Question 1

If 6x4 = 12, 4x12 = 24 and 12x6 = 36 under a special operation x, then what is the value of 6x9 under that same rule?

Accepted Answer

Introduction / Context: Here the symbol x does not stand for usual multiplication. We must infer the special operation from three examples and then compute 6x9 using the same rule. Notice that the outputs 12, 24, and 36 relate closely to the ordinary product of the two numbers. Given Data / Assumptions: 6x4 = 12. 4x12 = 24. 12x6 = 36. We must find 6x9. Concept / Approach: Compare each result with the regular product of the two numbers. The regular products are 6×4 = 24, 4×12 = 48, and 12×6 = 72. Each of these is exactly twice the coded result (12, 24, 36), suggesting that the operation x is defined as half the usual product. Step-by-Step Solution: Step 1: Test the rule a x b = (a × b) / 2. For 6x4: (6 × 4) / 2 = 24 / 2 = 12, which matches. For 4x12: (4 × 12) / 2 = 48 / 2 = 24, which matches. For 12x6: (12 × 6) / 2 = 72 / 2 = 36, which matches. Step 2: The pattern is confirmed: x means \"half the product\". Step 3: Apply this rule to 6x9. Compute the normal product: 6 × 9 = 54. Now take half: 54 / 2 = 27. Verification / Alternative check: No other simple function of 6 and 4 (such as sum, difference, or average) will produce all given examples correctly. The half-product interpretation works cleanly for all three, so it is the intended rule. Why Other Options Are Wrong: Values like 35, 24, and 31 arise from incorrect operations, such as adding extra constants or misapplying multiplication. Only 27 equals half of 54, which is 6 × 9. Common Pitfalls: Many learners initially assume x is normal multiplication and are confused when 6×4 ≠ 12. The key is always to compare the given result with normal arithmetic to discover the hidden operation. Final Answer: Under this operation, 6x9 evaluates to 27.

Question 2

If 23@5 = 56, 6@7 = 26 and 5@2 = 14 under a certain rule, then what is the value of 7@5 under the same rule?

Accepted Answer

Introduction / Context: Another custom operator @ is defined on two numbers, but not as ordinary addition or multiplication. We are given three examples and must use them to deduce the rule and then apply it to 7@5. Given Data / Assumptions: 23@5 = 56. 6@7 = 26. 5@2 = 14. We must compute 7@5. Concept / Approach: We look for a simple arithmetic relationship between the two numbers and the result. Notice that 6@7 = 26 and 5@2 = 14 are both exactly twice the sum of the two numbers. We can check if the same pattern applies to 23@5 as well. Step-by-Step Solution: Step 1: Check 6@7 = 26. 6 + 7 = 13. Twice this sum: 2 × 13 = 26, which matches. Step 2: Check 5@2 = 14. 5 + 2 = 7. Twice this sum: 2 × 7 = 14, which matches. Step 3: Check 23@5 = 56. 23 + 5 = 28. Twice this sum: 2 × 28 = 56, which matches. Step 4: Therefore, the rule is a @ b = 2 × (a + b). Step 5: Apply this rule to 7@5. 7 + 5 = 12. 2 × 12 = 24. Verification / Alternative check: All three given examples are consistent with this simple formula. No other straightforward operation, such as product or difference, fits everything so neatly. Hence we are confident about the rule. Why Other Options Are Wrong: Values like 26, 19, and 52 require different formulas that would contradict at least one of the given examples. For instance, 26 is correct for 6@7 but not for 7@5 when the rule is fixed. Common Pitfalls: Some learners are tempted to mix different rules for different examples or treat the first case (23@5) separately. In all such coding puzzles, a single consistent rule must work for every case. Final Answer: Using the same rule, the value of 7@5 is 24.

Question 3

In a coded arithmetic expression, "S" denotes "multiplied by", "P" denotes "subtracted from", "R" denotes "added to" and "Q" denotes "divided by". Using these operator codes, what is the numerical value of 14641 Q 121 P 100 S 2 R 100 ?

Accepted Answer

Introduction / Context: This coding and decoding problem tests understanding of how familiar arithmetic operators are replaced by symbolic letters and how to correctly substitute and evaluate a compound expression. Many competitive exams use such questions to check whether candidates follow operator meaning and precedence rules carefully rather than performing operations mechanically. Given Data / Assumptions: "S" denotes multiplication. "P" denotes subtraction. "R" denotes addition. "Q" denotes division. Expression to evaluate: 14641 Q 121 P 100 S 2 R 100. Standard arithmetic precedence applies: division and multiplication before addition and subtraction, and evaluation is from left to right within the same precedence level. Concept / Approach: The key idea is to translate each coded symbol back to the usual arithmetic operator and then compute the value step by step. Once the operators are decoded, we must apply the normal BODMAS or PEMDAS rule, giving priority to division and multiplication over addition and subtraction. Although the text uses the phrase "subtracted from" for P, in this common exam pattern P simply acts as the minus operator between left and right operands after decoding. Step-by-Step Solution: Step 1: Replace each coded symbol with its corresponding arithmetic operator. 14641 Q 121 P 100 S 2 R 100 becomes 14641 ÷ 121 - 100 × 2 + 100. Step 2: Apply operator precedence and first handle the division 14641 ÷ 121. Step 3: 14641 is 121 squared, so 14641 ÷ 121 = 121. Step 4: Now evaluate the multiplication 100 × 2 = 200. Step 5: After these operations, the expression becomes 121 - 200 + 100. Step 6: Now perform subtraction and addition from left to right: first compute 121 - 200 = -79. Step 7: Add 100 to the result: -79 + 100 = 21. Step 8: Therefore, the numerical value represented by the coded expression is 21. Verification / Alternative check: We can quickly verify by recomputing in a compact way. Once decoded, the expression is 14641 ÷ 121 - 100 × 2 + 100. Since 14641 ÷ 121 = 121 and 100 × 2 = 200, we obtain 121 - 200 + 100. Grouping the last two terms as -200 + 100 = -100 gives 121 - 100 = 21. This independent recomputation confirms that 21 is correct, so there is no arithmetic mistake in the stepwise solution. Why Other Options Are Wrong: Option 48 would arise if division and multiplication precedence were ignored or misapplied. Option 61 and option 31 typically come from doing the operations strictly left to right without respecting that multiplication and division should be performed before addition and subtraction. Another incorrect value can appear if a candidate misinterprets P and changes operand order, but with the standard exam convention used here, such an interpretation is not intended. Hence these options are distractors based on common calculation errors. Common Pitfalls: A frequent mistake is to replace the coded symbols correctly but then apply operations strictly from left to right, which violates operator precedence rules. Another common trap is overthinking the phrase "subtracted from" and reversing the order of subtraction, even though such questions usually expect candidates to treat P as the normal minus sign once decoded. Errors in observing that 14641 equals 121 squared can also introduce division mistakes. Working carefully and simplifying each part systematically prevents these issues and leads to the correct answer. Final Answer: After decoding each symbol and evaluating using correct arithmetic precedence, the coded expression 14641 Q 121 P 100 S 2 R 100 is equal to 21, so the correct option is 21.

Question 4

In a certain language, the word "BROTHER" is written as "CSPUIFS". Using the same letter-shift code, how will the word "SISTER" be written in that language?

Accepted Answer

Introduction / Context: This question belongs to the coding and decoding category where each letter of a word is transformed using a fixed rule. The candidate must observe the pattern in the given example and apply it consistently to a new word. This is a very common type in verbal reasoning sections of competitive exams. Given Data / Assumptions: "BROTHER" is coded as "CSPUIFS". The transformation is letter by letter and deterministic. We need to find the coded form of "SISTER" using the same rule. All letters are in English uppercase alphabet, so standard alphabetical positions from A to Z apply. Concept / Approach: To decode the rule, we compare each letter in the original word "BROTHER" with its corresponding letter in the coded word "CSPUIFS". By checking alphabetical positions, we notice that every letter has been shifted forward by one place in the alphabet. For example, B goes to C, R goes to S and so on. Once the consistent pattern is recognized, we apply the same shift of plus one to each letter in the new word "SISTER". Step-by-Step Solution: Step 1: Write "BROTHER" and "CSPUIFS" in parallel and examine each pair of letters. Step 2: B becomes C, R becomes S, O becomes P, T becomes U, H becomes I, E becomes F and R becomes S. Step 3: In every case, the coded letter is one step ahead in the alphabet: B to C, R to S, O to P, T to U, H to I, E to F and R to S. Step 4: Conclude that the rule is "shift each letter one position forward in the alphabet." Step 5: Apply this rule to "SISTER". Step 6: S becomes T, I becomes J, S becomes T, T becomes U, E becomes F and R becomes S. Step 7: Therefore the coded form of "SISTER" is TJTUFS. Verification / Alternative check: We can check quickly by converting letters to numerical positions. S is 19, so S plus one is 20 which corresponds to T. I is 9, so I plus one is 10 which corresponds to J. Repeating this for all letters reproduces TJTUFS without inconsistency. Since the mapping is uniform and reversible, the code is consistent and reliable. Why Other Options Are Wrong: TJTFUS and TJTSFU differ from the correct form by swapping or misplacing letters, which would violate the uniform shift rule. SFUTJT mixes the letters in a more complex way and cannot be derived by adding one to each original letter. These options exist to trap candidates who guess or misread the order of letters instead of applying the precise pattern from the example. Common Pitfalls: The most common mistakes include shifting letters in the wrong direction, such as subtracting one instead of adding one, or accidentally altering the order of letters while coding. Another error is to assume a more complicated pattern than necessary. Carefully comparing each original letter with its coded counterpart usually reveals a simple shift rule that should then be applied consistently to the target word. Final Answer: Using the same plus one alphabetical shift that turns "BROTHER" into "CSPUIFS", the word "SISTER" is coded as TJTUFS.

Question 5

If the symbols A, B, C and D are code replacements for arithmetic operations such that A means "+", B means "−", C means "×" and D means "÷", then which of the following coded equations is mathematically true after decoding the symbols?

Accepted Answer

Introduction / Context: This problem tests the ability to decode symbolic representations of arithmetic operations and then check which full equation is valid. It combines knowledge of basic arithmetic with logical checking of each option and is a staple pattern in verbal reasoning and aptitude tests. Given Data / Assumptions: A represents addition, that is A means plus. B represents subtraction, that is B means minus. C represents multiplication, that is C means times. D represents division, that is D means divided by. We must decode each option and test whether the resulting numerical equation is correct. Standard operator precedence for multiplication and division over addition and subtraction applies. Concept / Approach: The method is straightforward. For each option, replace the coded letters A, B, C and D with their actual arithmetic operators. Then, evaluate the left side using proper precedence rules and see whether it equals the right side of the equation. Only one of the given options will satisfy the equality, and that will be the correct answer. Step-by-Step Solution: Step 1: Decode option A: 12 D 6 A 4 C 3 = 12 becomes 12 ÷ 6 + 4 × 3 = 12. Step 2: Evaluate option A: 12 ÷ 6 = 2 and 4 × 3 = 12, so left side is 2 + 12 = 14, which is not equal to 12. So option A is false. Step 3: Decode option B: 48 D 3 C 2 = 31 becomes 48 ÷ 3 × 2 = 31. Step 4: Evaluate option B: 48 ÷ 3 = 16 and 16 × 2 = 32, not 31. So option B is false. Step 5: Decode option C: 14 C 2 D 7 A 3 = 6 becomes 14 × 2 ÷ 7 + 3 = 6. Step 6: Evaluate option C: 14 × 2 = 28, 28 ÷ 7 = 4 and 4 + 3 = 7, not 6. So option C is also false. Step 7: Decode option D: 24 C 3 B 14 = 58 becomes 24 × 3 − 14 = 58. Step 8: Evaluate option D: 24 × 3 = 72 and 72 − 14 = 58, which matches the right side. So option D is the only correct equation. Verification / Alternative check: To quickly verify, we note that in option D the multiplication yields 72 and the subsequent subtraction by 14 gives 58. None of the other options can be adjusted or rearranged to match their claimed results without breaking operator precedence or altering the expression. Therefore, option D alone satisfies the equation exactly as written and decoded. Why Other Options Are Wrong: Option A gives 14 instead of 12, option B produces 32 instead of 31 and option C yields 7 instead of 6. These mismatches result from straightforward arithmetic after decoding and cannot be corrected without changing the operators or order of operations, which is not allowed. Hence they are included purely as distractors for candidates who miscalculate under time pressure. Common Pitfalls: Candidates sometimes ignore operator precedence and compute from left to right, which can accidentally make a wrong equation appear correct. Another frequent mistake is misreading which letter stands for which operation. Carefully rewriting each expression with standard symbols before calculating helps avoid these errors. Double checking the multiplication and division steps is especially important since small mistakes there propagate to the final result. Final Answer: After decoding the operations and evaluating all options, the only true equation is 24 C 3 B 14 = 58.

Question 6

If the word "MEAT" is coded as the number 135120 by writing the alphabet positions of its letters in sequence, then what will be the corresponding numerical code for the word "ZEBRA"?

Accepted Answer

Introduction / Context: This coding and decoding question converts words into long numbers using the positions of letters in the English alphabet. Recognizing the exact pattern used for the example word is essential before applying it to a new word. Such problems check familiarity with alphabetical order and attention to detail when concatenating digits. Given Data / Assumptions: "MEAT" is coded as 135120. We must determine the code for "ZEBRA". Letters are mapped to their positions in the English alphabet, where A is 1, B is 2, up to Z which is 26. There is no indication of additional arithmetic operations, so the code likely forms by direct concatenation of positional values. Concept / Approach: The approach is to translate each letter of the example word "MEAT" into its alphabetical position and see how these numbers combine to produce the given code 135120. If the concatenation matches, we can apply the same mapping to the word "ZEBRA". For two digit positions such as 13 or 20 the digits are simply written next to each other, not added or multiplied. The digits for all letters are appended in order to form a single continuous integer code. Step-by-Step Solution: Step 1: Determine the positions of the letters in "MEAT". Step 2: M is the 13th letter, E is the 5th letter, A is the 1st letter and T is the 20th letter. Step 3: Write these numeric positions in sequence: 13, 5, 1 and 20. Step 4: Concatenate them as digits: 13 5 1 20 becomes 135120, which matches the given code. This confirms the pattern. Step 5: Now apply the same idea to "ZEBRA". Step 6: Z is 26, E is 5, B is 2, R is 18 and A is 1 in the alphabet. Step 7: Concatenate these as 26 5 2 18 1, which gives 2652181 when written as one continuous number. Step 8: Therefore, the correct code for "ZEBRA" is 2652181. Verification / Alternative check: As a quick check, we can ensure that none of the other options correspond to a reasonable misinterpretation such as reversing letters or using different positions. Changing any of the letter positions would break the match with the alphabet order, and inserting extra digits would destroy the simple one to one mapping. Since the pattern is very clear from MEAT to 135120, any deviation from 2652181 would be unjustified. Why Other Options Are Wrong: Options 2652191, 2662181 and 2662191 alter one or more digits relative to the correct mapping. These changes would require treating some letter positions incorrectly, for example using 19 instead of 18 for R or incorrectly assigning 26 to multiple letters. None of these errors can be supported by the original example, so those answers are invalid distractions intended to catch miscalculations or memory slips about alphabet positions. Common Pitfalls: Candidates sometimes make mistakes by adding the numeric positions instead of concatenating them, or by misremembering that Z is 26 and not 25. Another error is to compress double digit positions into a single digit, which changes the number pattern entirely. Keeping track of each letter position carefully and writing all digits in order without dropping or merging them is the surest way to avoid mistakes. Final Answer: Using the same alphabetical position concatenation that maps "MEAT" to 135120, the correct numerical code for "ZEBRA" is 2652181.

Question 7

In a code language, the word "AILMENT" is written as 1923540 by using the last digit of each letter's alphabetical position. Based on the same pattern, what is the numerical code for the word "DISEASE"?

Accepted Answer

Introduction / Context: This coding question uses alphabet positions but keeps only the unit digit of each position. The task is to infer the digit pattern from the given example "AILMENT" and then apply that pattern to another word, "DISEASE". Such questions check attention to small numerical details and pattern observation rather than calculations alone. Given Data / Assumptions: AILMENT is coded as 1923540. We must find how DISEASE is coded. The English alphabet positions are used: A is 1, B is 2, up to Z which is 26. The example suggests that only the last digit of each position is used in the code. Concept / Approach: First decode the pattern from "AILMENT". Determine the position of each letter, then observe how the code 1923540 is formed. If the digit for each letter matches the unit digit of its alphabetical index, we have the rule. Once this is confirmed, we repeat the process for DISEASE. Each letter is translated to its alphabetical position, but only the unit digit of that number is written, and all such digits are concatenated to form the final code. Step-by-Step Solution: Step 1: Write the letters of AILMENT and their positions in the alphabet. Step 2: A is 1, I is 9, L is 12, M is 13, E is 5, N is 14 and T is 20. Step 3: Take the last digit of each position: 1, 9, 2, 3, 5, 4 and 0. Step 4: Concatenate these digits to get 1923540, which matches the given code and confirms the rule. Step 5: Now determine the positions for DISEASE. Step 6: D is 4, I is 9, S is 19, E is 5, A is 1, S is 19 again and E is 5 again. Step 7: Take the last digit of each: 4, 9, 9, 5, 1, 9 and 5. Step 8: Concatenate the digits: 4 9 9 5 1 9 5 gives 4995195. Verification / Alternative check: To double check, verify a couple of letters carefully. S is the 19th letter, and its last digit is 9, which appears every time S occurs in DISEASE. E is 5, and the digit 5 correctly appears wherever E appears in the word. This confirms that the pattern is applied consistently and there is no misplacement of digits. Why Other Options Are Wrong: Options 4985195, 4905195 and 4995196 modify one of the digits, implying a wrong last digit for one of the letters. For example, using 8 instead of 9 for S or 6 instead of 5 for E would contradict the pattern established by AILMENT. These variations are specifically designed to capture errors in computing alphabet positions or in extracting the final digit. Common Pitfalls: A common mistake is to use the full alphabet position rather than just the last digit, which would give a longer code and not match the given example. Others may miscount letter positions or reverse digits accidentally during concatenation. Systematically writing the alphabet positions and then extracting the unit digit for each letter is the most reliable way to avoid such mistakes. Final Answer: Following the same last digit rule that converts "AILMENT" to 1923540, the correct code for "DISEASE" is 4995195.

Question 8

In a certain code language, the word "KINDLE" is written as "ELDNIK" by reversing the order of its letters. Using the same coding rule, how is the word "FASHION" written in that language?

Accepted Answer

Introduction / Context: This coding and decoding question uses a very simple but important transformation: reversing the sequence of letters in a word. The example "KINDLE" to "ELDNIK" shows exactly how the pattern works. Candidates must recognize that no shifting or substitution is involved, only reversing the order, and then apply this idea to "FASHION". Given Data / Assumptions: KINDLE is written as ELDNIK in the code language. We are asked to find the coded form of FASHION. No letter replacement or arithmetic on letter positions is indicated, so the code is likely a positional reversal. Concept / Approach: The straightforward approach is to check whether "ELDNIK" is simply "KINDLE" written backwards. K I N D L E reversed is E L D N I K, which matches the given coded word. Once confirmed, we can apply this same reversal to FASHION. That means writing its letters from last to first, without changing the letters themselves. Step-by-Step Solution: Step 1: Write KINDLE and then write it in reverse order. Step 2: KINDLE has letters K, I, N, D, L and E. Reversing gives E, L, D, N, I and K, which spells ELDNIK. Step 3: This exactly matches the given code, so we confirm that the rule is "reverse the word". Step 4: Now apply the same rule to FASHION. Step 5: FASHION has letters F, A, S, H, I, O and N in order. Step 6: Reverse the order: N, O, I, H, S, A and F. Step 7: This reversed sequence spells NOIHSAF. Step 8: Therefore, the correct code for FASHION is NOIHSAF. Verification / Alternative check: To verify quickly, we can mentally reverse NOIHSAF and confirm that we obtain FASHION again. Reversing N O I H S A F gives F A S H I O N. This confirms that the transformation is a pure reversal and that the answer is consistent with the rule demonstrated by KINDLE and ELDNIK. Why Other Options Are Wrong: The other options, such as NOISHAF or NIOHSAF, contain the same letters but with incorrect internal ordering. They may come from attempts to reverse parts of the word or from letter swaps, but they do not match a complete reversal of the original sequence. Because the example clearly shows a full reversal, any option that does not preserve that exact pattern cannot be correct. Common Pitfalls: A common error is to reverse only a substring of the word or to accidentally change the order of two letters when writing quickly. Some candidates also try to combine reversal with letter shifting, even though the example does not require it. Focusing on the precise transformation shown in the example and carefully writing the reversed sequence helps avoid such mistakes. Final Answer: Since the rule is to reverse the letters of the word, the word "FASHION" is coded as NOIHSAF in the given language.

Question 9

The equation 12 - 6 × 5 + 20 ÷ 4 = 31 is incorrect. If the arithmetic signs in this expression are coded so that two of them are interchanged, which pair of signs must be swapped to make the equation mathematically correct?

Accepted Answer

Introduction / Context: This problem tests understanding of operator precedence and logical adjustment of arithmetic signs. The equation is currently false, and the task is to identify which two operators must be interchanged so that the left hand side evaluates exactly to 31. These kinds of puzzles are common in aptitude tests to examine both calculation skills and logical reasoning about symbol manipulation. Given Data / Assumptions: Original expression: 12 - 6 × 5 + 20 ÷ 4. Right side of the equation is 31. We may interchange exactly two signs from among plus, minus, multiplication and division. Arithmetic precedence (multiplication and division before addition and subtraction) must still be followed after any interchange. Concept / Approach: Instead of guessing randomly, test each suggested pair of signs systematically. For each option, substitute the new signs into the expression, then evaluate using correct precedence to see if the result equals 31. Since the numbers remain the same, only the operations change. The correct pair will produce an exact match with the right side of the equation. Step-by-Step Solution: Step 1: Evaluate the original expression: 12 - 6 × 5 + 20 ÷ 4. Step 2: Compute 6 × 5 = 30 and 20 ÷ 4 = 5. The expression becomes 12 - 30 + 5 = -13, which is not 31. Step 3: Option A suggests interchanging + and ÷. This turns the expression into 12 - 6 × 5 ÷ 20 + 4. Step 4: Evaluate option A: 6 × 5 = 30, 30 ÷ 20 = 1.5, so 12 - 1.5 + 4 = 14.5, not 31. So option A is incorrect. Step 5: Option B suggests interchanging + and ×. Now × becomes + between 6 and 5, and + becomes × between 5 and 20. The expression becomes 12 - 6 + 5 × 20 ÷ 4. Step 6: Evaluate option B: 5 × 20 = 100 and 100 ÷ 4 = 25. The expression simplifies to 12 - 6 + 25 = 6 + 25 = 31. Step 7: Since this equals 31, option B works. We do not need to test the remaining options for equality, though they can be checked to confirm they fail. Verification / Alternative check: To verify, we may also check quickly that options C and D do not produce 31. Changing - and + only rearranges addition and subtraction signs and cannot correct the large negative result fully. Swapping ÷ and × similarly yields different products and quotients but does not hit 31 exactly. Therefore, only swapping the plus and multiplication symbols leads to the accurate evaluation, confirming that option B is unique and correct. Why Other Options Are Wrong: When testing option A, the result is 14.5. Option C yields a different integer but not 31, and option D also fails to reach 31 after applying proper precedence. In each of these cases, numerical evaluation directly exposes the discrepancy from the target value, so they must be rejected. Common Pitfalls: Some candidates forget to apply precedence after swapping operators and instead compute strictly from left to right. Others might misinterpret "interchange" as changing only one occurrence of a sign instead of both. It is important to alter every instance of the two specified operators in the expression and then recompute using the usual arithmetic rules. Final Answer: The equation becomes correct when the plus and multiplication signs are interchanged, so the required pair of signs is + and ×.

Question 10

Consider the pattern in the sequence of eight-letter terms: XYXYXYxy, XYXYXyxY, XYXYxyXY, XYXyxYXY, XYxyXYXY. Following the same pattern of shifting lowercase letters, which of the given options comes next in the series?

Accepted Answer

Introduction / Context: This question tests pattern recognition with respect to capitalization and position of letters in a repeating sequence. The terms are built from the letters X and Y, with some positions uppercase and some positions lowercase. The candidate must observe how the lowercase pair "xy" or "yx" moves and alternates across the series. Given Data / Assumptions: Given sequence: XYXYXYxy, XYXYXyxY, XYXYxyXY, XYXyxYXY, XYxyXYXY. Each term has eight positions filled with X or Y, either uppercase or lowercase. Exactly two consecutive letters are lowercase in each term. The lowercase pair alternates between the orders "xy" and "yx". The lowercase pair also shifts one position left at each step in the sequence. Concept / Approach: We observe both the position and order of the lowercase letters in each term. First, we note where the lowercase block appears in each term and whether it is "xy" or "yx". Then, we see that the pair moves one place to the left with each new term while alternating its internal order. After confirming this movement for all given terms, we extend the pattern one more step to identify the correct next term. Step-by-Step Solution: Step 1: Examine the first term: XYXYXYxy. The lowercase block "xy" is at positions 7 and 8. Step 2: Second term: XYXYXyxY. The lowercase block is now "yx" at positions 6 and 7. Step 3: Third term: XYXYxyXY. The lowercase block "xy" is at positions 5 and 6. Step 4: Fourth term: XYXyxYXY. The lowercase block "yx" has shifted to positions 4 and 5. Step 5: Fifth term: XYxyXYXY. The lowercase block "xy" is further left at positions 3 and 4. Step 6: From these observations, the pattern is clear: the lowercase pair moves one step left each time and alternates between "xy" and "yx". Step 7: The next term should therefore have the lowercase pair "yx" (alternating from "xy") at positions 2 and 3. Step 8: Start from the base uppercase pattern XYXYXYXY and replace positions 2 and 3 with lowercase y and x, giving XyxYXYXY. Verification / Alternative check: We can quickly check all given options. The only option where the lowercase pair is at positions 2 and 3 and in the order "yx" is XyxYXYXY. The other options either repeat earlier terms or place the lowercase letters in incorrect positions, breaking the established trend. Therefore, XyxYXYXY uniquely fits the continuation of the sequence. Why Other Options Are Wrong: Option XYXYXYxy is the first term repeated and does not move the lowercase pair left. Option XYXYXyxY is the second term and again repeats an earlier configuration. Option xyXYXYXY has the lowercase letters at positions 1 and 2 but in the wrong order, and it does not respect the alternating pattern. Hence none of them can be the next logical term after XYxyXYXY. Common Pitfalls: Candidates often focus only on whether the letters are lowercase without tracking their exact positions, or they ignore the alternation between "xy" and "yx". Another frequent error is to choose a term that looks visually similar but actually repeats an earlier step rather than extending the pattern. Counting positions explicitly and writing down which positions are lowercase in each term helps avoid such confusion. Final Answer: The lowercase block moves one place left each time and alternates between "xy" and "yx". Therefore, the next term in the series is XyxYXYXY.

Question 11

A custom operator "@" is defined so that 40 @ 8 = -5, 30 @ 3 = -10 and 20 @ 5 = -4. Using the same rule, what is the value of 60 @ 3 ?

Accepted Answer

Introduction / Context: This is an example of an artificial or custom operator, where "@" represents some mathematical rule between two numbers. The task is not to guess randomly, but to infer the precise numerical relationship from the examples and then apply it to a new pair of numbers. Such questions test pattern recognition and basic arithmetic reasoning. Given Data / Assumptions: 40 @ 8 = -5. 30 @ 3 = -10. 20 @ 5 = -4. We must find the value of 60 @ 3 using the same rule. The operator likely involves a simple combination such as division, multiplication or subtraction between the two numbers. Concept / Approach: To discover the rule, look for a simple calculation that converts the left pair into the result. Notice that in each case, the first number divided by the second gives a small positive integer, and the result shown is the negative of that quotient. Checking this pattern for all given examples helps confirm that the rule is consistent before applying it to the new pair. Step-by-Step Solution: Step 1: Evaluate 40 ÷ 8. This is 5. The given result is -5, which is the negative of the quotient. Step 2: Evaluate 30 ÷ 3. This is 10. The given result is -10, again the negative of the quotient. Step 3: Evaluate 20 ÷ 5. This is 4. The given result is -4, which continues the same pattern. Step 4: Conclude from all three examples that a @ b is defined as negative of a divided by b, or a @ b = - (a ÷ b). Step 5: Now apply this rule to 60 @ 3. Step 6: Compute 60 ÷ 3 = 20. Step 7: Take the negative of this quotient: -20. Step 8: Therefore, 60 @ 3 equals -20. Verification / Alternative check: We can verify by checking that no other simple pattern fits all three examples so neatly. For instance, subtraction 40 - 8 is 32, not related to -5 in a simple way. Similarly, ratios reversed as 8 ÷ 40 or products 40 × 8 do not produce the given outputs through a consistent simple rule. The negative quotient pattern uniquely matches each example exactly, which reinforces our conclusion. Why Other Options Are Wrong: Options 45 and 25 are positive numbers that would arise only if a candidate forgot to take the negative sign or used multiplication instead of division. Option -36 could come from miscomputing 60 ÷ 3 as 18 or from using some incorrect combination. Since the correct quotient is 20 and the rule requires a negative result, only -20 is valid. Common Pitfalls: A typical mistake is to apply a different rule to each example rather than seeking one rule that fits all of them. Another error is confusing the roles of the two numbers, for example dividing the smaller by the larger. Always test any guessed pattern on all given examples. If a proposed rule fails even once, it must be rejected. Final Answer: Using the rule a @ b = negative of a divided by b, the value of 60 @ 3 is -20.

Question 12

In a certain code language, the planet name "VENUS" is written as "TVOFW" by reversing the letters and shifting each one step forward in the alphabet. Using the same coding rule, how is the word "FAMILY" written in that language?

Accepted Answer

Introduction / Context: This coding and decoding problem combines two distinct operations: reversing the order of letters in a word and then applying a one step forward shift to each letter in the alphabet. The example given for "VENUS" helps us derive the exact rule, which is then applied to the new word "FAMILY". Such layered patterns are common in reasoning questions to test attention and multi step thinking. Given Data / Assumptions: VENUS is coded as TVOFW. The encoding involves both reordering and shifting letters. We need the coded form of FAMILY under the same rule. The alphabet positions are used: A is 1, B is 2, up to Z which is 26, and letter shifts wrap forward through the alphabet. Concept / Approach: First, check how VENUS transforms into TVOFW. If we simply shift letters, the mapping looks inconsistent. However, when we reverse VENUS to S U N E V and then shift each letter one place forward in the alphabet, we obtain T V O F W, which matches the code exactly. Therefore, the rule is: reverse the word, then move each letter one step forward in the alphabet. Applying this systematically to FAMILY gives the required coded word. Step-by-Step Solution: Step 1: Reverse the word VENUS to check the pattern. VENUS becomes S U N E V. Step 2: Shift each reversed letter forward by one in the alphabet: S to T, U to V, N to O, E to F and V to W, which yields TVOFW. Step 3: This matches the given coded word, so we confirm the two step rule: reverse then shift forward by one. Step 4: Now reverse the word FAMILY. The letters F, A, M, I, L and Y become Y, L, I, M, A and F. Step 5: Shift each of these reversed letters forward by one alphabet position. Step 6: Y moves to Z, L moves to M, I moves to J, M moves to N, A moves to B and F moves to G. Step 7: The resulting code is Z M J N B G, written as ZMJNBG. Step 8: Therefore FAMILY is coded as ZMJNBG. Verification / Alternative check: We can cross check by taking the final code ZMJNBG, shifting each letter one step back and then reversing the word again. Z goes back to Y, M to L, J to I, N to M, B to A and G to F, giving YLIMAF. Reversing this yields FAMILY, confirming that the encoding rule is reversible and has been applied correctly. Why Other Options Are Wrong: GBNJMZ, EZLQKX and XKHLZQ assume different kinds of rearrangements or shift directions. They may include the right letters but place them in incorrect order or apply shifts inconsistently. None of them can be obtained by first reversing FAMILY and then shifting each letter exactly one step forward, so they do not follow the rule established by VENUS. Common Pitfalls: Some candidates attempt to shift letters first and then reverse, which would produce a different word. Others reverse only part of the word or forget to apply the shift to all letters. Carefully following the order of operations, reverse first and then shift, ensures the correct result. Final Answer: Applying the rule "reverse the word and then shift each letter one step forward in the alphabet" to FAMILY, we get the code ZMJNBG.

Question 13

In a code language, the word "BURN" is written as "YFIM" using a reverse alphabet (Atbash) substitution. Using the same coding scheme, what is the code for the word "WOUND"?

Accepted Answer

Introduction / Context: This is a classic example of coding based on the reverse alphabet, also known as the Atbash cipher. Under this scheme, A is paired with Z, B with Y, C with X and so on, reflecting letters across the center of the alphabet. The question demonstrates this with BURN and asks for the corresponding code of WOUND. Given Data / Assumptions: BURN is coded as YFIM. We must encode WOUND using the same substitution. Mapping pairs are A with Z, B with Y, C with X, D with W, E with V, F with U, G with T, H with S, I with R, J with Q, K with P, L with O, M with N, and vice versa. Concept / Approach: The Atbash mapping is symmetric. For each letter in BURN, we find its partner in the reversed alphabet and compare to the code letter. Once we confirm this mapping works for each position, we apply the same substitution to WOUND. The conversion is purely letter by letter, with no reordering or arithmetic involved. Step-by-Step Solution: Step 1: Write BURN and the coded word YFIM in parallel to confirm the substitution. Step 2: Under Atbash, B pairs with Y, U pairs with F, R pairs with I and N pairs with M. This perfectly matches BURN to YFIM. Step 3: Now apply the same mapping to WOUND. Step 4: W pairs with D, because D is the fourth letter from the start and W is the fourth from the end. Step 5: O pairs with L, since O and L are symmetric around the center of the alphabet. Step 6: U pairs with F, N pairs with M and D pairs with W according to the same rule. Step 7: Putting these together, W, O, U, N, D become D, L, F, M, W, giving DLFMW. Step 8: Therefore the code for WOUND is DLFMW. Verification / Alternative check: We can check the mapping for each letter independently. For instance, check that both B and Y sum to 27 when expressed as positions (2 plus 25). The same holds for W and D (23 plus 4), O and L (15 plus 12), U and F (21 plus 6) and N and M (14 plus 13). This constant sum property of 27 is another hallmark of the Atbash cipher and shows that the substitution is consistent. Why Other Options Are Wrong: DLFMD changes the last letter from W to D, breaking the Atbash pairing for D. DNFMW and DPFMW alter the middle letters, implying incorrect partners for O or U. None of these options maintain a proper reverse alphabet mapping for all letters of WOUND, so they cannot be correct under the established coding scheme. Common Pitfalls: Sometimes candidates try shifting letters forward or backward instead of using the exact reverse pairing, or they mistakenly map each letter using different rules. A systematic way is to write the full alphabet and its reverse beneath it, then directly map each letter. This consistency avoids confusion and ensures the correct code word is obtained. Final Answer: Using the reverse alphabet (Atbash) substitution, the correct code for "WOUND" is DLFMW.

Question 14

If the symbol "A" denotes "added to", "B" denotes "divided by", "C" denotes "multiplied by" and "D" denotes "subtracted from", then what is the value of the coded expression 116 B 29 C 6 A 24 D 45 ?

Accepted Answer

Introduction / Context: This coded arithmetic expression replaces the usual operators plus, minus, multiplication and division with letters. The challenge is to translate each symbol back into its corresponding operation and then evaluate the expression step by step while respecting standard precedence rules. Such questions are common in reasoning sections to check clarity about operations and the order in which they should be applied. Given Data / Assumptions: "A" means added to, so A corresponds to plus. "B" means divided by, so B corresponds to division. "C" means multiplied by, so C corresponds to multiplication. "D" means subtracted from, used here as the minus operation between the operands. The expression to evaluate is 116 B 29 C 6 A 24 D 45. Standard precedence applies: division and multiplication before addition and subtraction. Concept / Approach: First decode the entire expression by replacing the letters with their mathematical operators. Then simplify it step by step, starting with division and multiplication. Only after these are completed do we perform addition and subtraction in order from left to right. Keeping the correct sequence of operations is the key to avoiding errors and obtaining the correct final value. Step-by-Step Solution: Step 1: Replace each coded symbol with its corresponding operator. Step 2: 116 B 29 C 6 A 24 D 45 becomes 116 ÷ 29 × 6 + 24 − 45. Step 3: Perform the division 116 ÷ 29 first. Since 29 × 4 = 116, this quotient is 4. Step 4: Now perform the multiplication 4 × 6 = 24. Step 5: Substitute back to get 24 + 24 − 45. Step 6: Add 24 + 24 = 48. Step 7: Subtract 45 from 48: 48 − 45 = 3. Step 8: Therefore, the value of the coded expression is 3. Verification / Alternative check: We can verify by quickly recomputing with mental arithmetic. Once simplified, the expression is 116 ÷ 29 × 6 + 24 − 45. Recognizing that 116 ÷ 29 is exactly 4, the rest becomes 4 × 6 + 24 − 45. That is 24 + 24 − 45 = 48 − 45 = 3. Since this recomputation matches our previous result, the answer is confirmed. Why Other Options Are Wrong: Answers 4, 5 and 6 result from various mistakes such as ignoring operator precedence, reversing the subtraction or miscomputing 116 ÷ 29 or 4 × 6. Because the intermediate calculations yield clear integers and combine to 3, any other value must arise from an arithmetic slip or misinterpretation of the coded operators. Common Pitfalls: Candidates sometimes treat "subtracted from" as reversing the order of subtraction or they perform addition and subtraction before finishing multiplication and division. Another source of error is misreading 29 as 30 or miscalculating the quotient 116 ÷ 29. Careful reading of the operator definitions and stepwise calculation prevent such issues. Final Answer: After decoding and evaluating the expression, we find that 116 B 29 C 6 A 24 D 45 equals 3.

Question 15

In a certain code language, the word "CONDITION" is written as "@#^$*!*#^" by assigning special symbols to letters. Using the same one to one mapping, how is the word "NOTION" written in that code language?

Accepted Answer

Introduction / Context: This coding and decoding problem uses a substitution of letters with special symbols such as @, #, ^, $ and so on. The example "CONDITION" to "@#^$*!*#^" defines a fixed mapping between particular letters and specific symbols. The candidate must read off that mapping and apply it to the new word "NOTION". Given Data / Assumptions: CONDITION is coded as @#^$*!*#^. Each letter is replaced by exactly one symbol, and the same letter always receives the same symbol. We must find the coded form of NOTION. The word CONDITION contains the letters C, O, N, D, I and T, which appear multiple times and define the mapping for all letters that also appear in NOTION. Concept / Approach: The idea is to match each letter of CONDITION to its corresponding symbol in the given code. Once we know how C, O, N, D, I and T are encoded, we can encode any word made only from those letters. The word NOTION uses letters N, O, T and I, all of which already appear in CONDITION, so no new mapping is needed. Then we simply write the symbols in the correct order. Step-by-Step Solution: Step 1: Write CONDITION above its code @#^$*!*#^ and match each letter. Step 2: From the first positions we see C maps to @, O maps to # and N maps to ^. Step 3: The fourth letter D maps to $, the fifth letter I maps to * and the sixth letter T maps to !. Step 4: Check repeated letters: the seventh letter I is again coded as *, the eighth O as # and the ninth N as ^. This confirms a consistent mapping. Step 5: Now encode the word NOTION, which consists of N, O, T, I, O and N. Step 6: Using the mapping, N becomes ^, O becomes #, T becomes !, I becomes * and again O becomes # and N becomes ^. Step 7: So NOTION is written as ^ # ! * # ^, that is ^#!*#^. Verification / Alternative check: We can quickly verify by reversing the mapping on the candidate code ^#!*#^. Mapping ^ back to N, # back to O, ! back to T and * back to I reconstructs N O T I O N in order. This confirms that our encoding and decoding are consistent and that no letters have been mismapped. Why Other Options Are Wrong: The other options reorder the symbols or insert an incorrect symbol at one position, which corresponds to swapping letters or changing one letter in NOTION. However, there is no justification for such changes because the mapping from CONDITION is fixed and unambiguous. Only ^#!*#^ respects the exact letter to symbol relationship in the correct order of the target word. Common Pitfalls: A common mistake is to assume that similar looking symbols such as # and ^ might be interchangeable or to misalign letters when reading the mapping from CONDITION. Another error is to try to derive a numerical rule for the symbols, which is not needed. Carefully pairing each letter with its symbol exactly as shown in the example avoids these complications. Final Answer: By applying the same symbol substitution used for CONDITION, the word "NOTION" is coded as ^#!*#^.

Question 16

If "*" denotes "added to", "&" denotes "divided by", "@" denotes "multiplied by" and "%" denotes "subtracted from", then what is the value of the coded expression 135 & 15 @ 10 % 3 * 6 ?

Accepted Answer

Introduction / Context: This question presents an arithmetic expression in a coded form where operators are represented by special symbols. The task is to interpret each symbol correctly and then evaluate the expression using standard arithmetic precedence. These operator coding problems are very common in aptitude exams to test careful reading and correct application of basic arithmetic rules. Given Data / Assumptions: "*" means added to, representing the plus operation. "&" means divided by, representing the division operation. "@" means multiplied by, representing multiplication. "%" means subtracted from, used here as the minus operation. The coded expression is 135 & 15 @ 10 % 3 * 6. Standard precedence of operations applies: division and multiplication before addition and subtraction. Concept / Approach: The approach is to decode the expression by replacing each symbol with the corresponding arithmetic operator. After that, simplify the expression step by step, ensuring that multiplication and division are handled before addition and subtraction. Only once these priority operations are complete should we perform subtraction and then addition from left to right. Step-by-Step Solution: Step 1: Replace "&" with ÷, "@" with ×, "%" with − and "*" with +. Step 2: The coded expression 135 & 15 @ 10 % 3 * 6 becomes 135 ÷ 15 × 10 − 3 + 6. Step 3: Apply division first: 135 ÷ 15 = 9. Step 4: Now perform the multiplication: 9 × 10 = 90. Step 5: Substitute back to get 90 − 3 + 6. Step 6: Evaluate the subtraction first: 90 − 3 = 87. Step 7: Now add 6: 87 + 6 = 93. Step 8: Hence, the value of the coded expression is 93. Verification / Alternative check: We can recompute quickly to verify. After decoding, the expression is 135 ÷ 15 × 10 − 3 + 6. Computing 135 ÷ 15 gives 9, then 9 × 10 is 90. Subtract 3 to get 87 and then add 6 to reach 93. Because both the detailed and quick calculations agree, the result is reliable. Why Other Options Are Wrong: Option 47 and option 89 can result from performing subtraction or addition prematurely or from miscomputing 135 ÷ 15. Option 100 may come from incorrectly using addition instead of subtraction, for example turning 90 − 3 + 6 into 90 + 3 + 6. All these errors show violations of precedence or incorrect handling of the coded symbols. Only 93 corresponds to a correct decoding followed by correct arithmetic. Common Pitfalls: A frequent mistake is to apply the phrase "subtracted from" as reversing the order of subtraction or to forget that division and multiplication must be resolved before the other operations. Some candidates also get confused by the presence of multiple special symbols and interpret one of them incorrectly. Writing down the full decoded expression with ordinary operators and then proceeding stepwise avoids such problems. Final Answer: After decoding symbols and applying arithmetic precedence, the value of 135 & 15 @ 10 % 3 * 6 is 93.

Question 17

In a certain code language, the word "NIGHT" is written as "ODDGM" and the word "DARK" is written as "GOYC". Using the same pattern of letter shifts and ordering, how is the word "GREEN" written in that code language?

Accepted Answer

Introduction / Context: This coding and decoding question uses a two step transformation on the letters of each word: first shifting letters backward through the alphabet by increasing amounts and then reversing the entire sequence. The example words "NIGHT" and "DARK" illustrate how the pattern works for words of different lengths. We must apply the same pattern to "GREEN". Given Data / Assumptions: NIGHT is coded as ODDGM. DARK is coded as GOYC. We must determine the code for GREEN. The English alphabetical positions are used, and letter shifts are applied modularly so that going backwards from A wraps around through Z if needed. Concept / Approach: Consider the transformation of NIGHT. Write the letters and inspect the difference between the original and coded letters. It turns out the code is created by first shifting the letters backward by 1, 2, 3, 4 and 5 positions in order, then reversing the result. For DARK, the same idea applies with sequential backward shifts followed by reversal. For GREEN, which has five letters like NIGHT, we apply the same pattern of backward shifts 1, 2, 3, 4 and 5, then reverse the sequence to obtain the final code. Step-by-Step Solution: Step 1: For NIGHT, write its letters with positions: N, I, G, H, T. Step 2: Shift N back by 1 to M, I back by 2 to G, G back by 3 to D, H back by 4 to D and T back by 5 to O. This gives the intermediate sequence M G D D O. Step 3: Reverse this intermediate sequence to O D D G M, which matches ODDGM. So the rule for five letter words is confirmed. Step 4: Now apply the same backward shifts to GREEN. Step 5: Write GREEN as G, R, E, E, N. Step 6: Shift G back by 1 to F, R back by 2 to P, E back by 3 to B, E back by 4 to A and N back by 5 to I. This gives intermediate letters F, P, B, A, I. Step 7: Reverse this sequence to obtain I, A, B, P, F, which spells IABPF. Step 8: Therefore GREEN is coded as IABPF. Verification / Alternative check: We can test the pattern once more with DARK. D shifted back by 1 becomes C, A back by 2 becomes Y, R back by 3 becomes O and K back by 4 becomes G. The intermediate sequence is C Y O G, which when reversed becomes G O Y C, matching GOYC. This second example confirms that the method of sequential backward shifts followed by reversal is consistently used and justifies applying it to GREEN. Why Other Options Are Wrong: Options MCBNB, OGHVL and FPBAI involve different orderings or shift directions. They do not arise from the exact sequence of backward shifts by 1 through 5 followed by reversal. In particular, FPBAI appears as the unreversed intermediate sequence for GREEN, while the final code is the reversed form IABPF. Because the examples show that reversal is always applied, the unreversed sequence cannot be correct. Common Pitfalls: Many candidates correctly compute the intermediate shifted letters but forget the final reversal step, leading them to choose FPBAI. Others miscalculate one or more backward shifts, especially for letters near the beginning of the alphabet. A structured approach that carefully applies each shift and then reverses the sequence prevents these errors. Final Answer: Using the same shifting and reversal pattern that converts NIGHT to ODDGM, the word "GREEN" is coded as IABPF.

Question 18

If the alphabet is coded in reverse order so that A is replaced by Z, B by Y, C by X and so on, then using this rule how is the word "EDITOR" written in the coded form?

Accepted Answer

Introduction / Context: This question explicitly states that the alphabet is reversed in coding. The mapping is symmetrical: A corresponds to Z, B to Y, C to X and so on. This is again the Atbash cipher. The task is to apply this reverse mapping consistently to each letter of the word "EDITOR". Given Data / Assumptions: A is coded as Z, B as Y, C as X and so on, reflecting the alphabet. The coding pairs each letter with its mirror image across the center of the alphabet. We must encode the word EDITOR under this scheme. The mapping is one to one and fixed, with no reordering of letters. Concept / Approach: The core idea is to find the reverse alphabet partner for each letter in EDITOR. This can be done by writing the alphabet forward and backward in two rows and reading off each mapping. There is no shifting beyond the reflection, and there is no change in letter order in the word. After mapping each letter, we join the corresponding letters to obtain the coded word. Step-by-Step Solution: Step 1: Establish the Atbash pairs: A with Z, B with Y, C with X, D with W, E with V, F with U, G with T, H with S, I with R, J with Q, K with P, L with O, M with N and vice versa. Step 2: Apply this to each letter in EDITOR. Step 3: E maps to V, because E is the fifth from the start and V is the fifth from the end. Step 4: D maps to W, I maps to R, T maps to G, O maps to L and R maps to I. Step 5: Put these coded letters together in order: V W R G L I. Step 6: Therefore EDITOR is coded as VWRGLI. Verification / Alternative check: We can cross check by encoding a simpler word or by decoding VWRGLI back to EDITOR. Mapping V back to E, W back to D, R back to I, G back to T, L back to O and I back to R reproduces EDITOR exactly. Since the mapping is symmetric and the word comes back unchanged through this round trip, the code is confirmed. Why Other Options Are Wrong: Options VWRGVI, VWVGLI and VWRLLI change one or more letters from the correct code. These errors correspond to misassigning partners, such as mapping O incorrectly, or duplicating letters where no duplication exists in EDITOR. Because the rule is completely determined once the reverse alphabet is fixed, any deviation from VWRGLI is inconsistent with the stated coding scheme. Common Pitfalls: Candidates may mistakenly apply a simple shift or assume some letters, especially vowels, map in a different way. Others might forget that the word order is preserved and attempt to reverse the word as well. Writing the full A to Z and Z to A lines and tracing each letter visually avoids such confusion. Final Answer: Using the reverse alphabet coding where A maps to Z and B to Y, the word "EDITOR" is written as VWRGLI.

Question 19

If A means "+", B means "×", C means "÷" and D means "−", and the coded expression is 9 A 2 B 6 D 4 C 2, then what is the numerical value of this expression after decoding and evaluating it correctly?

Accepted Answer

Introduction / Context: This is another coded arithmetic expression where letters represent standard operations. The candidate must decode A, B, C and D into plus, multiplication, division and subtraction respectively, then compute the value of the resulting numerical expression. Such expressions test the ability to juggle symbolic and numeric reasoning under exam conditions. Given Data / Assumptions: A means plus. B means multiplied by. C means divided by. D means minus. The coded expression to evaluate is 9 A 2 B 6 D 4 C 2. Standard arithmetic precedence applies: multiplication and division before addition and subtraction. Concept / Approach: The method is to decode the expression and then apply BODMAS or PEMDAS rules. We first replace each letter with its corresponding operator. After that, we simplify the expression by handling multiplication and division first, working from left to right for operations of the same precedence, and finally resolving addition and subtraction. The goal is a single numeric answer that matches one of the options. Step-by-Step Solution: Step 1: Replace each coded symbol in 9 A 2 B 6 D 4 C 2. Step 2: A becomes +, B becomes ×, C becomes ÷ and D becomes −. Step 3: The decoded expression is 9 + 2 × 6 − 4 ÷ 2. Step 4: Apply multiplication and division first. Compute 2 × 6 = 12 and 4 ÷ 2 = 2. Step 5: Substitute back to get 9 + 12 − 2. Step 6: Now perform addition and subtraction from left to right: first 9 + 12 = 21. Step 7: Subtract 2 from 21: 21 − 2 = 19. Step 8: Therefore, the correct value of the coded expression is 19. Verification / Alternative check: We can quickly recompute the key steps: 2 × 6 is clearly 12, and 4 ÷ 2 is 2. Adding 9 and 12 gives 21, and subtracting 2 yields 19. Since there are no fractions or tricky operations, the result is stable and easy to check a second time. Why Other Options Are Wrong: Option 16 could arise if a candidate miscomputed one of the products or quotients. Option 27 and option 30 can appear if one ignores precedence and evaluates strictly from left to right without prioritizing multiplication and division. These values do not follow the correct order of operations or the given mapping of symbols to arithmetic functions, so they are incorrect. Common Pitfalls: A common issue is forgetting that multiplication and division must be done before addition and subtraction and treating A, B, C and D as if they were new operations with unknown precedence. In fact, once decoded, they are normal arithmetic operations and follow the usual rules. Another pitfall is copying the expression incorrectly or misreading one of the digits. Writing the decoded expression clearly and then solving stepwise greatly reduces these risks. Final Answer: After decoding the symbols and applying arithmetic precedence, the expression 9 A 2 B 6 D 4 C 2 evaluates to 19.

Question 20

In a certain code language, the word "TIRED" is written as the number 56 and the word "BRAIN" is written as the number 44. Using the same rule, what number represents the word "LAZY"?

Accepted Answer

Introduction / Context: This coding question converts words into numbers. The numeric code is based on the positions of letters in the alphabet, but the operation is not concatenation; rather, it is a total sum. The example words TIRED and BRAIN and their codes 56 and 44 hint at this pattern. We must find the code for LAZY under the same rule. Given Data / Assumptions: TIRED is coded as 56. BRAIN is coded as 44. We must determine the code for LAZY. Letters are associated with their alphabet positions: A is 1, B is 2, up to Z which is 26. The code likely equals the sum of the positions of all letters in the word. Concept / Approach: To confirm the rule, convert each letter of TIRED and BRAIN into its alphabetical position and sum them. If the result matches the given code, then the pattern is established as a letter sum. Once confirmed, repeat the same process for LAZY. This type of question checks whether the candidate can move comfortably between letters and numbers and see patterns across multiple examples. Step-by-Step Solution: Step 1: Convert TIRED into letter positions: T, I, R, E, D. Step 2: T is 20, I is 9, R is 18, E is 5 and D is 4. Step 3: Sum these: 20 + 9 + 18 + 5 + 4 = 56, which matches the code for TIRED. Step 4: Now convert BRAIN into letter positions: B, R, A, I, N. Step 5: B is 2, R is 18, A is 1, I is 9 and N is 14. Step 6: Sum these: 2 + 18 + 1 + 9 + 14 = 44, matching the code given for BRAIN. The rule is confirmed. Step 7: Apply the same rule to the word LAZY. Step 8: L is 12, A is 1, Z is 26 and Y is 25. Step 9: Sum them: 12 + 1 + 26 + 25 = 64. Step 10: Therefore LAZY is coded as 64. Verification / Alternative check: As a quick check, consider whether any alternative pattern such as product or difference could yield the same results. Products of letter positions would be extremely large, so they are unlikely. Differences would be small or negative and do not match the given positive codes. Simple addition fits both example words exactly, so it is the most reasonable and consistent pattern. Why Other Options Are Wrong: Options 61, 54 and 51 result from partial sums, omitted letters or miscounted positions. Because the mapping from letters to numbers is well defined and the addition rule has been confirmed twice, only the exact sum 64 can be correct. Any other total indicates a mistake at some stage in converting or adding the letter values. Common Pitfalls: Errors often occur when counting letter positions, especially for letters near the end of the alphabet like Y and Z. Another pitfall is misreading the pattern and trying to concatenate digits instead of summing values. Writing out the alphabet with positions or double checking suspicious letters helps avoid such errors. Final Answer: Using the same letter position sum rule that maps TIRED to 56 and BRAIN to 44, the word "LAZY" is coded as 64.

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