" order demonstrated by the examples. Choosing any of them would ignore the clear pattern of the given equalities. Common Pitfalls:Some candidates attempt to treat "x" as multiplication and look for numeric formulas like products or sums, which do not work here. Others notice the digits but mis identify the exact ordering. In pattern questions with small fixed examples, always check the position of each digit carefully before generalising to a new triple. Final Answer:According to the pattern, 6 x 8 x 9 corresponds to 698.

Question 18

In a certain code language, the phrase "go home" is written as "ta na" and the phrase "nice little home" is written as "na ja pa". Using only this information, how is the individual word "go" written in that code language?

Accepted Answer

Introduction:This question is a classic example of a coding and decoding problem from verbal reasoning. We are given coded forms of two short phrases and are asked to determine how a single word, namely "go", is written in that particular code language. The key idea in such questions is to compare the phrases, identify common words, and then match them with common code terms so that we can isolate the remaining mappings. Given Data / Assumptions:We are told that "go home" is written as "ta na" and "nice little home" is written as "na ja pa". The order of coded words is not necessarily tied to the order of original words, so we work with sets of words rather than positions. We assume that each distinct word is consistently represented by a single distinct code in this language and that there is no trick such as one code standing for more than one word in the same question. Concept / Approach:The standard approach for this pattern is to look for a word that is common between both phrases, and then match it with the code element that is also common between both coded forms. Once we identify the common mapping, we can remove the common word and its code from the comparison and focus on the leftover words and codes to find the required mapping for the target word "go". Step-by-Step Solution:Step 1: Observe that "home" appears in both phrases: "go home" and "nice little home".Step 2: The coded forms are "ta na" for "go home" and "na ja pa" for "nice little home". The code "na" is common to both coded phrases.Step 3: Therefore, the natural mapping is that the common word "home" corresponds to the common code "na".Step 4: In the phrase "go home", the codes are "ta" and "na". Since "home" is already matched with "na", the remaining code "ta" must correspond to the remaining word "go".Step 5: Hence "go" is written as "ta" in the given code language. Verification / Alternative check:If we assign "home" to "na" and "go" to "ta", then in the second phrase "nice little home" the codes "na ja pa" can logically be interpreted as "home nice little" or "nice home little" or "little nice home". The exact word to code alignment among "nice" and "little" is not needed, and nothing contradicts our mapping, so the solution is consistent. Why Other Options Are Wrong:Option "na" is already associated with "home", so it cannot correctly stand for "go". Option "ja" appears only in the second coded phrase where "go" does not occur, so it is more naturally tied to either "nice" or "little". Option "na or ta" suggests ambiguity, but once we use the intersection method, the mapping becomes precise and there is no real ambiguity. Common Pitfalls:A frequent mistake is to assume that the order of words and the order of codes always match position by position. In many exam questions, the code positions can be scrambled, so we must rely on the logic of common words and common codes rather than positional matching. Another error is to overcomplicate the mapping and consider multiple codes for the same word, which is not implied here. Final Answer:The word "go" is written as ta in the given code language.

Question 19

If P denotes division, Q denotes multiplication, R denotes addition and S denotes subtraction, then what is the numerical value of the expression 18 Q 12 P 4 R 5 S 6 according to the usual rules of operator precedence?

Accepted Answer

Introduction:This problem belongs to the category of coded mathematical operations in verbal reasoning. Instead of the usual symbols for addition, subtraction, multiplication, and division, we are given letters P, Q, R, and S, each representing a different operation. Our task is to decode the expression correctly and then evaluate it using the standard order of operations (also called BODMAS or PEMDAS rules). Given Data / Assumptions:The statement tells us that P denotes division, Q denotes multiplication, R denotes addition, and S denotes subtraction. The coded expression to be evaluated is 18 Q 12 P 4 R 5 S 6. We assume that there is no trick in bracketing beyond the ordinary precedence rules and that multiplication and division are performed before addition and subtraction, working from left to right within each precedence level. Concept / Approach:The key concept is to first rewrite the coded expression in terms of the actual arithmetic symbols and then apply the usual precedence. If we substitute the correct operations, the expression becomes a standard arithmetic sentence. From there, we simply evaluate step by step, taking care not to change the order of operations. Step-by-Step Solution:Step 1: Replace Q by multiplication, P by division, R by addition, and S by subtraction.Step 2: The coded expression 18 Q 12 P 4 R 5 S 6 becomes 18 * 12 / 4 + 5 - 6.Step 3: Apply operation precedence. First handle multiplication and division from left to right: 18 * 12 = 216.Step 4: Now divide 216 by 4 to get 216 / 4 = 54.Step 5: The expression is now 54 + 5 - 6.Step 6: Perform addition and subtraction from left to right: 54 + 5 = 59.Step 7: Next, 59 - 6 = 53.Step 8: Therefore, the final result of the coded expression is 53. Verification / Alternative check:We can quickly verify by recalculating the intermediate steps. Multiplying 18 by 12 gives 216, dividing by 4 yields 54, adding 5 gives 59, and subtracting 6 brings the answer to 53. Any other sequencing that respects precedence leads to the same result, confirming that no bracketing has been missed. Why Other Options Are Wrong:The value 54 would arise if someone incorrectly stopped after evaluating 18 * 12 / 4 and forgot to process the rest of the expression. The value 57 could appear if the subtraction and addition were combined incorrectly, such as doing 54 + (5 - 2) by mistake. The value 59 corresponds to stopping at 54 + 5 and ignoring the final subtraction. The value 95 would belong to a completely misinterpreted or incorrectly ordered evaluation. Common Pitfalls:Students often confuse the order of operations when faced with unfamiliar symbols. It is easy to treat the expression as strictly left to right, which is incorrect. Another pitfall is to misread which letter stands for which operation, especially when there are four different mappings. Carefully rewriting the expression with standard symbols before calculating helps avoid these errors. Final Answer:The value of the expression is 53.

Question 20

In a certain numerical coding pattern, 23 x 16 is defined to be equal to 184 and 37 x 10 is defined to be equal to 185. Following the same hidden rule, what should be the value of 85 x 12 in this pattern?

Accepted Answer

Introduction:This is a numerical reasoning question based on an artificial coding pattern rather than on ordinary multiplication. The symbol x does not represent simple multiplication in the usual sense. Instead, we are given two examples that follow a hidden rule, and we must deduce that rule and apply it consistently to a third case involving 85 and 12. Such questions test pattern recognition, numerical manipulation, and logical consistency. Given Data / Assumptions:We are told that 23 x 16 = 184 and 37 x 10 = 185 under a special rule. We must assume that the same rule applies uniformly to all expressions of the form a x b in this question. Our goal is therefore to find the value of 85 x 12 according to the same pattern. We also assume that there is a single, simple arithmetic relationship rather than multiple conflicting rules. Concept / Approach:The natural strategy is to try basic operations using the usual product of the two numbers in each example and see how that product is transformed into the given coded result. Often, coded operations involve adding or subtracting a constant, halving or doubling, or performing some combination of digits. We test these possibilities on the first pair and then see if the same relation works for the second pair. Once the rule is discovered, it can be directly applied to the new pair. Step-by-Step Solution:Step 1: Compute the ordinary product of 23 and 16. We get 23 * 16 = 368.Step 2: Compare this with the coded value 184. Notice that 184 is exactly half of 368, so 368 / 2 = 184.Step 3: Now test the same idea on the second example. Compute 37 * 10 = 370.Step 4: Half of 370 is 370 / 2 = 185, which matches the coded value given as 185.Step 5: Since the same rule, "take half of the usual product", works consistently for both examples, we adopt it as the underlying pattern: a x b = (a * b) / 2.Step 6: Apply this rule to 85 x 12. First find the ordinary product: 85 * 12 = 1020.Step 7: Now take half of 1020 to get 1020 / 2 = 510.Step 8: Therefore, 85 x 12 should be equal to 510 in this coding scheme. Verification / Alternative check:If we attempted any other simple transformation, such as adding or subtracting a constant or swapping digits, those rules would not match both original examples simultaneously. The halving rule is the only straightforward and consistent operation that converts 368 to 184 and 370 to 185. Hence, applying it to 85 and 12 is justified. Why Other Options Are Wrong:The value 511 would require adding 1 to the correct coded result without any justification from the pattern. The values 610 and 410 correspond to rearranging digits or subtracting wrong constants from the product, but such operations do not hold for the given base examples. The value 512 is also close numerically but does not arise from a consistent rule applied to all three pairs. Common Pitfalls:Learners sometimes invent overcomplicated digit operations before checking simple arithmetic transformations such as halving or doubling. Others may check a rule on only one example without verifying it on the second, which can lead to incorrect generalizations. Always confirm a suspected rule with all given examples. Final Answer:The value of 85 x 12 according to the pattern is 510.

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