Question 1

In a letter value code, the single letter D has a value of 4 and the word DOG has a value of 26 based on the positions of its letters in the alphabet. Using the same coding rule, what is the total coded value of the word ANIMAL?

Accepted Answer

Introduction / Context: This coding and decoding problem again uses the popular alphabet position technique where each letter is assigned a numerical value equal to its position in the English alphabet. The value of a word is typically obtained by adding the values of its letters. You are given the codes for D and DOG and must extend the same logic to find the code for ANIMAL. Given Data / Assumptions: The letter D has a code value of 4. The word DOG has a code value of 26. We must calculate the code value of ANIMAL. We assume the usual mapping: A = 1, B = 2, C = 3, up to Z = 26. The total value of a word is the sum of its letter values. Concept / Approach: We first check whether the given examples are consistent with the standard alphabet position mapping. If D and DOG both fit that scheme, then it is safe to use the same method for ANIMAL. This type of question mainly checks attention to detail and basic addition rather than advanced reasoning. Step-by-Step Solution: Step 1: Confirm the code for D. In the alphabet, A is the 1st letter, B the 2nd, C the 3rd and D the 4th. So D = 4, agreeing with the question.Step 2: Confirm the code for DOG. The positions are D = 4, O = 15 and G = 7.Step 3: Add these values: 4 + 15 + 7 = 26. This matches the given code for DOG and confirms the rule.Step 4: Now apply the same method to ANIMAL. Find the positions: A = 1, N = 14, I = 9, M = 13, A = 1, L = 12.Step 5: Add the values step by step. First 1 + 14 = 15.Step 6: Then 15 + 9 = 24; 24 + 13 = 37; 37 + 1 = 38; 38 + 12 = 50.Step 7: Therefore, the coded value of ANIMAL is 50. Verification / Alternative check: You can verify by re-adding the numbers with a different grouping, such as (1 + 9 + 1) + (14 + 13 + 12) = 11 + 39 = 50. Since both methods give 50, the arithmetic is correct. Also, because D and DOG clearly fit the alphabet sum pattern, applying the same rule to ANIMAL is logically consistent. Why Other Options Are Wrong: The options 47, 48 and 49 represent sums that are slightly smaller than the true total, which might result from dropping or miscounting one letter value. The option 52 is larger than the correct sum, perhaps arising from adding an extra value by mistake. Only 50 exactly matches the sum of the positions for A, N, I, M, A and L. Common Pitfalls: Miscounting alphabetical positions, especially for letters beyond M, or making small addition errors are the most frequent problems. Sometimes students assume more complex rules even when a simple sum of letter values is sufficient. Writing down the letter positions clearly and adding them carefully step by step helps to avoid these mistakes. Final Answer: Using the letter position sum rule, the coded value of ANIMAL is 50.

Question 2

In this question, some equations are solved according to a specific pattern. Using the same pattern, where 3 X 4 X 5 = 435 and 4 X 3 X 2 = 342, what should be the value of 2 X 3 X 4?

Accepted Answer

Introduction / Context: This coding question presents three numbers separated by X and equates them to a three digit result. The symbol X here does not represent ordinary multiplication but a special arrangement pattern. By examining the given examples, we must discover how the digits are rearranged and then apply that pattern to find the result corresponding to the third expression. Given Data / Assumptions: 3 X 4 X 5 is coded as 435. 4 X 3 X 2 is coded as 342. We must find the code for 2 X 3 X 4. The X symbol indicates that the numbers are to be combined or rearranged, not multiplied. The pattern must be consistent in all given examples. Concept / Approach: When the coded answers are three digit numbers built from the same digits as the original three numbers, the most likely pattern is a rearrangement of the order of those numbers. The task becomes identifying which position each original number occupies in the result. Once we determine this mapping for one example, we must confirm it with the other example to ensure that the pattern is reliable. Step-by-Step Solution: Step 1: Look at 3 X 4 X 5 = 435. The three numbers are 3, 4 and 5, while the result 435 uses the digits 4, 3 and 5.Step 2: Observe that 435 can be seen as the middle number first (4), then the first number (3), followed by the last number (5). So the mapping seems to be (first, second, third) → (second, first, third).Step 3: Check this mapping with the second example 4 X 3 X 2 = 342. Using the same rule, the second number is 3, the first number is 4 and the third number is 2, giving 342, which matches the given result.Step 4: Since the mapping works for both examples, the rule is confirmed: the output is formed as second number, first number, third number.Step 5: Apply the rule to 2 X 3 X 4. Here the first number is 2, the second is 3 and the third is 4.Step 6: According to the rule, the result is second, first, third, which is 3, 2, 4, or 324. Verification / Alternative check: To verify, you can quickly encode 2 X 3 X 4 using any other plausible rearrangement, such as first, third, second or third, second, first. None of these patterns will give the previously established results for the earlier equations. Only the second, first, third pattern fits both the provided examples and the desired equation, confirming that 324 is the correct code. Why Other Options Are Wrong: The option 342 corresponds to the pattern second, third, first, which does not match the given example 3 X 4 X 5 = 435. The option 432 corresponds to third, second, first, again inconsistent with 435. The option 243 or 234 come from other arbitrary reorderings of 2, 3 and 4 that do not fit the verified rule. Only 324 respects the pattern discovered from the given equations. Common Pitfalls: One common mistake is to assume that multiplication is involved because of the symbol X and therefore spend time computing products or sums instead of noticing that only permutations of digits appear. Another mistake is to choose a rearrangement that works for one equation but not for the others. Always confirm the mapping across all examples before applying it to the target. Final Answer: Applying the same rearrangement pattern, the correct coded value of 2 X 3 X 4 is 324.

Question 3

In a certain language code, the word TEACHER is written as QBXZEBO by shifting each letter. Using the same coding rule, how will the word STUDENT be written in that code?

Accepted Answer

Introduction / Context: This is another letter shifting or Caesar cipher question. The word TEACHER is converted into QBXZEBO using a consistent shift applied to every letter. Once the exact shift is identified, we must apply the same transformation to each letter of the word STUDENT in order to obtain its coded form. Given Data / Assumptions: TEACHER is coded as QBXZEBO. The same shifting rule is applied to every letter. We need to code the word STUDENT. The alphabet positions A = 1 through Z = 26 are used implicitly. Shifts wrap around cyclically if they move past A or Z. Concept / Approach: We compare each letter in TEACHER with the corresponding letter in QBXZEBO and compute the difference between their positions in the alphabet. If this difference is the same for all pairs, we have found the uniform shift that defines the code. Then we apply this shift to each letter of STUDENT, ensuring we move in the correct direction (forward or backward) and handle wrap around correctly. Step-by-Step Solution: Step 1: Determine the positions of the letters in TEACHER: T = 20, E = 5, A = 1, C = 3, H = 8, E = 5, R = 18.Step 2: Determine the positions for the code QBXZEBO: Q = 17, B = 2, X = 24, Z = 26, E = 5, B = 2, O = 15.Step 3: Find the shift for each letter: T (20) to Q (17) is minus 3; E (5) to B (2) is minus 3; A (1) to X (24) is minus 3 with wrap around; C (3) to Z (26) is minus 3; H (8) to E (5) is minus 3; E (5) to B (2) is minus 3; R (18) to O (15) is minus 3.Step 4: The rule is therefore a uniform shift of three letters backward in the alphabet.Step 5: Apply this rule to STUDENT. The positions are S = 19, T = 20, U = 21, D = 4, E = 5, N = 14, T = 20.Step 6: Shift each letter back by three positions: S (19) → P (16), T (20) → Q (17), U (21) → R (18), D (4) → A (1), E (5) → B (2), N (14) → K (11), T (20) → Q (17).Step 7: Combining these letters gives the coded word PQRABKQ. Verification / Alternative check: You can reverse check by shifting PQRABKQ three letters forward. P → S, Q → T, R → U, A → D, B → E, K → N and Q → T, which reconstructs STUDENT perfectly. Also, applying the same reverse shift from QBXZEBO to TEACHER confirms that the rule works uniformly both ways. Why Other Options Are Wrong: Options such as PQRBAQK, PQRKBAQ, PRKQBAQ and PQRABQK differ in the order of letters or in one or more positions. They do not correspond to a uniform shift of three positions backward from the original word STUDENT. Since the code must follow the exact same Caesar shift rule as TEACHER to QBXZEBO, any deviation from PQRABKQ is incorrect. Common Pitfalls: Students may mistakenly apply a forward shift instead of a backward one, or miscount the shift by one position. Another error is to forget the wrap around effect, especially when letters are near the beginning of the alphabet. To avoid mistakes, always compute the numeric positions and subtract or add carefully, checking each letter pair. Final Answer: Using the same backward shift of three letters, STUDENT is coded as PQRABKQ.

Question 4

In a coded arithmetic system, the symbols are redefined as follows: x means addition, the minus sign means division, the division sign means subtraction and the plus sign means multiplication. Under these rules, which one of the following coded equa…

Accepted Answer

Introduction / Context: This coding and decoding question involves operator substitution. The usual arithmetic symbols are redefined so that each symbol now represents a different operation. To identify the correct equation, you must translate each coded equation into a standard arithmetic expression using the new meanings, then check which one yields a true statement. Given Data / Assumptions: x means addition. The minus sign (−) means division. The division sign (÷) means subtraction. The plus sign (+) means multiplication. Four or more coded equations are given, and exactly one of them should evaluate correctly when decoded. Normal precedence rules apply after decoding: multiplication and division before addition and subtraction. Concept / Approach: The key is to systematically decode each option. Every time you see x, you replace it with plus, every minus with division, every division sign with subtraction and every plus with multiplication. After decoding, you simplify each expression step by step. Only the decoded equation that matches the stated result on the right hand side is considered correct. Step-by-Step Solution: Step 1: Decode option (c) because it contains all the symbols and often reveals the pattern well: 16 + 5 - 10 x 4 ÷ 3 = 9.Step 2: Apply the replacements. The plus sign (+) means multiplication, so 16 + 5 becomes 16 * 5. The minus sign (−) means division, so the symbol after 5 becomes division by 10. The x sign means addition, so 10 x 4 becomes 10 + 4. The division sign (÷) means subtraction, so 4 ÷ 3 becomes 4 − 3.Step 3: Combining these, the decoded expression is 16 * 5 / 10 + 4 − 3.Step 4: Now evaluate with the standard order of operations. First compute 16 * 5 = 80.Step 5: Then divide by 10 to get 80 / 10 = 8.Step 6: Now handle addition and subtraction from left to right: 8 + 4 = 12 and 12 − 3 = 9.Step 7: The left hand side evaluates to 9, which exactly matches the right hand side of option (c), so option (c) is a true equation under the given coding. Verification / Alternative check: To ensure that option (c) is uniquely correct, you can similarly decode options (a), (b), (d) and (e). When decoded, each of those yields a left hand side value that does not match the number given on the right hand side, or produces a noninteger result that clearly differs from the stated value. Therefore, option (c) is the only coded equation that becomes a correct arithmetic statement once the operators are translated. Why Other Options Are Wrong: In option (a), after decoding, the left hand side evaluates to a noninteger value around 7.67, not 19. In option (b), the decoded operations lead to a much larger number than 9. In option (d), the decoded expression gives a value close to 1.2, not 12. In option (e), the substitutions again produce a value that does not match the stated result 11. Only for option (c) does the decoding yield exactly 9. Common Pitfalls: Students often forget to apply all replacements correctly or they unintentionally treat some symbols as if they still had their usual meanings. Another frequent mistake is ignoring the precedence rules and performing operations strictly from left to right. Carefully decoding each symbol and then applying the correct order of operations is essential to avoid these errors. Final Answer: The only coded equation that becomes a true arithmetic statement is 16 + 5 - 10 x 4 ÷ 3 = 9.

Question 5

In a special three number code, the expressions 4 x 5 x 2 = 524, 3 x 7 x 2 = 723 and 6 x 8 x 7 = 876 follow the same rearrangement rule. Using this rule, what is the coded value of 9 x 4 x 5?

Accepted Answer

Introduction / Context: This question uses a simple rearrangement code involving three numbers. Instead of multiplying or adding them, the three numbers are rearranged to form a three digit number. By comparing the examples, we can infer the positional pattern used and then apply it to the new triple 9, 4 and 5 to determine the coded value. Given Data / Assumptions: 4 x 5 x 2 is coded as 524. 3 x 7 x 2 is coded as 723. 6 x 8 x 7 is coded as 876. We have to find the code for 9 x 4 x 5. The symbol x here indicates a special pattern, not multiplication. Concept / Approach: The outputs 524, 723 and 876 all contain the same digits as the input numbers but in different positions. This strongly suggests a rearrangement scheme. Our goal is to identify which input number becomes the hundreds digit, which becomes the tens digit and which becomes the units digit. Once we find a consistent mapping that works for all three given equations, we apply that mapping to the new set of numbers. Step-by-Step Solution: Step 1: Look at 4 x 5 x 2 = 524. The input numbers are 4, 5 and 2. The result uses digits 5, 2 and 4.Step 2: This suggests the pattern (first, second, third) → (second, third, first). In other words, hundreds digit is the second number, tens digit is the third number and units digit is the first number.Step 3: Check the second example. For 3 x 7 x 2, using the same pattern gives digits 7, 2 and 3, which forms 723. This matches the given result.Step 4: Check the third example. For 6 x 8 x 7, applying the pattern gives 8, 7 and 6, forming 876, which again matches the given value.Step 5: Since the pattern is consistent across all examples, we can confidently apply it to 9 x 4 x 5.Step 6: Here, the first number is 9, the second is 4 and the third is 5. Applying the mapping (first, second, third) → (second, third, first) gives digits 4, 5 and 9.Step 7: Thus, the coded result for 9 x 4 x 5 is 459. Verification / Alternative check: If you attempt other rearrangements, such as (third, first, second) or (third, second, first), they will not reproduce all the given examples correctly. Only the mapping second, third, first matches all three coded equations. Rechecking the digits for each case confirms that 459 is the correct and consistent code for 9 x 4 x 5. Why Other Options Are Wrong: The option 495 corresponds to a different digit order and would not be produced by the established pattern. Similarly, 549 and 954 represent rearrangements that do not match what happens for the earlier examples. The option 945 also breaks the verified mapping. Therefore, these options are inconsistent with the discovered rule and must be rejected. Common Pitfalls: Some students get misled by the multiplication sign and attempt to compute products or sums instead of noticing that the results are simply permutations of the original digits. Others find a rearrangement that works for just one example and do not test it against the others. Always ensure that your pattern is valid for all given examples before using it to solve the final part. Final Answer: Using the same rearrangement pattern, the value of 9 x 4 x 5 in this code is 459.

Question 6

In a coded operator system, the plus sign means divided by, the minus sign means multiplied by, the cross sign x means minus and the division sign ÷ means plus. Using these meanings, what is the value of the coded expression 16 ÷ 8 - 4 + 2 x 4?

Accepted Answer

Introduction / Context: This is an operator substitution problem where familiar arithmetic symbols are assigned new meanings. Instead of directly computing with the visible operators, you must first decode the expression by replacing each symbol with the operation it now represents, and then evaluate the resulting standard arithmetic expression using normal precedence rules. Given Data / Assumptions: The plus sign (+) represents division. The minus sign (−) represents multiplication. The cross sign x represents subtraction. The division sign (÷) represents addition. The expression to be evaluated is 16 ÷ 8 - 4 + 2 x 4. After decoding, apply the usual order of operations: multiplication and division before addition and subtraction. Concept / Approach: We decode each operator according to the given rules, rewrite the entire expression in standard arithmetic and then simplify it step by step. The core reasoning skills tested here are careful reading, systematic substitution and accurate application of arithmetic precedence. Any slip in substitution or order can lead to an incorrect result. Step-by-Step Solution: Step 1: Start with the coded expression 16 ÷ 8 - 4 + 2 x 4.Step 2: Replace ÷ with its real meaning, which is addition. So 16 ÷ 8 becomes 16 + 8.Step 3: Replace the minus sign with its real meaning, which is multiplication. So the symbol between 8 and 4 becomes multiplication, turning that segment into 8 * 4.Step 4: Replace the plus sign with its real meaning, which is division. Thus the symbol between 4 and 2 becomes division, giving 4 ÷ 2.Step 5: Replace x with its real meaning, which is subtraction. So 2 x 4 becomes 2 − 4.Step 6: Putting all substitutions together, the decoded expression is 16 + 8 * 4 ÷ 2 − 4.Step 7: According to the order of operations, first compute multiplication and division from left to right. Calculate 8 * 4 = 32.Step 8: Next compute 32 ÷ 2 = 16.Step 9: Substitute back into the expression to get 16 + 16 − 4.Step 10: Now perform the remaining operations from left to right: 16 + 16 = 32, and 32 − 4 = 28. Verification / Alternative check: You can verify the answer by directly substituting the real operators in one pass: 16 plus becomes 16 ÷ 8? No, you interpret them as 16 + 8 * 4 ÷ 2 − 4 exactly as in the decoded expression and then recompute. Any attempt to evaluate with the original meanings of the symbols or to calculate left to right without following precedence will yield the wrong result. Repeating the calculation confirms that the decoded value is 28. Why Other Options Are Wrong: The option 16 might result if a student misreads the rules and only evaluates 16 ÷ 8 with normal meaning. The option 32 appears if someone decodes correctly but forgets the final subtraction of 4. The option 44 or 24 arise from misordered operations or incorrect substitutions of one or more symbols. Only 28 matches the correctly decoded and properly evaluated expression. Common Pitfalls: Frequent errors include using usual operator meanings instead of the coded ones, skipping one substitution, or performing addition and subtraction before finishing all multiplication and division. To avoid these mistakes, write down the fully decoded expression explicitly and then simplify it carefully in stages. Final Answer: After decoding the operators and evaluating, the value of the expression 16 ÷ 8 - 4 + 2 x 4 is 28.

Question 7

Some equations are solved according to a fixed three number coding pattern: 2 x 3 x 5 = 523, 6 x 4 x 1 = 164 and 8 x 2 x 4 = 482. Using the same pattern, what is the value of 6 x 8 x 2?

Accepted Answer

Introduction / Context: This is a three number rearrangement code similar to other coding questions. Instead of performing arithmetic operations, the three input numbers are rearranged to form a three digit output. By analyzing the provided examples, we must deduce the consistent pattern in which the positions are swapped and then apply that pattern to 6, 8 and 2. Given Data / Assumptions: 2 x 3 x 5 is coded as 523. 6 x 4 x 1 is coded as 164. 8 x 2 x 4 is coded as 482. We must determine the code for 6 x 8 x 2. The symbol x represents a special pattern, not multiplication. Concept / Approach: Because the outputs are three digit numbers composed of the same digits as the inputs, the most likely code is a positional rearrangement. We must identify which original number becomes the hundreds digit, which becomes the tens digit and which becomes the units digit. Once a consistent mapping is established across all examples, we apply it to the new triple. Step-by-Step Solution: Step 1: Examine 2 x 3 x 5 = 523. The inputs are 2, 3 and 5. The output 523 uses the digits 5, 2 and 3.Step 2: This suggests the pattern (first, second, third) → (third, first, second). Here, hundreds digit is the third number, tens digit is the first number and units digit is the second number.Step 3: Confirm this with the second equation. For 6 x 4 x 1, the digits are 6, 4, 1. Using the pattern third, first, second gives 1, 6 and 4, which forms 164. This matches the given result.Step 4: Confirm again with the third equation. For 8 x 2 x 4, the digits are 8, 2, 4. Applying the same pattern yields 4, 8 and 2, which produces 482, again matching the provided value.Step 5: The mapping is now firmly established as (first, second, third) → (third, first, second).Step 6: Apply this pattern to 6 x 8 x 2, where the first number is 6, the second is 8 and the third is 2.Step 7: According to the rule, the hundreds digit is the third number (2), the tens digit is the first number (6) and the units digit is the second number (8), giving 2, 6 and 8.Step 8: Combine these digits to get the coded number 268. Verification / Alternative check: No other simple rearrangement such as second, third, first or first, third, second will produce all three given codes 523, 164 and 482 correctly. Testing these alternatives quickly shows mismatches. The third, first, second pattern is the only one that fits every example and therefore must be used for the target triple. Rechecking the ordering for 6, 8 and 2 confirms that 268 is correct. Why Other Options Are Wrong: The options 826, 286, 628 and 682 correspond to different permutations of 2, 6 and 8 that are not generated by the established mapping. They might look superficially plausible but they do not respect the rule confirmed by the earlier equations. Since the pattern is consistent across all examples, any option that does not follow it must be rejected. Common Pitfalls: Some candidates immediately assume multiplication because of the x symbols and spend time computing products, which leads nowhere. Others pick a rearrangement based on only one example. The correct approach is to examine all given equations to find a rule that works every time and then apply that rule without alteration. Final Answer: Using the same rearrangement pattern, the correct coded value of 6 x 8 x 2 is 268.

Question 8

In a certain code, the word TEACHER is written as VGCEJGT by shifting letters. Using the same code, how is the word CHILDREN written?

Accepted Answer

Introduction / Context: This coding and decoding question is based on a Caesar cipher with a forward shift. The word TEACHER is converted into VGCEJGT by moving each letter forward in the alphabet by the same number of positions. Our job is to detect that shift and use it to encode the word CHILDREN in exactly the same way. Given Data / Assumptions: TEACHER is coded as VGCEJGT. The same uniform shifting rule applies to all letters. We must find the code for CHILDREN. The alphabet positions A = 1 through Z = 26 are used implicitly. Shifts wrap around if they cross Z. Concept / Approach: We examine each pair of corresponding letters in TEACHER and VGCEJGT to determine the size and direction of the shift. If every pair shows the same difference in alphabet positions, that difference gives us the coding rule. Then we apply the same forward shift to each letter of CHILDREN and join the results to obtain the coded word. Step-by-Step Solution: Step 1: Find the positions of the letters in TEACHER: T = 20, E = 5, A = 1, C = 3, H = 8, E = 5, R = 18.Step 2: Find the positions of the letters in VGCEJGT: V = 22, G = 7, C = 3, E = 5, J = 10, G = 7, T = 20.Step 3: Compute the difference for each pair. From T to V is +2, from E to G is +2, from A to C is +2, from C to E is +2, from H to J is +2, from E to G is +2 and from R to T is +2. Thus, each letter is shifted two positions forward.Step 4: The coding rule is therefore: replace each letter with the letter two positions ahead in the alphabet.Step 5: Apply this rule to CHILDREN. First write positions: C = 3, H = 8, I = 9, L = 12, D = 4, R = 18, E = 5, N = 14.Step 6: Shift each letter by +2 positions: C → E (3 to 5), H → J (8 to 10), I → K (9 to 11), L → N (12 to 14), D → F (4 to 6), R → T (18 to 20), E → G (5 to 7), N → P (14 to 16).Step 7: Combining these letters, we get EJKNFTGP as the coded form of CHILDREN. Verification / Alternative check: To verify, shift each letter of EJKNFTGP two positions backward and confirm that it returns to CHILDREN. E → C, J → H, K → I, N → L, F → D, T → R, G → E and P → N, which reconstructs the original word exactly. This confirms that the rule has been applied correctly and that EJKNFTGP is the correct answer. Why Other Options Are Wrong: Options such as EJKNEGTP, EJKNFTGH, EJKNFTPG and EJKNFTGT differ in one or more letters or their order. These differences do not correspond to a consistent shift of two positions from the letters in CHILDREN. Since the cipher is uniform and exact, any option that contains even a single incorrect letter cannot be the correct code. Common Pitfalls: Students may miscount the two position shift, especially for letters at the end of the alphabet, or mix up the order of letters when writing the final code. Others guess an answer that looks similar without checking all eight letters. To avoid errors, carefully compute each shift and verify the result by decoding it back to the original word. Final Answer: Using a forward shift of two letters in the alphabet, CHILDREN is written in code as EJKNFTGP.

Question 9

In a coded arithmetic expression, the letters L, M, P and Q stand for different operators as follows: L denotes multiplication, M denotes division, P denotes addition and Q denotes subtraction. What is the numerical value of the expression 16P24M8Q6…

Accepted Answer

Introduction / Context: This problem combines coding and arithmetic operations using letters instead of the usual symbols. Each letter corresponds to a standard operator, and you must decode the expression into ordinary arithmetic and then evaluate it correctly. The question tests both decoding skills and accurate application of the order of operations. Given Data / Assumptions: L denotes multiplication (×). M denotes division (÷). P denotes addition (+). Q denotes subtraction (−). The coded expression is 16P24M8Q6M2L3. After decoding, normal arithmetic precedence holds: multiplication and division before addition and subtraction. Concept / Approach: The task is to systematically replace each letter with its corresponding operator, rewrite the entire expression in standard mathematical form and then evaluate it step by step. It is important not to change the order of the numbers, only the operators. Once decoding is done, apply the usual order of operations to find the final value. Step-by-Step Solution: Step 1: Write the coded expression clearly: 16P24M8Q6M2L3.Step 2: Replace P with addition. So 16P24 becomes 16 + 24.Step 3: Replace M with division. The first M between 24 and 8 becomes ÷, giving 24 ÷ 8. The second M between 6 and 2 also becomes ÷, giving 6 ÷ 2.Step 4: Replace Q with subtraction, so Q between 8 and 6 becomes −, giving − 6.Step 5: Replace L with multiplication, so L between 2 and 3 becomes ×, giving 2 × 3.Step 6: The fully decoded expression is 16 + 24 ÷ 8 − 6 ÷ 2 × 3.Step 7: Now evaluate using precedence rules. Division and multiplication come first, left to right. Compute 24 ÷ 8 = 3.Step 8: Next compute 6 ÷ 2 = 3, and then 3 × 3 = 9.Step 9: Substitute these values back into the expression to obtain 16 + 3 − 9.Step 10: Finally, perform addition and subtraction from left to right: 16 + 3 = 19, and 19 − 9 = 10.Step 11: Thus, the value of the expression 16P24M8Q6M2L3 is 10. Verification / Alternative check: You can check the result by recomputing the expression using a calculator or by grouping the operations slightly differently while still respecting precedence. For example, compute all divisions first, then the multiplication and finally the additions and subtractions. Every correct approach yields the same final value 10, confirming that the decoding and arithmetic steps are correct. Why Other Options Are Wrong: The fractional options 13/6 and −1/6 come from misordering the operations or incorrectly combining the division and multiplication parts. The value 14.5 and 9.5 can arise if a student performs operations strictly from left to right or misapplies subtraction instead of division in one segment. None of these correspond to the correctly decoded and evaluated expression, which gives an exact integer value. Common Pitfalls: Students often misplace one of the operators when decoding, for example treating M as multiplication instead of division, or they forget to apply the order of operations and compute from left to right. Another frequent error is to stop after partially simplifying the expression. Writing each substitution explicitly and following the precedence step by step avoids these problems. Final Answer: After decoding the letters and correctly evaluating the expression, the value of 16P24M8Q6M2L3 is 10.

Question 10

In a certain coding scheme, the six letter word AMOUNT is written as BNPTMS. Using the same pattern of letter shifts applied to the first and second halves of the word, how is the word AROUND written in that code?

Accepted Answer

Introduction / Context: This coding question uses a mixed shifting rule: the first half of the letters in the word are shifted forward in the alphabet while the second half are shifted backward. The word AMOUNT becomes BNPTMS under this rule. We must detect exactly how the shifts work and apply the same idea to the six letter word AROUND. Given Data / Assumptions: AMOUNT is written as BNPTMS in the code. The word has six letters, naturally split into two halves of three letters each. The same coding rule must be applied to AROUND, which also has six letters. The mapping uses alphabet positions from A = 1 to Z = 26, with wrap around. We assume a consistent rule across corresponding positions. Concept / Approach: We compare AMOUNT with BNPTMS letter by letter. By computing the positional differences, we see how the first three letters are transformed and how the last three letters are transformed. This reveals a pattern of shifting forward for the first half and backward for the second half. Then we apply the same forward and backward shifts to the letters of AROUND. Step-by-Step Solution: Step 1: Split AMOUNT into two halves: AMO and UNT.Step 2: For the first half AMO, write positions: A = 1, M = 13, O = 15. For the corresponding coded letters BNP, the positions are B = 2, N = 14, P = 16.Step 3: The shift from A to B is +1, from M to N is +1 and from O to P is +1. So the first half letters are shifted forward by one position.Step 4: For the second half UNT, write positions: U = 21, N = 14, T = 20. For the coded letters TMS, positions are T = 20, M = 13, S = 19.Step 5: The shift from U to T is −1, from N to M is −1 and from T to S is −1. So the second half letters are shifted backward by one position.Step 6: Therefore, the coding rule is: for a six letter word, shift the first three letters forward by one and the last three letters backward by one.Step 7: Now apply this rule to AROUND. Split AROUND into ARO and UND.Step 8: For the first half ARO: A = 1, R = 18, O = 15. Shifting forward by one gives B = 2, S = 19 and P = 16, forming BSP.Step 9: For the second half UND: U = 21, N = 14, D = 4. Shifting backward by one gives T = 20, M = 13 and C = 3, forming TMC.Step 10: Combine the two halves BSP and TMC to form the coded word BSPTMC. Verification / Alternative check: A quick reverse check by shifting the letters of BSPTMC back in the opposite direction restores AROUND. B back to A, S back to R, P back to O, T forward to U, M forward to N and C forward to D. This confirms that the coding rule has been applied correctly and that BSPTMC is the valid code. Why Other Options Are Wrong: The options BSPUNT, BSUPTN, ZSPVOE and BSPUMT do not respect the exact pattern of +1 for the first three letters and −1 for the last three letters. Some shift all letters in the same direction while others alter only a few letters correctly. Because the coding scheme is fully systematic, any deviation in even one position makes the option invalid. Common Pitfalls: Some students try to shift all letters forward or all letters backward and therefore generate a partly correct but overall incorrect code. Others forget to treat the word as two separate halves. It is crucial to compare each position carefully and notice that the direction of shift changes halfway through the word. Final Answer: Using the same mixed shifting pattern as in AMOUNT, the correct code for AROUND is BSPTMC.

Question 11

In a three number coding system, 5 x 4 x 0 is written as 405 and 3 x 2 x 8 is written as 283. Using the same coding pattern, what should be the value of 1 x 7 x 6?

Accepted Answer

Introduction / Context: This verbal reasoning question presents a simple three number code where expressions like 5 x 4 x 0 and 3 x 2 x 8 are converted into three digit numbers. The symbol x does not indicate multiplication but an arrangement of digits. By inspecting the examples, we must infer the order in which the three numbers are written to form the coded output. Given Data / Assumptions: 5 x 4 x 0 is coded as 405. 3 x 2 x 8 is coded as 283. We are asked to find the coded value of 1 x 7 x 6. The three digits in the result must come from the three original numbers. The same arrangement rule is applied consistently in all cases. Concept / Approach: The outputs 405 and 283 clearly use the same digits as the inputs but in different positions. This indicates that the code is a permutation of the original numbers. We must determine which input number becomes the hundreds digit, which becomes the tens digit and which becomes the units digit by analyzing the examples, and then apply this pattern to 1, 7 and 6. Step-by-Step Solution: Step 1: Look at 5 x 4 x 0 = 405. The inputs are 5, 4 and 0, while the result 405 uses the digits 4, 0 and 5.Step 2: This suggests the pattern (first, second, third) → (second, third, first), where the hundreds digit is the second number, the tens digit is the third number and the units digit is the first number.Step 3: Check the second example. For 3 x 2 x 8, the digits are 3, 2 and 8. Using the pattern second, third, first, we get 2, 8 and 3, which forms 283. This matches the given code.Step 4: Since the pattern holds for both examples, we can confidently apply it to 1 x 7 x 6.Step 5: For 1 x 7 x 6, the first number is 1, the second is 7 and the third is 6.Step 6: According to the mapping, hundreds digit is the second number (7), tens digit is the third number (6) and units digit is the first number (1), giving 7, 6 and 1.Step 7: Therefore, 1 x 7 x 6 should be coded as 761. Verification / Alternative check: Trying other permutations such as third, first, second or third, second, first on the examples would not reproduce both 405 and 283 correctly. Only the second, third, first order consistently matches the provided coded results. Reapplying this confirmed rule to 1, 7 and 6 gives 761, so the answer is reliable. Why Other Options Are Wrong: The options 617, 716, 167 and 671 correspond to different permutations of 1, 7 and 6. None of those follow the discovered pattern that places the second number first, the third number second and the first number last. Therefore they cannot match the coding rule that was used for the given examples. Common Pitfalls: Some students treat x as multiplication and attempt to compute products before noticing that the outputs are simply rearrangements. Others find a pattern that works for only one example and do not check the others. Always ensure that your inferred rule fits every given equation, not just one, before applying it to find the final answer. Final Answer: Using the same rearrangement pattern as in the examples, the coded value of 1 x 7 x 6 is 761.

Question 12

In a certain code language, the word EXPLAIN is written as BUMIXFK by shifting each letter three places backward in the alphabet. Using the same rule, how will the word GYM be coded?

Accepted Answer

Introduction / Context: This is another Caesar cipher style coding question where each letter is replaced by a letter that is a fixed number of positions away in the alphabet. The word EXPLAIN becomes BUMIXFK when each letter is shifted three places backward. We must apply this same uniform shift to the word GYM to find its coded form. Given Data / Assumptions: EXPLAIN is coded as BUMIXFK. The alphabet positions A = 1 through Z = 26 are considered. The code is formed by shifting letters backward by three positions. We need to code the word GYM using the same rule. Wrap around is used if the shift passes A. Concept / Approach: We first confirm the shift using EXPLAIN and BUMIXFK. Each letter of EXPLAIN maps to a letter three positions earlier. Once this is confirmed, we apply the same backward shift of three positions to each letter in GYM, and then combine the results to get the final coded word. Step-by-Step Solution: Step 1: Check the shift for EXPLAIN. E (5) to B (2) is a shift of −3. X (24) to U (21) is −3. P (16) to M (13) is −3. L (12) to I (9) is −3. A (1) to X (24) is also −3 with wrap around. I (9) to F (6) is −3. N (14) to K (11) is −3.Step 2: Since each letter is shifted three positions backward, the rule is confirmed.Step 3: Now apply this rule to GYM. Find the positions: G = 7, Y = 25, M = 13.Step 4: Shift each letter three places backward. G (7) minus 3 gives D (4). Y (25) minus 3 gives V (22). M (13) minus 3 gives J (10).Step 5: Combine these letters to form the coded word DVJ. Verification / Alternative check: To verify, shift the letters of DVJ three positions forward: D → G, V → Y and J → M, which reconstructs GYM exactly. This backward and forward check confirms that the shift has been applied correctly to each letter. Why Other Options Are Wrong: The options YHN, UJM, IKL and XJL do not result from shifting G, Y and M three positions backward. Some may involve different shifts or mixed directions, but they do not correspond to a consistent −3 shift from each letter. Therefore, only DVJ adheres to the established coding rule derived from EXPLAIN. Common Pitfalls: Students often miscount three places backward or accidentally shift forward instead. Another common error is to apply different shifts to different letters. Carefully computing numeric positions and subtracting three from each one avoids these mistakes. Final Answer: Using the same three letter backward shift as in EXPLAIN, the word GYM is coded as DVJ.

Question 13

In a certain code language for arithmetic, the symbol plus represents multiplication, minus represents addition, x represents division and the division sign ÷ represents subtraction. Using this code, what is the result of the expression 825 x 25 - 2…

Accepted Answer

Introduction / Context: This coding and decoding problem uses operator substitution in arithmetic expressions. Each common operator is given a new meaning. To solve the expression 825 x 25 - 27 ÷ 10, you must decode the operators into their real operations first and then evaluate the resulting standard arithmetic expression using the usual order of operations. Given Data / Assumptions: The plus symbol (+) represents multiplication. The minus symbol (−) represents addition. The symbol x represents division. The division sign (÷) represents subtraction. The coded expression is 825 x 25 - 27 ÷ 10. After decoding, we use normal precedence: division and multiplication before addition and subtraction. Concept / Approach: The crucial step is to rewrite the coded expression in true arithmetic form by replacing each operator with what it actually stands for in the code language. Once that is done, we use standard arithmetic rules to simplify. This approach prevents the common error of trying to solve the expression directly with the visible symbols. Step-by-Step Solution: Step 1: Begin with the coded expression 825 x 25 - 27 ÷ 10.Step 2: Replace x with its real meaning, which is division. Thus 825 x 25 becomes 825 ÷ 25.Step 3: Replace the minus sign with its real meaning, which is addition. So the symbol between 25 and 27 becomes a plus, giving + 27.Step 4: Replace the division sign ÷ with its real meaning, which is subtraction. So ÷ 10 becomes − 10.Step 5: The fully decoded expression is 825 ÷ 25 + 27 − 10.Step 6: Now apply the order of operations. First compute the division: 825 ÷ 25.Step 7: Perform the division: 25 goes into 825 exactly 33 times, so 825 ÷ 25 = 33.Step 8: Substitute back to get 33 + 27 − 10.Step 9: Now do addition and subtraction from left to right. First 33 + 27 = 60.Step 10: Then 60 − 10 = 50.Step 11: Therefore, the value of the coded expression is 50. Verification / Alternative check: You can verify the calculation by recomputing 825 ÷ 25 using long division or breaking it into 25 × 33 = 825. Recalculating 33 + 27 − 10 again gives 50. Since all operator substitutions have been applied consistently and the arithmetic checks out, the answer 50 is confirmed. Why Other Options Are Wrong: The option 100 might come from misinterpreting x as multiplication and computing 825 × 25, which is completely different. The option 25 may occur if someone divides 825 by 33 or makes a slip in the final subtraction. The options 20 and 40 could arise from incorrect intermediate additions or subtractions. None of these values match the correctly decoded and evaluated expression. Common Pitfalls: Students frequently forget one of the substitutions, for example treating the minus sign as subtraction instead of addition. Another mistake is ignoring operator precedence and evaluating from left to right. A third pitfall is performing the division 825 ÷ 25 incorrectly. Carefully applying each substitution and then simplifying stepwise prevents these errors. Final Answer: After performing the correct substitutions and calculations, the value of 825 x 25 - 27 ÷ 10 is 50.

Question 14

In a number code, the expression 9 x 3 is equal to 3, 15 x 3 is equal to 5 and 60 x 5 is equal to 12. Using the same coding rule, what is the value of 27 x 3?

Accepted Answer

Introduction / Context: This coding and decoding question involves a simple relationship between two numbers. The expressions 9 x 3, 15 x 3 and 60 x 5 do not mean ordinary multiplication. Instead, each expression is converted to a smaller number according to a straightforward pattern. We must detect that pattern and apply it to compute the value of 27 x 3. Given Data / Assumptions: 9 x 3 is coded as 3. 15 x 3 is coded as 5. 60 x 5 is coded as 12. We must find the coded value of 27 x 3. The symbol x denotes a special operation defined by the pattern, not standard multiplication. Concept / Approach: Given that the coded results are smaller and that each pair involves a larger first number and a smaller second number, division is a natural operation to test. We check whether the result corresponds to the first number divided by the second number for all examples. If it does, we then apply this rule to the new pair 27 and 3. Step-by-Step Solution: Step 1: Consider 9 x 3 = 3. If we treat x as division, 9 ÷ 3 = 3, which matches the coded result.Step 2: Check the second example with the same rule. For 15 x 3, compute 15 ÷ 3 = 5. This matches the coded value 5.Step 3: Check the third example. For 60 x 5, compute 60 ÷ 5 = 12. This matches the coded value 12.Step 4: Since all three given equations fit the rule result = first number divided by second number, we can accept this as the coding pattern.Step 5: Apply the rule to 27 x 3. Compute 27 ÷ 3.Step 6: The division 27 ÷ 3 = 9.Step 7: Therefore, the coded value of 27 x 3 is 9. Verification / Alternative check: To verify, note that any alternative pattern that does not rely on simple division would struggle to fit all three given examples simultaneously. Recomputing each division confirms that 9 ÷ 3 is 3, 15 ÷ 3 is 5 and 60 ÷ 5 is 12, making division the natural and consistent rule. Applying it to 27 and 3 again gives 9, confirming the answer. Why Other Options Are Wrong: The option 30 might arise if someone multiplies instead of divides, computing 9 × 3 or 15 × 3. The options 3 and 6 represent incorrect divisions or partial reasoning applied inconsistently. The option 12 is the result for 60 x 5 in the pattern, not for 27 x 3. None of these values are equal to 27 ÷ 3, so they do not satisfy the discovered rule. Common Pitfalls: Some students try to invent a more complicated relationship involving both numbers when a simple division pattern already explains all examples. Others may mistakenly invert the division or confuse which number should be the numerator. Always start by testing the simplest operations like addition, subtraction, multiplication and division before assuming a more complex rule. Final Answer: According to the discovered coding rule, the value of 27 x 3 is 9.

Question 15

In a certain code language, the English word "MARBLES" is written as "PDUEOHV". Using the same letter shifting rule, how will the word "GIN" be written in that code language?

Accepted Answer

Introduction: This question belongs to the coding and decoding section of verbal reasoning. A familiar English word is converted to a coded form by systematically shifting each letter in the alphabet. We are told how the word MARBLES is coded and must apply the same rule to find the code for GIN. This tests pattern recognition and knowledge of alphabetical positions. Given Data / Assumptions: The word MARBLES is written as PDUEOHV in the code language. We assume: 1) Each letter in the original word is replaced by one letter only. 2) The same transformation is applied to every letter of any word. 3) The alphabet is treated cyclically, so after Z the sequence may wrap back to A if needed. Concept / Approach: The standard approach is to compare each letter of MARBLES with each letter of PDUEOHV using alphabetical positions. Once we know how many positions each letter is shifted, we verify that the shift is constant for all letters. That constant shift becomes our rule, which we then apply to the letters G, I, and N to obtain the final code for GIN. Step-by-Step Solution: Step 1: Write down letter positions: M=13, A=1, R=18, B=2, L=12, E=5, S=19.Step 2: For the coded form PDUEOHV, the positions are P=16, D=4, U=21, E=5, O=15, H=8, V=22.Step 3: Compute the shift from original to coded letters: M to P is 13 to 16 (plus 3), A to D is 1 to 4 (plus 3), R to U is 18 to 21 (plus 3), and similarly for every other pair.Step 4: Since every letter is shifted forward by 3 positions, the rule is: coded letter = original letter shifted forward by 3.Step 5: Apply this to GIN. G=7 goes to J=10, I=9 goes to L=12, and N=14 goes to Q=17, again a forward shift of 3 positions.Step 6: Therefore, GIN is coded as JLQ. Verification / Alternative check: If we reverse the shift by subtracting 3 from each coded letter of JLQ, we should return to GIN. J back by 3 letters becomes G, L back by 3 becomes I, and Q back by 3 becomes N. This confirms that our shift rule works consistently in both directions, so the decoding is reliable. Why Other Options Are Wrong: SEG, BHU, WGI, and HKO do not arise from a uniform shift of 3 positions applied to GIN. Each of them would require either unequal shifts for different letters or movement in the wrong direction along the alphabet, which contradicts the pattern used for MARBLES. Common Pitfalls: A common error is to miscount alphabet positions, especially near the beginning or end of the alphabet, or to mix forward and backward shifts. Another pitfall is to guess the pattern from only the first pair of letters without verifying it on the entire word. Always check that the same shift works for every letter. Final Answer: The word "GIN" will be coded as JLQ in this code language.

Question 16

In a certain code language, the symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operations, what is the numerical value of 54 x 9 - 3…

Accepted Answer

Introduction: This problem is a classic operator coding question from verbal reasoning. The familiar arithmetic symbols +, -, x, and ÷ are assigned new meanings. We must first decode the expression based on these new meanings, then evaluate it correctly using normal arithmetic precedence. The example tests careful reading and disciplined application of standard calculation rules. Given Data / Assumptions: The symbol meanings are redefined as: 1) "+" represents multiplication (times). 2) "-" represents addition (plus). 3) "x" represents division (divide). 4) "÷" represents subtraction (minus). The given coded expression is 54 x 9 - 3 ÷ 4. After decoding the symbols, we assume the usual precedence of operations: division and multiplication first, followed by addition and subtraction from left to right. Concept / Approach: The key idea is to rewrite the entire expression with its true operations before attempting any calculation. Once we have a standard arithmetic expression, we simply apply BODMAS or PEMDAS. Many mistakes in these questions come from mixing the original and redefined meanings of the symbols, so a clean translation step is essential. Step-by-Step Solution: Step 1: Replace each symbol with its new meaning. The "x" stands for division, so 54 x 9 becomes 54 / 9.Step 2: The "-" symbol stands for addition, so - 3 becomes + 3.Step 3: The "÷" symbol stands for subtraction, so ÷ 4 becomes - 4.Step 4: The decoded expression is therefore 54 / 9 + 3 - 4.Step 5: Apply precedence rules. First, perform the division: 54 / 9 = 6.Step 6: Substitute this value to obtain 6 + 3 - 4.Step 7: Now perform addition and subtraction from left to right: 6 + 3 = 9, then 9 - 4 = 5.Step 8: The final result of the coded expression is 5. Verification / Alternative check: We can quickly recheck by repeating the translation: 54 divided by 9 plus 3 minus 4. Evaluating again gives 6 + 3 - 4 = 5. There is no alternative bracketing indicated in the question, so our calculation is consistent and complete. Why Other Options Are Wrong: The value 10 would arise if someone added 6 and 4 instead of subtracting. The value 8 might come from evaluating 54 / 9 first, then doing 6 + (3 - 1) due to a misread of the operations. The value 2 could come from incorrectly grouping as 54 / 9 + (3 - 5). None of these follow the correct translation and precedence in a systematic way. Common Pitfalls: Students often forget to change all the operators before starting the calculation, or they unconsciously treat the symbols according to their usual meanings. Another common error is to perform the operations strictly from left to right, ignoring that division must be done before addition and subtraction. Writing the decoded expression clearly on paper helps avoid these mistakes. Final Answer: After decoding and evaluating, the value of the expression is 5.

Question 17

In a certain number code, the operator "%" does not mean the usual percentage. Instead, 14 % 32 is given as 46 and 52 % 20 is given as 72. Using the same hidden rule, what is the value of 35 % 14?

Accepted Answer

Introduction: This question involves a nonstandard numeric operator, represented by the "%" sign. Here it does not mean percentage. Instead, two example equations are provided, and we must discover the pattern or rule connecting the numbers. Once that rule is clear, we apply it to a new pair to find the required value of 35 % 14. It is a straightforward test of pattern recognition in arithmetic puzzles. Given Data / Assumptions: We are given two sample relations: 1) 14 % 32 = 46 2) 52 % 20 = 72 We must determine 35 % 14. We assume: 1) The operator % represents the same operation in all three cases. 2) The operation is likely simple and based on addition, subtraction, or another basic arithmetic combination of the two numbers. Concept / Approach: When unknown operators appear in reasoning questions, a good first step is to check basic operations: sum, difference, product, or ratios of the given numbers. Since the results 46 and 72 are modest and close to the sum of each pair, examining the sum is a natural starting point. If the same rule explains both examples, we accept it as the underlying pattern and then use it to compute the third case. Step-by-Step Solution: Step 1: For 14 % 32, compute the sum 14 + 32 = 46. This exactly matches the given result 46.Step 2: For 52 % 20, compute the sum 52 + 20 = 72. This also matches the given result 72.Step 3: Since both examples fit the simple rule "a % b = a + b", we adopt this rule.Step 4: Apply the rule to the required expression: 35 % 14 = 35 + 14.Step 5: Add the numbers: 35 + 14 = 49.Step 6: Therefore, the value of 35 % 14 is 49. Verification / Alternative check: We can confirm by checking whether any alternative simple pattern, such as difference or product, fits both examples. The difference 32 - 14 equals 18, which does not match 46, and 52 - 20 equals 32, which does not match 72. The products 14 * 32 and 52 * 20 are far larger than the results. So the sum rule is the most natural and consistent explanation. Why Other Options Are Wrong: The values 39, 29, and 19 are much smaller and would require subtracting something from the sum without any hint from the examples. The value 59 is larger than the sum and would need unjustified addition. None of these candidate values can be obtained from both given examples with a single simple arithmetic rule. Common Pitfalls: Learners sometimes look for overly complex patterns involving squares, cubes, or digit manipulations when a very simple rule suffices. Another error is to test a rule on only one example and assume it is correct without verifying it on the second given relation. Always ensure that the same rule explains all provided examples before using it on the target expression. Final Answer: Using the pattern, the value of 35 % 14 is 49.

Question 18

In a certain code language, the English word "FLOTSAM" is written as "UOLGHZN". Using the same letter substitution pattern, how will the word "PIN" be written in that code language?

Accepted Answer

Introduction: This coding and decoding problem is based on a positional substitution cipher applied to letters of the alphabet. The word FLOTSAM is written as UOLGHZN in a certain code. We must uncover the exact transformation and apply it to the word PIN. This tests familiarity with simple alphabet-based ciphers and careful matching of individual letters. Given Data / Assumptions: The code language maps FLOTSAM to UOLGHZN. We assume: 1) Each letter of the original word is replaced by exactly one letter in the code word. 2) The transformation is consistent for every occurrence of a given letter. 3) The same substitution pattern is used for any other word, including PIN. Concept / Approach: One of the classic coding patterns in such questions is the mirror or Atbash cipher, where A pairs with Z, B with Y, C with X, and so on. To test if this is the case, we compare each letter of FLOTSAM with the corresponding letter in UOLGHZN and see whether each is its mirror in the alphabet. If this holds for every letter, we confidently apply the same mapping to P, I, and N. Step-by-Step Solution: Step 1: Pair the letters: F with U, L with O, O with L, T with G, S with H, A with Z, and M with N.Step 2: In an Atbash style mapping, A maps to Z, B to Y, C to X, D to W, E to V, F to U, and so on. Check each pair: F indeed mirrors to U, L to O, O to L, T to G, S to H, A to Z, and M to N.Step 3: Since every pair fits the mirror pattern, the code uses the alphabet reversal rule.Step 4: Apply the same rule to P, I, and N. The mirror of P is K, because P is the sixteenth letter and K is the eleventh (positions summing to 27). The mirror of I is R, and the mirror of N is M.Step 5: Therefore, PIN is encoded as KRM in this code language. Verification / Alternative check: If we reverse the mapping for the code KRM, we should come back to PIN. Using the same Atbash rule, K maps back to P, R maps back to I, and M maps back to N. This two way consistency confirms that our understanding of the cipher is correct. Why Other Options Are Wrong: GEH, OBI, DVW, and RKO cannot all be produced by the alphabet reversal cipher starting from P, I, and N. Each of those options places at least one letter that is not the correct mirror partner of the original letter, so they violate the discovered pattern. Common Pitfalls: Students sometimes attempt to view the code as a simple fixed shift (for example, plus two or minus three) without checking the full set of letter pairs. Others stop after confirming the pattern for only one or two letters instead of checking all of them. A reliable solution always verifies that the inferred rule fits every letter in the given example. Final Answer: The word "PIN" is written as KRM in the given code language.

Question 19

In a certain code language, the arithmetic symbols are redefined as follows: "+" stands for multiplication, "-" stands for addition, "x" stands for division and "÷" stands for subtraction. Using these coded operators, what is the value of 234 x 9 - …

Accepted Answer

Introduction: This question is another example of operator coding in verbal reasoning. The standard arithmetic operators +, -, x, and ÷ are assigned new meanings. Our task is to decode the expression 234 x 9 - 12 + 4, rewrite it with true operations, and then evaluate it correctly using normal arithmetic precedence. The challenge lies in careful symbol translation and disciplined computation. Given Data / Assumptions: The special meanings are: 1) "+" represents multiplication. 2) "-" represents addition. 3) "x" represents division. 4) "÷" represents subtraction. The coded expression is 234 x 9 - 12 + 4. Once decoded, we follow the usual order of operations: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: The safest method is to ignore normal meanings of the symbols and instead replace each with its assigned meaning before doing any arithmetic. After conversion, we obtain a standard looking expression in terms of /, *, + and -, which we then evaluate step by step. Misinterpreting even one symbol can lead to an incorrect final answer. Step-by-Step Solution: Step 1: Replace the symbol "x" with its meaning division, so 234 x 9 becomes 234 / 9.Step 2: Replace the symbol "-" with addition, so - 12 becomes + 12.Step 3: Replace the symbol "+" with multiplication, so + 4 becomes * 4.Step 4: The decoded expression is 234 / 9 + 12 * 4.Step 5: Apply operation precedence: first perform the division and multiplication from left to right.Step 6: Compute 234 / 9. Since 9 * 26 = 234, we get 234 / 9 = 26.Step 7: Compute 12 * 4 = 48.Step 8: Now the expression becomes 26 + 48.Step 9: Add the numbers: 26 + 48 = 74.Step 10: Thus, the value of the coded expression is 74. Verification / Alternative check: We can quickly verify by re translating verbally: 234 divided by 9 plus 12 multiplied by 4. That is 26 plus 48, which is 74. There are no other hidden brackets or exceptions, so the answer is stable. Why Other Options Are Wrong: The value 48 would arise if someone evaluated only the product 12 * 4 and ignored 234 / 9. The values 94, 82, or 56 could result from adding or subtracting one of the intermediate numbers incorrectly or from misreading a symbol and turning an addition into subtraction or vice versa. None of these alternative results follow directly from the correct translation and precedence rules. Common Pitfalls: Many learners accidentally treat the symbol "+" as addition out of habit, which completely changes the calculation. Others perform the operations strictly from left to right without doing division and multiplication first. Writing out the fully decoded expression before computing makes it much easier to avoid these mistakes. Final Answer: The correctly evaluated value of the expression is 74.

Question 20

In a certain numerical code, the symbol "$" represents a special operation between two numbers. It is given that 23 $ 35 = 13 and 3 $ 5 = 8. Using the same rule, what is the value of 4 $ 13?

Accepted Answer

Introduction: This question uses a special operator "$" applied to pairs of numbers. The operator does not carry its usual programming or financial meaning here. Instead, two example equations show how it behaves, and we must infer the underlying rule and then apply it to a new pair, 4 and 13. This is a typical pattern recognition exercise in numerical reasoning. Given Data / Assumptions: The relationships provided are: 1) 23 $ 35 = 13 2) 3 $ 5 = 8 We need to find 4 $ 13. We assume: 1) The operation $ is the same for every pair of numbers in the question. 2) The rule is built from simple operations on the digits of the numbers, since the outputs are much smaller than the original values. Concept / Approach: Because the results 13 and 8 are small compared to 23 and 35, it is natural to suspect that $ may involve the sum of individual digits. For 23 and 35, both are two digit numbers, so we can test if the sum of all their digits equals the result. If the same pattern also explains the second example, we can confidently apply it to 4 and 13. Step-by-Step Solution: Step 1: Consider 23 $ 35 = 13. Break 23 into digits 2 and 3, and 35 into digits 3 and 5.Step 2: Add all digits together: 2 + 3 + 3 + 5 = 13. This matches the given result, so the rule is consistent here.Step 3: Now test the rule on the second example 3 $ 5 = 8. Both numbers are single digits, so add them directly: 3 + 5 = 8, which again matches the provided value.Step 4: Since both examples are explained by "add all digits of both numbers", we adopt this as the rule for the $ operation.Step 5: Apply this rule to 4 $ 13. The digits are 4, 1, and 3.Step 6: Add them: 4 + 1 + 3 = 8.Step 7: Therefore, 4 $ 13 equals 8 under this operation. Verification / Alternative check: If we attempted any other simple pattern such as taking differences, products, or averages, they would not fit both examples simultaneously. For instance, 23 + 35 equals 58, not 13, and 23 minus 35 is negative, which is not used. Hence, the digit sum rule is the most straightforward and uniquely consistent explanation. Why Other Options Are Wrong: The value 14 would require an extra addition not supported by the examples. The value 6 would correspond to 4 + 2, with no reason to extract only a subset of digits. The value 49 is far from any simple digit based rule, and 10 would require adding an invented constant. None of these align with both given examples. Common Pitfalls: Sometimes learners immediately try to apply operations directly to the full numbers, like 23 + 35, and overlook digit wise patterns. Another mistake is to find a rule that fits only one example and then use it without testing on the other. Always verify your proposed rule on all given sample cases before generalising. Final Answer: According to the pattern, the value of 4 $ 13 is 8.

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