Question 1

The following coded arithmetic equation is incorrect when the ordinary meanings of the operators are used: 13 - 14 ÷ 30 x 7 + 15 = 13. By interchanging exactly two of the operator signs among plus (+), minus (-), division (÷), and multiplication (x)…

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Introduction / Context:This is a sign interchange puzzle where an equation appears incorrect under normal arithmetic rules. The task is to identify which two operator signs have been misplaced so that after swapping them, the equation becomes numerically correct. These questions test careful substitution, understanding of operator precedence, and a systematic trial of possible interchanges instead of random guessing. Given Data / Assumptions: • Original equation: 13 - 14 ÷ 30 x 7 + 15 = 13. • Available operators: plus (+), minus (-), division (÷), multiplication (x). • We must interchange exactly two operator signs. • After interchange, we evaluate the equation with usual precedence rules. Concept / Approach:The safest approach is to keep the numbers fixed and try interchanging pairs of operators one pair at a time. For each pair, rewrite the equation, apply normal precedence (division and multiplication before addition and subtraction), and then check whether the result equals 13. Rather than doing this completely at random, it is useful to suspect that the division or multiplication sign may be in the wrong place, because these operators have a larger impact on the result. Step-by-Step Solution: Step 1: Evaluate the original equation to confirm it is incorrect. 13 - 14 ÷ 30 x 7 + 15 is not equal to 13. Step 2: Now consider swapping + and ÷ in the expression. The minus and multiplication signs remain as they are. Step 3: After swapping, the operators between the numbers become: 13 minus 14 plus 30 x 7 ÷ 15. Step 4: In symbolic form, the new expression is 13 - 14 + 30 x 7 ÷ 15. Step 5: Apply operator precedence. First handle multiplication and division: 30 x 7 = 210, then 210 ÷ 15 = 14. Step 6: Now evaluate the remaining addition and subtraction from left to right: 13 - 14 + 14. Step 7: Compute 13 - 14 = -1, then -1 + 14 = 13. Step 8: The right hand side is 13, which matches the given value, so this interchange makes the equation correct. Verification / Alternative check:You can verify that no other pair of sign interchanges yields 13. For example, swapping - and +, or ÷ and x, or x and - leads to values that are clearly not equal to 13. With + and ÷ swapped, everything fits neatly with standard arithmetic, so this pair is uniquely correct. Once one valid pair is found and checked, there is no need to keep testing further if the options insist on a single correct choice. Why Other Options Are Wrong: Option "- and +" changes the balance of positive and negative contributions but does not fix the large effect of the division and multiplication, so the result does not become 13. Option "÷ and x" only swaps the two high precedence operators and results in a substantially different but still incorrect value. Option "x and -" alters both a high and a low precedence operator, producing an incorrect final total. Option "÷ and -" also fails to yield 13 and therefore cannot be the required interchange. Common Pitfalls:A common mistake is to forget to apply operator precedence after interchanging signs and instead evaluate strictly from left to right, which can give misleading results. Another pitfall is to change more than two operators at a time mentally, which does not correspond to the requirement of a single interchange of two signs. Writing each trial equation clearly helps avoid confusion. Final Answer:The equation becomes correct when the plus and division signs are interchanged. Therefore, the required interchange is + and ÷.

Question 2

In a certain letter code, the word DAY is represented by the sequence WZB. Using the same coding rule, how will the word MONDAY be written in that code language?

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Introduction / Context:This coding question uses a well known alphabet mirror or complement pattern often referred to as an Atbash type code. In such a system, letters are replaced by their mirror partners when the alphabet is written from A to Z and then from Z to A. By analyzing the mapping from DAY to WZB, we can discover how each letter is transformed and then apply the same rule to the longer word MONDAY. Given Data / Assumptions: • The word DAY is coded as WZB. • Target word to code: MONDAY. • There is a consistent one to one letter substitution. • Alphabet positions: A = 1, B = 2, …, Z = 26. Concept / Approach:The pattern can be recognized by observing that each coded letter seems to be the complement of the original letter with respect to the alphabet. In numeric terms, if a letter has position n, then its complement is the letter at position 27 − n. This maps the first letter A to the last letter Z, the second letter B to the second last letter Y, and so on. Once we confirm that this rule transforms every letter in DAY into WZB, we will apply it to each letter of MONDAY in turn. Step-by-Step Solution: Step 1: For D in DAY, position is 4. Its complement is at 27 − 4 = 23, which corresponds to W. This matches the code. Step 2: For A, position is 1. Complement is 27 − 1 = 26, which is Z. Again, this matches the code. Step 3: For Y, position is 25. Complement is 27 − 25 = 2, which is B. This matches the final coded letter. Step 4: This confirms that every letter is mapped to its mirror partner using the rule position to 27 minus position. Step 5: Now apply this rule to MONDAY. Write positions: M = 13, O = 15, N = 14, D = 4, A = 1, Y = 25. Step 6: Compute complements: for M, 27 − 13 = 14, which is N. Step 7: For O, 27 − 15 = 12, which is L. Step 8: For N, 27 − 14 = 13, which is M. Step 9: For D, 27 − 4 = 23, which is W. Step 10: For A, 27 − 1 = 26, which is Z. Step 11: For Y, 27 − 25 = 2, which is B. Step 12: Combining these gives NLMWZB as the code for MONDAY. Verification / Alternative check:A quick inspection of the options shows that only NLMWZB follows the same mirror mapping consistently from left to right. None of the other options aligns perfectly with the complement rule for all six letters. Therefore, the mapping is consistent and the answer is unique. Why Other Options Are Wrong: Option PLOWZB has incorrect first and second letters and does not follow the complement positions for M and O. Option NMLWZB swaps L and M in the middle, violating the correct complement for O and N. Option PQRWZB does not match the complement rule for any sequence of letters in MONDAY. Option NLOWZB alters the pattern in the third position and does not match the systematic mapping. Common Pitfalls:Students sometimes mistake this pattern for a simple forward or backward shift by a fixed number of positions. Another frequent error is to miscalculate alphabet positions, especially beyond the middle of the alphabet. Writing out A to Z with position numbers is a reliable way to avoid these errors in exam conditions. Final Answer:Using the mirror or complement coding rule, the word MONDAY is written as NLMWZB.

Question 3

In a coded arithmetic system, the meanings of the operators are changed as follows: the symbol + represents division, the symbol / represents subtraction, the symbol - represents multiplication, and the symbol x represents addition. Using this schem…

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Introduction / Context:Here we are given a numerical expression where the usual meanings of the arithmetic symbols have been changed. Instead of performing the operations implied by their standard meanings, we must interpret each symbol using the new code and then calculate the result following standard precedence rules. This type of question checks both careful reading of the symbol assignments and correct procedural execution of arithmetic once the expression has been decoded. Given Data / Assumptions: • In the code: + means division. • / means subtraction. • - means multiplication. • x means addition. • Expression given: 24 + 8 / 26 x 6. • After converting symbols to their real meanings, apply ordinary arithmetic precedence. Concept / Approach:The process has two stages. First, translate the expression by replacing each operator with its assigned real operation. Second, evaluate the translated expression carefully, respecting that multiplication and division are done before addition and subtraction. It is essential not to mix the coded meaning with the standard meaning during calculation, so we should write the decoded expression clearly on a separate line. Step-by-Step Solution: Step 1: Start with 24 + 8 / 26 x 6. Step 2: Replace + with division, so 24 + 8 becomes 24 ÷ 8. Step 3: Replace / with subtraction, so 8 / 26 becomes 8 − 26, but note that in the original sequence the slash sits between 8 and 26, and we have already accounted for 8 in the decoded structure as part of 24 ÷ 8. Interpreting as an expression with separate coded operators, the overall replacement produces 24 ÷ 8 − 26 + 6. Step 4: Replace x with addition, so 26 x 6 becomes 26 + 6, but in the decoded expression we already have subtraction and addition signs in place, leading to 24 ÷ 8 − 26 + 6. Step 5: The fully decoded expression to evaluate is 24 ÷ 8 − 26 + 6. Step 6: Apply precedence. First compute 24 ÷ 8 = 3. Step 7: Now handle addition and subtraction from left to right: 3 − 26 + 6. Step 8: Compute 3 − 26 = −23. Step 9: Then −23 + 6 = −17. Verification / Alternative check:As a check, note that the division produces a small positive value (3), then we subtract a large number (26) and finally add a smaller number (6). Intuitively this must lead to a negative result of moderate magnitude, which aligns with −17. None of the positive options, such as 12 or 21, can possibly be correct, and among the negative options only −17 matches the computed value. Why Other Options Are Wrong: Option −10 would arise from miscalculating either the division or one of the subsequent steps. Option −3 would come from incorrectly combining the subtraction and addition results. Option 12 ignores the fact that the large subtraction dominates and cannot produce a positive total. Option 21 similarly conflicts with both the sign and magnitude of the correct result. Common Pitfalls:Learners sometimes forget to rewrite the entire expression after decoding the operators, and instead try to convert and calculate simultaneously, which easily leads to errors. Another frequent error is to ignore operator precedence and perform operations strictly from left to right, which would produce a different and incorrect answer. Always decode first, then evaluate with proper order of operations. Final Answer:After applying the coded meanings of the operators and evaluating correctly, the value of the expression is −17.

Question 4

In the following pattern based system, some three number expressions are transformed in a consistent way: 7 x 6 x 8 becomes 678, 8 x 9 x 7 becomes 987, and 6 x 5 x 7 becomes 567. Using the same pattern, what number will replace the question mark in …

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Introduction / Context:This is a pattern recognition question where three numbers linked by a multiplication sign are transformed into a three digit number. The operation is not actual multiplication, but a simple rearrangement of the digits. Your job is to understand how the digits from the left side are rearranged to form the number on the right side, and then apply the same rule to the new triple 5, 4, and 6. Given Data / Assumptions: • 7 x 6 x 8 is written as 678. • 8 x 9 x 7 is written as 987. • 6 x 5 x 7 is written as 567. • Target expression: 5 x 4 x 6. • The symbol x here indicates a pattern separator, not real multiplication. Concept / Approach:These examples suggest that the three numbers on the left are simply rearranged to form the three digit number on the right. By comparing each triple with its result, we can see how the positions change. Once we find a consistent rule for the order in which the numbers appear, we apply it to the new triple 5, 4, and 6. There is no actual arithmetic computation, only positional rearrangement. Step-by-Step Solution: Step 1: Represent each triple as (a, b, c). Step 2: For 7 x 6 x 8, we have a = 7, b = 6, c = 8, and the result is 678. This corresponds to the order (b, a, c) = (6, 7, 8). Step 3: For 8 x 9 x 7, a = 8, b = 9, c = 7, and the result is 987. Again, this matches (b, a, c) = (9, 8, 7). Step 4: For 6 x 5 x 7, a = 6, b = 5, c = 7, and the result 567 corresponds to (b, a, c) = (5, 6, 7). Step 5: Thus the rule is clear: the three digit result is formed by writing b first, a second, and c third. Step 6: Apply this to 5 x 4 x 6. Here a = 5, b = 4, c = 6. Step 7: According to the rule (b, a, c), we write 4, 5, 6, which gives 456. Verification / Alternative check:You can check that this ordering rule works for every given example. Any other fixed ordering of a, b, and c, such as (a, b, c) or (c, b, a), would fail for at least one of the supplied cases. Since (b, a, c) is consistent in all three examples and also produces a meaningful result for 5, 4, and 6, we can be confident that 456 is the intended answer. Why Other Options Are Wrong: Option 564 corresponds to (a, c, b) and does not match the rule used in the examples. Option 645 corresponds loosely to (c, a, b) and is again inconsistent with the given pattern. Option 654 corresponds to (c, b, a) and fails to reproduce the sample mappings. Option 546 corresponds to (a, b, c), the original order, but the examples clearly show that the result is not a simple copy of the triple. Common Pitfalls:Some learners try to interpret the expression as actual multiplication or perform operations like a + b + c or a × b × c, which does not match the examples. Others may guess based on ascending or descending order alone without checking all given cases. Always verify a hypothesized pattern against every example provided before using it to find the missing term. Final Answer:Following the rule that the three digit number is formed in the order (b, a, c), the expression 5 x 4 x 6 is written as 456.

Question 5

In a letter coding system, each letter of the English alphabet is assigned a value equal to its position (A = 1, B = 2, C = 3, and so on). It is given that E has the value 5 and the word PEN has the value 35. Using the same coding rule, what is the …

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Introduction / Context:This problem is another letter sum coding question, where each letter of a word is replaced by its alphabetical position and then those values are combined by addition. The relationship E = 5 and PEN = 35 is given to help confirm the coding rule. Once we are sure of the pattern, we apply exactly the same logic to a new word, PAGE, and compute its total value. Given Data / Assumptions: • Letter positions: A = 1, B = 2, …, Z = 26. • E = 5 is explicitly stated and matches its position. • PEN = 35 under this code. • We must find the value of PAGE under the same system. Concept / Approach:We check whether PEN = 35 comes from summing the position values of P, E, and N. If it does, we accept this as the rule and apply it to PAGE. The main skill required is quick and accurate recall of letter positions and careful addition of a few small integers. Step-by-Step Solution: Step 1: Confirm the rule using PEN. Positions: P = 16, E = 5, N = 14. Step 2: Add these values: 16 + 5 = 21, 21 + 14 = 35. This matches the given code PEN = 35. Step 3: Now apply the same rule to PAGE. Determine positions: P = 16, A = 1, G = 7, E = 5. Step 4: Add them step by step. First 16 + 1 = 17. Step 5: Then 17 + 7 = 24. Step 6: Finally 24 + 5 = 29. Step 7: Therefore, under this code, PAGE has the value 29. Verification / Alternative check:You can perform the total addition again in a different grouping, for example (16 + 7) + (1 + 5) = 23 + 6 = 29, which confirms the earlier result. Also, notice that PAGE has four letters, and each letter has a value less than or equal to 16 here, so a total just under 30 fits expectations. This supports the correctness of 29. Why Other Options Are Wrong: Option 27 is smaller and would require a lesser sum than the actual positions provide. Option 28 is close but still does not match the exact sum of 29. Option 30 is larger and again does not correspond to the computed sum. Option 26 is significantly smaller than required and cannot be obtained from these letter values. Common Pitfalls:Typical mistakes involve misidentifying the position of G or P, or accidentally omitting one of the letters when adding. Some learners also confuse this kind of code with letter product or other operations, but the verification with PEN clearly shows that we are dealing with a simple sum of positions. Final Answer:Using the same letter position sum code, the word PAGE is assigned the value 29.

Question 6

In a coded arithmetic scheme, the meanings of the standard operators are changed as follows: the symbol plus (+) stands for division (÷), the symbol division (÷) stands for subtraction (-), the symbol minus (-) stands for multiplication (x), and the…

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Introduction / Context:This problem requires you to reinterpret an arithmetic expression in which the operator symbols are reassigned different meanings. Rather than treating the symbols in their usual sense, you must decode each one using the given mapping and then perform the calculation with standard precedence rules. Such problems help develop flexibility in understanding how symbolic rules can be changed and still interpreted consistently. Given Data / Assumptions: • + means division (÷). • ÷ means subtraction (-). • - means multiplication (x). • x means addition (+). • Expression: 48 + 16 x 4 - 2 ÷ 8. Concept / Approach:The steps are to decode each operator and then evaluate the resulting expression with normal rules. We must not mix the coded meaning with the usual meaning while decoding. Once the translation is complete, we treat the decoded expression like an ordinary arithmetic calculation, performing multiplication and division first, followed by addition and subtraction from left to right. Step-by-Step Solution: Step 1: Start with the expression 48 + 16 x 4 - 2 ÷ 8. Step 2: Decode each operator: + becomes ÷, x becomes +, - becomes x, and ÷ becomes -. Step 3: Replace in order: 48 + 16 becomes 48 ÷ 16. Step 4: 16 x 4 becomes 16 + 4. Step 5: The minus sign before 2 becomes a multiplication sign, so - 2 becomes x 2. Step 6: Finally, ÷ 8 becomes - 8. Step 7: Putting this together, the decoded expression is 48 ÷ 16 + 4 x 2 - 8. Step 8: Apply precedence. First compute 48 ÷ 16 = 3. Step 9: Compute 4 x 2 = 8. Step 10: Now evaluate 3 + 8 - 8 from left to right. First 3 + 8 = 11. Step 11: Then 11 - 8 = 3. Verification / Alternative check:If you repeat the entire translation and calculation carefully, you will again obtain 3, indicating that there is no arithmetic slip. Approximate reasoning also supports this result: the division 48 ÷ 16 gives a small number 3, the middle product gives 8, and then subtracting 8 at the end neutralizes that contribution, leaving the value from the first term, which is 3. Why Other Options Are Wrong: Option 6 would require the net effect of the operations to double the initial 3, which is not the case. Option 112 is far too large and could only arise from misinterpreting several operators as multiplication. Option −28 would require a large negative net effect that does not match the steps of the decoded expression. Option 10 also does not match the exact arithmetic sequence after correct decoding. Common Pitfalls:Learners often forget to apply operator precedence after decoding and simply calculate from left to right. Another frequent error is to only partially decode the expression or to accidentally revert to the original meaning of a symbol midway through the solution. Writing the translated expression clearly in one line before starting arithmetic is a very effective way to prevent confusion. Final Answer:After decoding the operators and evaluating step by step, the value of the expression is 3.

Question 7

Some three number expressions connected by the symbol * are transformed into three digit numbers according to a fixed pattern. For example, 7 * 4 * 3 becomes 437 and 8 * 6 * 4 becomes 648. Using the same pattern, what should be the result when 4 * 3…

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Introduction / Context:This is another pattern recognition question with three numbers and a special symbol *. The expression is not meant to be evaluated by multiplication. Instead, the three numbers are rearranged to form a three digit number according to a specific rule. By studying the given examples, we need to infer the order in which the three numbers are written on the right hand side, and then apply that rule to the new triple 4, 3, and 6. Given Data / Assumptions: • 7 * 4 * 3 is transformed to 437. • 8 * 6 * 4 is transformed to 648. • We must find the transformation for 4 * 3 * 6. • The symbol * represents a pattern separator, not actual multiplication. Concept / Approach:We denote the triple as (a, b, c) in the order they appear on the left. By comparing the examples, we attempt to express the right hand side three digit number in terms of a, b, and c in a fixed order, such as (b, c, a) or (b, a, c). Once we find an ordering that is consistent across all examples, we use that same ordering for the new triple (4, 3, 6). Step-by-Step Solution: Step 1: For 7 * 4 * 3, a = 7, b = 4, c = 3. The result is 437, which corresponds to digits 4, 3, 7. Step 2: The order 4, 3, 7 can be expressed as (b, c, a). Step 3: For 8 * 6 * 4, a = 8, b = 6, c = 4. The result is 648. This corresponds to digits 6, 4, 8, which again match (b, c, a). Step 4: Thus the consistent rule is: for any triple (a, b, c), the transformed number is (b, c, a). Step 5: Now consider 4 * 3 * 6. Here a = 4, b = 3, c = 6. Step 6: According to the rule (b, c, a), we should write 3, 6, 4. Step 7: Therefore the transformed result is 364. Verification / Alternative check:Check again with the given examples to ensure there is no other simpler explanation. For both sample triples, using (b, c, a) perfectly reproduces the given three digit numbers, and no alternative ordering, such as (b, a, c) or (c, a, b), can match both examples simultaneously. This confirms that the rule is correctly identified and that 364 is the only valid result for 4 * 3 * 6. Why Other Options Are Wrong: Option 346 corresponds to (c, a, b), which does not fit either of the given examples. Option 643 corresponds to (c, b, a) and fails in reproducing the sample mappings. Option 463 corresponds to (a, c, b) and is inconsistent with the established rule. Option 436 corresponds to (a, b, c), the original order, whereas the examples clearly show a rearranged order. Common Pitfalls:One common mistake is to look for arithmetic operations like a + b + c or a × b × c, although the structure of the answers strongly suggests a concatenation rather than a computed product or sum. Another pitfall is to infer the wrong ordering from only one example without verifying it against the second example, which may lead to a contradiction. Final Answer:Applying the consistent pattern that transforms (a, b, c) into (b, c, a), the expression 4 * 3 * 6 becomes 364.

Question 8

In a coding system where each letter of the English alphabet is given a value equal to its position (A = 1, B = 2, C = 3, and so on), it is known that A = 1, E = 5 and the code for the word HEAR is required. Using the same rule of summing the letter…

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Introduction / Context:This coding question again relies on the simple but very common rule that each letter is replaced by its alphabetical position, and the code for a word is obtained by adding the values of its letters. A and E are given as 1 and 5 respectively to remind you of the position based scheme. You need to apply this standard mapping to the word HEAR and compute the sum of the positions of all its letters. Given Data / Assumptions: • Alphabet positions: A = 1, B = 2, …, Z = 26. • A = 1 and E = 5 are explicitly mentioned. • We must find the code for HEAR. • The code is obtained by summing the position values of the letters. Concept / Approach:The approach is straightforward: identify the alphabetical position of each letter in HEAR, then calculate the sum of these values. The result of this addition is the numerical code for the word. This tests basic recall of letter positions and simple addition skills. Step-by-Step Solution: Step 1: Write down the letters of HEAR and their positions. Step 2: H is the 8th letter of the alphabet, so H = 8. Step 3: E is the 5th letter, so E = 5. Step 4: A is the 1st letter, so A = 1. Step 5: R is the 18th letter, so R = 18. Step 6: Add these values: first 8 + 5 = 13. Step 7: Then 13 + 1 = 14. Step 8: Finally 14 + 18 = 32. Step 9: Therefore, the code for HEAR is 32. Verification / Alternative check:You can rearrange the order of addition as (8 + 18) + (5 + 1) = 26 + 6 = 32, which further confirms the result. Also, since HEAR has four letters and most of them are in the first half of the alphabet, a total in the low thirties is reasonable and consistent with similar examples, reinforcing that 32 is correct. Why Other Options Are Wrong: Option 38 is too large and would require higher letter values than the alphabet positions provide. Option 31 is close but does not match the exact computed sum of 32. Option 30 is even smaller and clearly inconsistent with the sum of 8, 5, 1, and 18. Option 35 also does not equal the correct total of 32. Common Pitfalls:The main source of error is misremembering the position of R or H, or accidentally omitting one letter in the sum. Since the pattern is simple addition, careful checking of positions and a quick mental recalculation can help avoid such mistakes. Final Answer:Using the letter position sum rule, the numerical value assigned to HEAR is 32.

Question 9

In a coded arithmetic expression, the symbols P, Q, R, and S are used in place of ordinary operators as follows: P denotes addition (+), Q denotes subtraction (-), R denotes division (÷), and S denotes multiplication (x). Using this code, evaluate t…

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Introduction / Context:This problem uses letter symbols to stand for basic arithmetic operations. Instead of directly reading plus, minus, multiplication and division, you must first translate the coded letters P, Q, R, and S into their respective operations. After decoding, the expression can be evaluated using normal arithmetic rules with correct precedence. This kind of question tests precision in substitution and understanding of the order of operations. Given Data / Assumptions: • P denotes + (addition). • Q denotes - (subtraction). • R denotes ÷ (division). • S denotes x (multiplication). • Expression: 18 S 36 R 12 Q 6 P 7. Concept / Approach:First convert the coded expression into an ordinary arithmetic expression by replacing each letter with its corresponding operator. Then compute the value step by step, remembering that multiplication and division must be performed before addition and subtraction. This systematic decoding and evaluation ensures that you do not mix the symbolic and actual meanings during calculation. Step-by-Step Solution: Step 1: Start with 18 S 36 R 12 Q 6 P 7. Step 2: Replace S with multiplication: 18 x 36. Step 3: Replace R with division: ÷ 12. Step 4: Replace Q with subtraction: − 6. Step 5: Replace P with addition: + 7. Step 6: The decoded expression is 18 x 36 ÷ 12 − 6 + 7. Step 7: Apply precedence, performing multiplication and division from left to right. First, 18 x 36 = 648. Step 8: Then 648 ÷ 12 = 54. Step 9: Now handle addition and subtraction: 54 − 6 + 7. Step 10: Compute 54 − 6 = 48. Step 11: Then 48 + 7 = 55. Verification / Alternative check:To verify, repeat the arithmetic quickly: 18 x 36 = 648, 648 ÷ 12 = 54, and 54 − 6 + 7 = 48 + 7 = 55. There is no ambiguity once the operators are decoded. The size of the numbers also makes sense; the multiplication followed by division brings the value back to a moderate range, and the final subtraction and addition adjust it slightly, yielding 55. Why Other Options Are Wrong: Option 115 is too large and would require a different sequence of operations or misinterpretation of the division. Option 65 might result from partial miscalculation after the division step. Option 25 is far from the correct value and indicates a more serious arithmetic or decoding error. Option 75 also does not correspond to any reasonable reworking of the decoded expression. Common Pitfalls:A common mistake is to evaluate 18 x 36 ÷ 12 as 18 x (36 ÷ 12) = 18 x 3 = 54, which, although numerically the same in this particular case, can cause confusion in other expressions. The safest habit is to move strictly from left to right for operators of the same precedence. Another pitfall is to forget to translate one of the coded symbols, especially near the end of the expression. Final Answer:After decoding and evaluating the expression, the correct value of 18 S 36 R 12 Q 6 P 7 is 55.

Question 10

In a certain letter code, each eight letter word is coded by swapping letters in fixed adjacent pairs. For example, DECEMBER is coded as EDECBMRE. Using the same pattern of adjacent letter interchange, how will the word FEBRUARY be coded?

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Introduction / Context:This question involves a fixed positional rearrangement of letters, where an eight letter word is encoded by swapping letters in adjacent pairs. The example DECEMBER to EDECBMRE demonstrates how each pair of letters is interchanged. Once you recognize the exact swapping pattern, you simply apply the same step by step process to another eight letter word, FEBRUARY, to obtain its code. Given Data / Assumptions: • Original word: DECEMBER. • Code: EDECBMRE. • Target word to be coded: FEBRUARY. • Both words have eight letters. Concept / Approach:The key idea is that each adjacent pair of letters (positions 1 and 2, 3 and 4, 5 and 6, 7 and 8) is swapped. So the second letter moves to the first position of the pair and the first letter moves to the second position of the pair. We can confirm that this rule transforms DECEMBER into EDECBMRE, and then apply the same swapping to the pairs in FEBRUARY. Step-by-Step Solution: Step 1: Write DECEMBER with positions: 1 D, 2 E, 3 C, 4 E, 5 M, 6 B, 7 E, 8 R. Step 2: Group letters into adjacent pairs: (D, E), (C, E), (M, B), (E, R). Step 3: Swap letters in each pair: (E, D), (E, C), (B, M), (R, E). Step 4: The swapped sequence is E D E C B M R E which matches the given code EDECBMRE. Step 5: Now write FEBRUARY with positions: 1 F, 2 E, 3 B, 4 R, 5 U, 6 A, 7 R, 8 Y. Step 6: Group into pairs: (F, E), (B, R), (U, A), (R, Y). Step 7: Swap each pair: (E, F), (R, B), (A, U), (Y, R). Step 8: Combine to get the sequence E F R B A U Y R. Step 9: Thus the code for FEBRUARY is EFRBAUYR. Verification / Alternative check:If you try any other reordering rule, such as reversing the entire word or rotating letters, it will not match the given example DECEMBER to EDECBMRE. The pairwise swap rule is both simple and fully consistent. Re checking the swap for each pair in FEBRUARY confirms the code EFRBAUYR, and only one option among those given matches this pattern exactly. Why Other Options Are Wrong: Option EFRBUAYR has U and A in the wrong order in the middle pair, ignoring the swap rule. Option EFBRAUYR places B and R incorrectly and breaks the logic of swapping each adjacent pair. Option EFRBUARY keeps the last pair A and R unswapped, again deviating from the pattern used for DECEMBER. Option EFBRAURY misplaces multiple letters and does not correspond to systematic pairwise swapping. Common Pitfalls:Learners sometimes miscount positions or forget to treat all four pairs uniformly, especially the last pair. Others attempt complex patterns when a simple adjacent swap rule is sufficient. Writing the letters with explicit position numbers and working pair by pair helps avoid these mistakes. Final Answer:By swapping letters in each adjacent pair, the word FEBRUARY is coded as EFRBAUYR.

Question 11

In a coded arithmetic system, the meanings of the operation symbols are changed as follows: the symbol x represents addition (+), the symbol + represents division (÷), the symbol minus (-) represents multiplication (x), and the symbol division (÷) r…

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Introduction / Context:This coded arithmetic question replaces standard operation symbols with different meanings. Instead of interpreting x, +, -, and ÷ in their usual roles, we must translate each symbol into the corresponding actual operation, and then evaluate the expression. Questions of this type test your ability to carefully track symbolic meanings and to respect standard precedence of operations in the decoded expression. Given Data / Assumptions: • x means + (addition). • + means ÷ (division). • - means x (multiplication). • ÷ means - (subtraction). • Expression given: 8 x 7 - 8 + 40 ÷ 2. Concept / Approach:The method is to first decode each coded operator into its real meaning, thereby rewriting the expression in standard arithmetic notation. After that, we calculate the value by applying the usual precedence rules: perform multiplication and division before addition and subtraction, moving from left to right among operations of the same precedence. It is crucial not to confuse the symbolic appearance of the operators with their coded definitions during the evaluation. Step-by-Step Solution: Step 1: Start from 8 x 7 - 8 + 40 ÷ 2. Step 2: Decode x as +, so 8 x 7 becomes 8 + 7. Step 3: Decode - as multiplication x, so - 8 becomes x 8. Step 4: Decode + as division ÷, so + 40 becomes ÷ 40. Step 5: Decode ÷ as subtraction -, so ÷ 2 becomes - 2. Step 6: Putting it together, the decoded expression is 8 + 7 x 8 ÷ 40 - 2. Step 7: Apply precedence. First handle multiplication and division from left to right. Step 8: Compute 7 x 8 = 56. Step 9: Then compute 56 ÷ 40 = 56 / 40 = 7 / 5 after simplifying. Step 10: Now the expression becomes 8 + 7/5 - 2. Step 11: Convert 8 and 2 into fractions with denominator 5 to add easily: 8 = 40/5 and 2 = 10/5. Step 12: Compute 40/5 + 7/5 = 47/5. Step 13: Subtract 10/5: 47/5 − 10/5 = 37/5. Verification / Alternative check:Merge the integer operations as decimals as a cross check: 7 x 8 ÷ 40 = 1.4, so the expression becomes 8 + 1.4 − 2. Then 8 + 1.4 = 9.4, and 9.4 − 2 = 7.4. Converting 7.4 to a fraction gives 7.4 = 74 / 10 = 37 / 5, which matches our earlier result. This confirms that the arithmetic is correct. Why Other Options Are Wrong: Option 1 is much smaller than the true value and would come from ignoring the contribution of the fraction 7/5. Option 83/5 is larger and does not follow from the correct sequence of operations. Option 44 corresponds to a simple integer calculation rather than a mixed fraction result and shows a misinterpretation of division. Option 9 is close numerically to 8 plus a small positive correction, but the final subtraction of 2 makes the correct value significantly smaller than 9. Common Pitfalls:Many learners forget to apply the precedence correctly after decoding and instead perform addition and subtraction first. Others misread one of the operator mappings, for example thinking that + still means addition instead of division in this system. Carefully rewriting the entire expression after decoding and only then doing the arithmetic helps avoid such errors. Final Answer:Under the given coded operator scheme, the value of 8 x 7 - 8 + 40 ÷ 2 is 37/5.

Question 12

In a letter to number coding pattern, the single letter C is coded as 3 and the four letter word DASH is coded as 32. Assuming that the code for a word is obtained by summing the alphabetical positions of its letters (A = 1, B = 2, C = 3, and so on)…

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Introduction / Context:This question again uses the simple yet widely used rule that each letter in a word is replaced by its position in the alphabet, and the code for the word is the sum of these values. The fact that C is coded 3 and DASH is coded 32 fits well with this letter sum system. Once we validate the pattern using DASH, we can apply the same method to calculate the code for the word DANCE. Given Data / Assumptions: • Alphabet positions: A = 1, B = 2, C = 3, …, Z = 26. • C = 3 is consistent with its position. • DASH = 32 under the code. • We must find the code for DANCE. Concept / Approach:We first verify that DASH = 32 by summing the positions of D, A, S, and H. If the sum matches 32, we can assume the same sum of positions rule applies to and then compute the value for DANCE. The task mainly involves recalling letter positions accurately and adding several small numbers correctly. Step-by-Step Solution: Step 1: Confirm the coding for DASH. Positions: D = 4, A = 1, S = 19, H = 8. Step 2: Add these: 4 + 1 = 5, 5 + 19 = 24, 24 + 8 = 32. This matches the given code, so the pattern is confirmed. Step 3: Now apply the same rule to DANCE. Identify the positions: D = 4, A = 1, N = 14, C = 3, E = 5. Step 4: Begin adding: 4 + 1 = 5. Step 5: Add N: 5 + 14 = 19. Step 6: Add C: 19 + 3 = 22. Step 7: Add E: 22 + 5 = 27. Step 8: Therefore DANCE is coded as 27. Verification / Alternative check:A quick alternative addition sequence, such as (4 + 14) + (1 + 3 + 5) = 18 + 9 = 27, confirms the same result. The total is reasonable for a five letter word whose letters mainly lie in the first half of the alphabet. This makes 27 a consistent and reliable answer. Why Other Options Are Wrong: Option 20 is too small and does not match the calculated sum. Option 25 is slightly smaller than the correct value and indicates incomplete addition. Option 26 is close but not equal to 27 and does not correspond to the exact positions. Option 23 is significantly below the correct sum and therefore incorrect. Common Pitfalls:Common errors include forgetting one letter while adding or misremembering the position of N or E. Careful writing of all letters with their corresponding numbers and a systematic addition eliminates these mistakes. Final Answer:Under the given letter sum coding rule, the word DANCE is coded as 27.

Question 13

In a coded arithmetic system, the meanings of the operators are changed as follows: the symbol plus (+) means minus (-), the symbol minus (-) means multiplication (x), the symbol division (÷) means plus (+), and the symbol x means division (÷). Usin…

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Introduction / Context:This problem again changes the meanings of all four basic arithmetic operators. To solve it, we must first translate the given coded expression to a normal arithmetic expression using the provided mapping. After that, we compute the numerical value using ordinary precedence rules. The question checks your ability to keep track of operator meanings and to perform multi step calculations accurately. Given Data / Assumptions: • + means minus (-). span style="display:block;">• - means multiplication (x). • ÷ means plus (+). • x means division (÷). • Expression: 15 - 3 + 10 x 5 ÷ 5. Concept / Approach:We decode the expression by substituting each symbol with its actual operation. Then we apply the established arithmetic rule that multiplication and division have higher precedence than addition and subtraction. Finally, we perform the operations step by step. It is very useful to rewrite the entire expression in decoded form before starting the calculation to avoid mixing coded and real meanings in your mind. Step-by-Step Solution: Step 1: Start with 15 - 3 + 10 x 5 ÷ 5. Step 2: Decode - as multiplication, so 15 - 3 becomes 15 x 3. Step 3: Decode + as minus, so + 10 becomes − 10. Step 4: Decode x as division, so 10 x 5 becomes 10 ÷ 5. Step 5: Decode ÷ as plus, so ÷ 5 becomes + 5. Step 6: Putting all replacements together, the decoded expression is 15 x 3 − 10 ÷ 5 + 5. Step 7: Apply precedence. First compute the multiplication and division: 15 x 3 = 45. Step 8: Compute 10 ÷ 5 = 2. Step 9: Now the expression becomes 45 − 2 + 5. Step 10: Evaluate from left to right: 45 − 2 = 43. Step 11: Finally 43 + 5 = 48. Verification / Alternative check:As a verification, perform the arithmetic again quickly: 15 times 3 is 45, 10 divided by 5 is 2, then 45 minus 2 plus 5 equals 43 plus 5 which is 48. The sequence is straightforward once decoded, and no alternative interpretation of the mapping is consistent with the given statement, so 48 is confirmed as the correct result. Why Other Options Are Wrong: Option 52 would require a final addition result of 9 instead of 5, which does not match the decoded expression. Option 22 is far too small and must result from major decoding or arithmetic errors. Option 5 ignores the large contribution from the multiplication 15 x 3 and therefore cannot be correct. Option 18 also fails to reflect the correct combination of the intermediate results 45 and 2. Common Pitfalls:A common mistake is to treat the operators with their usual meanings and ignore the coding, which leads to a completely different value. Another error is to forget that multiplication and division must be done before subtraction and addition after decoding. Rewriting the entire decoded expression and underlining the high precedence operations is a practical strategy to avoid these traps. Final Answer:After decoding and evaluating step by step, the value of 15 - 3 + 10 x 5 ÷ 5 under the given operator scheme is 48.

Question 14

In a certain system of writing three number expressions of the form a x b x c, the numbers on the left side are simply rearranged to form a three digit number on the right side. For example, 7 x 4 x 9 is written as 479, 9 x 5 x 2 is written as 592, …

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Introduction / Context:This question deals with a purely symbolic pattern where three numbers separated by x are rearranged to form a three digit number. The x symbol is not a multiplication sign in the usual sense, but a separator showing the pattern structure. The task is to observe how the positions of a, b, and c change from left to right and then apply that same ordering rule to the new triple 8, 6, and 2. Given Data / Assumptions: • 7 x 4 x 9 becomes 479. • 9 x 5 x 2 becomes 592. • 6 x 9 x 5 becomes 965. • We must find the result of 8 x 6 x 2. • The operation x is not real multiplication here. Concept / Approach:We represent the three numbers as a, b, and c, and then examine how they appear in the three digit result. By comparing the triples with their codes, we can determine the position of each of a, b, and c in the result. Once this pattern is identified, we apply it directly to the triple 8, 6, and 2. No arithmetic operations like multiplication or addition are needed, only positional rearrangement. Step-by-Step Solution: Step 1: For 7 x 4 x 9, write a = 7, b = 4, c = 9. Step 2: The result is 479, which has digits 4, 7, and 9. Step 3: This can be written as (b, a, c) = (4, 7, 9). Step 4: For 9 x 5 x 2, a = 9, b = 5, c = 2. The result 592 corresponds to digits (5, 9, 2). Step 5: Again this is (b, a, c). Step 6: For 6 x 9 x 5, a = 6, b = 9, c = 5, and the result 965 equals (9, 6, 5), which is once more (b, a, c). Step 7: So the rule is consistent: the code is always b, then a, then c. Step 8: Now apply this to 8 x 6 x 2, where a = 8, b = 6, c = 2. Step 9: The code is (b, a, c) = (6, 8, 2), giving 682. Verification / Alternative check:Check that there is no other simple ordering rule that fits all examples. For instance, (a, b, c) would yield 749, 952, and 695, which do not match. (b, c, a) would give 4, 9, 7 as 497, and so on, also failing to align with all given codes. Only (b, a, c) consistently produces the results 479, 592, and 965, confirming that 682 is the correct continuation of the pattern. Why Other Options Are Wrong: Option 286 corresponds to (a, c, b) and does not match the pattern used in the examples. Option 628 corresponds roughly to (c, a, b) and is inconsistent with the established rule. Option 268 corresponds to (c, b, a) and fails to reproduce the sample codes. Option 826 corresponds to (a, b, c), which is clearly not the rearrangement used in the examples. Common Pitfalls:Learners sometimes assume x means multiplication and start computing numeric products, which is not supported by the right hand side format. Another mistake is to look only at one of the examples and infer an ordering that does not work for the others. It is essential to verify that the proposed pattern matches all given cases before applying it to the new triple. Final Answer:Following the consistent rearrangement rule (b, a, c), the expression 8 x 6 x 2 is written as 682.

Question 15

In a simple letter shift code, each letter of a word is replaced by the letter that comes immediately after it in the English alphabet (so L becomes M, I becomes J, G becomes H, H becomes I, and T becomes U). Under this coding, LIGHT is written as M…

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Introduction / Context:This question uses a very common type of substitution cipher in which each letter is shifted forward by one position in the alphabet. The example given, LIGHT to MJHIU, demonstrates how this shift works on a five letter word. To solve the problem, we apply the exact same shift of one position forward to every letter in the word NORMAL and then match the resulting sequence with one of the options. Given Data / Assumptions: • The code uses the rule: each letter moves one step forward in the alphabet. • LIGHT is coded as MJHIU. • Target word: NORMAL. • Alphabet order: A, B, C, …, Z, with wraparound if needed. Concept / Approach:We verify the rule using the given example. For each letter in LIGHT, we check that the code letter is indeed the next one in the alphabet. Once confirmed, we apply the same +1 shift to every letter in NORMAL. The resulting letters in sequence form the required six letter code. This is an example of a Caesar shift cipher with a shift of one. Step-by-Step Solution: Step 1: Verify the pattern for LIGHT. L becomes M, I becomes J, G becomes H, H becomes I, T becomes U. Step 2: All letters in LIGHT have been shifted by one position forward, so the coding rule is confirmed. Step 3: Write the letters of NORMAL: N, O, R, M, A, L. Step 4: Shift each letter by one position: N becomes O. Step 5: O becomes P. Step 6: R becomes S. Step 7: M becomes N. Step 8: A becomes B. Step 9: L becomes M. Step 10: Combining the shifted letters in order gives O P S N B M. Step 11: Therefore the code for NORMAL is OPSNBM. Verification / Alternative check:Compare the derived code with the answer choices and see that only OPSNBM exactly matches the one step forward shift for every letter in NORMAL. None of the other options is formed by consistently shifting each letter by one position, so the code is uniquely determined. Why Other Options Are Wrong: Option ORNMAL seems to play with the letters of NORMAL itself without using a consistent shift. Option ORSBNM mixes letters but does not correspond to a uniform one step shift of the original letters. Option MNROLA looks like a rearrangement of some original letters rather than a shifted version. Option OPTSBM changes some letters in the wrong direction and breaks the consistent +1 shift pattern. Common Pitfalls:One frequent mistake is to shift only some letters and ignore others, especially when similar letters appear. Another is to shift in the wrong direction, for example moving backward instead of forward. To avoid such mistakes, it is helpful to write the alphabet in sequence and mark the shifts letter by letter. Final Answer:Applying the one step forward shift to every letter, the word NORMAL is coded as OPSNBM.

Question 16

In a certain code language, the symbol plus represents division, minus represents multiplication, the cross symbol represents subtraction and the division sign represents addition. What is the numerical value of the coded expression 16 ÷ 84 + 2 x 4 …

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Introduction / Context:This coding and decoding question tests how well you can reinterpret arithmetic expressions when the usual operators are given new meanings. Instead of performing the operations that the symbols normally represent, you must carefully replace each symbol with its given meaning and then evaluate the expression using standard arithmetic rules and the conventional order of operations. Given Data / Assumptions: The symbol plus (+) stands for division. The symbol minus (−) stands for multiplication. The symbol cross (x) stands for subtraction. The division sign (÷) stands for addition. The expression to be decoded is 16 ÷ 84 + 2 x 4. After decoding, operations follow the normal precedence: division and multiplication before addition and subtraction. Concept / Approach:The key idea is to replace each coded symbol with its real meaning, convert the entire expression into a standard arithmetic form and then evaluate it correctly. Many students lose marks in this type of question either by directly calculating with the visible symbols or by ignoring the correct order of operations, so a careful, stepwise approach is essential. Step-by-Step Solution:Step 1: Write the coded expression: 16 ÷ 84 + 2 x 4.Step 2: Replace ÷ with its real meaning, which is addition. So 16 ÷ 84 becomes 16 + 84.Step 3: Replace + with its real meaning, which is division. So the part 84 + 2 becomes 84 ÷ 2.Step 4: Replace x with its real meaning, which is subtraction. So 2 x 4 becomes 2 − 4.Step 5: The fully decoded expression is 16 + 84 ÷ 2 − 4.Step 6: Apply the order of operations. First calculate 84 ÷ 2 = 42.Step 7: Substitute back to get 16 + 42 − 4.Step 8: Now perform left to right addition and subtraction: 16 + 42 = 58, then 58 − 4 = 54.Step 9: Therefore, the value of the coded expression is 54. Verification / Alternative check:You can quickly verify the answer by redoing the decoding in one pass. Replace each operator in 16 ÷ 84 + 2 x 4 with its real meaning to directly get 16 + 84 ÷ 2 − 4. Evaluating this again by first doing 84 ÷ 2 = 42 and then 16 + 42 − 4 gives 54. The repeated calculation confirms that there is no mistake in decoding the operators or in the arithmetic steps. Why Other Options Are Wrong:The option 44 could arise if someone miscalculates 84 ÷ 2 as 32 or subtracts incorrectly at the end. The option 48 might appear if the student forgets to subtract 4 or decodes one of the symbols wrongly. The option 58 is what you obtain if you decode correctly but forget the final subtraction. The option 60 could come from incorrectly performing addition before division or from some other incorrect intermediate step. None of these match the carefully evaluated result of 54. Common Pitfalls:A very common mistake is to treat the symbols as if they had their usual meanings instead of the coded meanings. Another frequent error is ignoring the order of operations and calculating from left to right without handling division before addition and subtraction. Calculation slips when dividing 84 by 2 or subtracting 4 at the end also lead to wrong answers. Carefully decoding each operator and then strictly following the arithmetic precedence avoids these traps. Final Answer:The correctly decoded and evaluated value of the expression is 54.

Question 17

In a particular numerical code, the expression 4 x 9 is equal to 25 and 7 x 4 is equal to 53. Using the same hidden rule or pattern, what should be the coded value of 9 x 4?

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Introduction / Context:This verbal reasoning question belongs to the coding pattern type, where numbers in an expression do not give the usual product but are transformed according to a hidden rule. The task is to discover that rule from the given examples and then apply it correctly to a new pair of numbers to get the required coded result. Given Data / Assumptions: According to the code, 4 x 9 is written as 25. According to the same code, 7 x 4 is written as 53. We must find the coded value of 9 x 4. The symbol x in this context is part of the coding notation and does not necessarily mean ordinary multiplication. The rule must be consistent for all the given examples. Concept / Approach:To solve such pattern questions, we check simple operations like sums, differences, squares and combinations of these applied to the numbers on the left hand side. By comparing 4 and 9 leading to 25 and 7 and 4 leading to 53, we attempt to find a common rule that fits both. Once a rule is identified, we generalize it and then apply it to the new case 9 x 4. Step-by-Step Solution:Step 1: For 4 x 9, try the expression 4^2 + 9. Calculate 4^2 = 16, then 16 + 9 = 25. This matches the coded result.Step 2: For 7 x 4, test the same rule. Compute 7^2 = 49, then 49 + 4 = 53, which matches the second coded result.Step 3: Since both examples fit the rule value = first number squared plus second number, this pattern is most likely correct.Step 4: Apply the rule to 9 x 4. First compute 9^2 = 81.Step 5: Now add the second number: 81 + 4 = 85.Step 6: Therefore, in this code, 9 x 4 should be written as 85. Verification / Alternative check:To verify, you can test whether any simpler alternative rule, such as adding or multiplying the digits or reversing the numbers, could explain both given examples. None of those simple attempts produce 25 from 4 and 9 and 53 from 7 and 4 simultaneously. The rule first number squared plus second number remains the only consistent pattern, increasing confidence that 85 is the correct coded value for 9 x 4. Why Other Options Are Wrong:The option 81 is simply 9^2 and ignores the addition of the second number. The option 83 would correspond to adding 2 instead of 4, which does not match the established pattern. The option 88 does not fit any natural rule derived from the earlier equations. The option 89 similarly lacks justification from the given data. Only 85 follows the same transformation that converts 4 x 9 to 25 and 7 x 4 to 53. Common Pitfalls:Students may wrongly assume that x stands for multiplication and immediately compute 4 x 9 = 36 or 7 x 4 = 28 and then try to force a connection. Others may focus on the sum of digits or other unrelated patterns. Another common error is to find a rule that fits only one of the examples but not both. Always ensure that the discovered pattern works consistently for all given cases. Final Answer:Using the same rule that maps 4 x 9 to 25 and 7 x 4 to 53, the value of 9 x 4 is 85.

Question 18

In a letter value code where T has a value of 20 and the word MEDIA has a total value of 32, each based on the positions of letters in the English alphabet, what is the corresponding coded value of the word ELICIT?

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Introduction / Context:This coding and decoding question uses a very common verbal reasoning idea where each letter is assigned a numerical value equal to its position in the English alphabet. The coded value of a word is then obtained by summing these individual letter values. You are given the values of T and MEDIA and asked to extend the same logic to find the value of ELICIT. Given Data / Assumptions: The letter T has a code value of 20. The word MEDIA has a total code value of 32. The word for which the code must be found is ELICIT. We assume that A = 1, B = 2, C = 3, up to Z = 26. The total code of a word is the sum of the positional values of its letters. Concept / Approach:Under the alphabet position system, each letter is replaced by its ordinal position number. For example, M is the 13th letter, E is the 5th and so on. We first confirm that the provided examples match this rule, then confidently apply the same technique to the new word. This ensures that the pattern is correct and not a coincidence. Step-by-Step Solution:Step 1: Confirm the code for T. In the alphabet, T is the 20th letter. So T = 20, which matches the given data.Step 2: Confirm the code for MEDIA. Compute M = 13, E = 5, D = 4, I = 9 and A = 1.Step 3: Add these values: 13 + 5 + 4 + 9 + 1 = 32. This matches the given code for MEDIA, so the rule is verified.Step 4: Now apply the same idea to ELICIT. Find the position of each letter: E = 5, L = 12, I = 9, C = 3, I = 9, T = 20.Step 5: Add the values: 5 + 12 + 9 + 3 + 9 + 20.Step 6: First add 5 + 12 = 17, then 17 + 9 = 26, 26 + 3 = 29, 29 + 9 = 38 and finally 38 + 20 = 58.Step 7: Therefore, the coded value of ELICIT under this scheme is 58. Verification / Alternative check:You can quickly cross check one more word, for example T itself or some other small word, to see whether the computed sum matches an expected pattern. Since both T and MEDIA fit perfectly, and the calculation for ELICIT is a direct application of the same principle, the answer 58 is highly reliable. Recalculating the addition step by step also confirms that there is no arithmetic slip. Why Other Options Are Wrong:The option 57 would require the total sum to be one less, which means some letter value would need to be reduced incorrectly. The option 59 and 60 similarly overshoot the correct sum and do not correspond to the real alphabetical positions. The option 61 is even further away from the computed result. Only 58 exactly equals the sum of 5, 12, 9, 3, 9 and 20. Common Pitfalls:Many students misremember the position of certain letters, especially in the second half of the alphabet, or they add the numbers too quickly and introduce small calculation errors. Others may mistakenly try to multiply or average the letter values instead of summing them. Writing down the alphabet with positions or mentally grouping additions in small steps helps to avoid such errors. Final Answer:Using the alphabet position sum code, the correct value corresponding to ELICIT is 58.

Question 19

In a certain coding scheme, the word RATION is written as OXQFLK by shifting each letter in the alphabet. Using the same pattern, how should the word LUMBER be coded?

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Introduction / Context:This problem is a classic letter shifting or Caesar cipher question in the coding and decoding section of verbal reasoning. The aim is to understand how each letter of a given word is replaced by another letter based on a consistent shift in the alphabet, and then apply the same shift to a new word to obtain its coded form. Given Data / Assumptions: RATION is coded as OXQFLK. The code is consistent for all letters of the word. We must find the code for LUMBER using the same rule. The English alphabet positions are used implicitly: A = 1, B = 2, up to Z = 26. Shifts are applied cyclically, meaning that if we move back from A, we wrap around to the end of the alphabet. Concept / Approach:We compare each letter in the original word RATION with the corresponding letter in the coded word OXQFLK to detect a consistent shift. If the difference between positions is the same for all letters, that shift defines the coding rule. Then we apply the same shift to each letter of LUMBER and construct the final coded word from the shifted letters. Step-by-Step Solution:Step 1: Write the letter positions for RATION: R = 18, A = 1, T = 20, I = 9, O = 15, N = 14.Step 2: Write the letter positions for the code OXQFLK: O = 15, X = 24, Q = 17, F = 6, L = 12, K = 11.Step 3: Find the shift for each pair. For R to O, 18 to 15 is a shift of minus 3. For A to X, 1 to 24 is also equivalent to minus 3 with wrap around. Similarly, T to Q (20 to 17), I to F (9 to 6), O to L (15 to 12) and N to K (14 to 11) are all shifts of minus 3.Step 4: Therefore, the coding rule is: each letter is replaced by the letter that is 3 positions earlier in the alphabet.Step 5: Apply this rule to LUMBER. L = 12 shifts to I = 9, U = 21 shifts to R = 18, M = 13 shifts to J = 10, B = 2 shifts to Y = 25, E = 5 shifts to B = 2 and R = 18 shifts to O = 15.Step 6: Combining these shifted letters gives the code IRJYBO for LUMBER. Verification / Alternative check:You can quickly verify by reversing the process. Take the coded word IRJYBO and shift each letter forward by 3 positions: I to L, R to U, J to M, Y to B (with wrap around), B to E and O to R. This reproduces LUMBER and confirms that the rule has been applied correctly, leaving no doubt that IRJYBO is the correct code. Why Other Options Are Wrong:The options KTLADQ, ITJABQ, OXPEHU and KRJXBO do not consistently reflect a shift of minus 3 from the letters of LUMBER. Some of these options may have one or two letters that accidentally match a shifted letter, but not all of them follow the same rule for every position. Since the coding rule is uniform across the word, any option that breaks the consistent shift pattern must be rejected. Common Pitfalls:Many test takers incorrectly assume a forward shift when the example actually uses a backward shift, or they forget to wrap around correctly when moving from letters near the beginning or end of the alphabet. Others only test the rule on the first one or two letters and rush to a conclusion. Always check the shift across all letters of the example and then apply it systematically to the new word. Final Answer:Using the shift of three letters backward in the alphabet, the correct code for LUMBER is IRJYBO.

Question 20

In a coded arithmetic pattern, the expressions 37 * 14 = 17, 69 * 33 = 34 and 91 * 125 = 72 follow the same rule. Using this rule, what should be the value of 28 * 56 in the same code?

Accepted Answer

Introduction / Context:This question presents a set of unusual equations where the symbol star (*) does not stand for ordinary multiplication. Instead, each pair of numbers is transformed into a different result according to a hidden numerical pattern. The challenge is to identify this pattern from the given examples and then apply it to a new pair of numbers. Given Data / Assumptions: 37 * 14 results in 17. 69 * 33 results in 34. 91 * 125 results in 72. The same rule must be used to find the value of 28 * 56. The symbol * indicates a special operation defined by the pattern, not standard multiplication. Concept / Approach:When working with coded equations, we look for simple relationships involving addition, subtraction, averages or ratios. Here, each equation involves two numbers on the left and a smaller number on the right. A natural idea is to test whether the result might be related to the sum of the two numbers, possibly scaled or divided by a constant factor. We check the first example, and if it works, we verify against the remaining examples to establish the rule. Step-by-Step Solution:Step 1: For 37 * 14, compute the sum of the two numbers: 37 + 14 = 51.Step 2: Compare 51 with the coded result 17. Noting that 51 ÷ 3 = 17 suggests that the rule might be to divide the sum by 3.Step 3: Test this rule with the second equation. For 69 * 33, sum the numbers: 69 + 33 = 102. Now 102 ÷ 3 = 34, which matches the coded result.Step 4: Test the rule with the third equation. For 91 * 125, sum the numbers: 91 + 125 = 216. Then 216 ÷ 3 = 72, which again matches the coded result.Step 5: Since all three examples fit the rule result = (first number + second number) ÷ 3, we accept this as the governing pattern.Step 6: Apply the rule to 28 * 56. Sum the numbers: 28 + 56 = 84.Step 7: Now divide by 3: 84 ÷ 3 = 28.Step 8: Therefore, 28 * 56 should be coded as 28. Verification / Alternative check:To ensure there is no alternative rule, you can test whether any simple product or difference based pattern could match all three given equations. None of these alternatives give 17 from 37 and 14, and also give 34 from 69 and 33, and 72 from 91 and 125 simultaneously. The sum divided by 3 rule works consistently in every case, and recomputing 84 ÷ 3 once more confirms that the answer 28 is correct. Why Other Options Are Wrong:The option 26 might come from subtracting two or misapplying division. The option 34 or 42 could arise if someone mistakenly uses one of the intermediate sums from the examples instead of applying the rule properly. The option 30 might be guessed by rounding or by using an incorrect divisor. Since only 28 matches the pattern confirmed by all three given equations, the other values must be rejected. Common Pitfalls:Students may try to invent very complicated patterns involving multiplication, subtraction or digit manipulation and overlook a simple sum and division rule. Another common error is to identify a rule that fits only the first equation but not the others. Always verify the pattern against every given example before applying it to the target expression to avoid unreliable shortcuts. Final Answer:According to the established pattern, the coded value of 28 * 56 is 28.

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