Question 1

If the word PONDERS is coded as ONMCDQR (each letter is replaced by the immediately previous letter in the alphabet, for example P→O, O→N, N→M, etc.), then how will the word MAT be coded using the same previous-letter coding rule?

Accepted Answer

Introduction / Context: This is a letter-coding question where each letter is transformed using a fixed alphabet relation. The example indicates that every original letter is replaced by the letter immediately before it in the English alphabet (a backward shift of 1). Given Data / Assumptions: PONDERS is coded as ONMCDQR. Rule: each letter becomes the previous alphabet letter. Alphabet is cyclic: A becomes Z when shifted backward by 1. Apply the same rule to MAT. Concept / Approach: Identify the shift from the example. Here, P→O and O→N clearly show a backward movement by 1 position. Apply the same backward shift to each character of the target word. Step-by-Step Solution: Rule: Replace each letter with the previous letter in the alphabet. M → L (previous of M is L) A → Z (previous of A is Z) T → S (previous of T is S) So MAT → LZS. Verification / Alternative check: Quick check using positions: M(13) becomes L(12), A(1) becomes Z(26), T(20) becomes S(19). All are exactly -1 shifts, confirming LZS. Why Other Options Are Wrong: NBU: implies forward shifting, not backward. KXR: inconsistent or excessive backward shifts. LZT: only two letters match the -1 rule. MZS: keeps M unchanged, breaking the rule. Common Pitfalls: Forgetting that A shifts to Z, using +1 instead of -1, or mixing shifts per letter can lead to wrong codes. Final Answer: LZS

Question 2

In a certain code language, the operator symbols are redefined as follows: '+' means multiplication (*), '-' means addition (+), 'x' means division (/), and '÷' means subtraction (-). Using this decoding, what is the correct value of: 80 x 16 ÷ 4 + …

Accepted Answer

Introduction / Context: This question checks decoding of swapped mathematical operators and correct evaluation using normal precedence rules. The expression must be translated into standard operations first, and only then computed. Given Data / Assumptions: '+' represents multiplication (*). '-' represents addition (+). 'x' represents division (/). '÷' represents subtraction (-). Use standard precedence after decoding. Concept / Approach: Convert each coded operator to its real meaning. Then compute the decoded expression using multiplication/division before addition/subtraction. Step-by-Step Solution: Original: 80 x 16 ÷ 4 + 2 - 8 Decode operators one by one: x means /, so: 80 / 16 ÷ means -, so between 16 and 4 it becomes: - 4 + means *, so between 4 and 2 it becomes: * 2 - means +, so between 2 and 8 it becomes: + 8 Decoded expression: 80 / 16 - 4 * 2 + 8 Compute division: 80 / 16 = 5 Compute multiplication: 4 * 2 = 8 Now: 5 - 8 + 8 = 5 Verification / Alternative check: Notice that - (4*2) + 8 cancels out to 0, leaving only 80/16 = 5. This confirms the answer quickly. Why Other Options Are Wrong: 64: comes from treating x as multiplication. 11: from incorrect decoding of - as subtraction. 30: from computing without precedence or wrong mapping. 13: from partial cancellation errors. Common Pitfalls: Evaluating the coded expression directly, forgetting to decode every operator, or doing subtraction before multiplication causes incorrect results. Final Answer: 5

Question 3

In a certain code language, letters are represented by digits. For example, FRAME is written as 79635 and TOWEL is written as 21854. Using the same letter-to-digit mapping, how will the word WORM be written in that code language?

Accepted Answer

Introduction / Context: This is a classic coding-decoding question based on a fixed substitution mapping between letters and digits. You must infer the digit corresponding to each letter from the given coded words, and then use that mapping to encode a new word. Given Data / Assumptions: FRAME → 79635 TOWEL → 21854 Same letter always maps to the same digit. Find code for WORM. Concept / Approach: Create a letter-to-digit dictionary from the examples. Use common letters across examples (like E) to confirm consistency. Then encode each letter of WORM in order. Step-by-Step Solution: From FRAME → 79635: F=7, R=9, A=6, M=3, E=5 From TOWEL → 21854: T=2, O=1, W=8, E=5, L=4 Notice E=5 appears in both, confirming mapping consistency. Now encode WORM: W = 8 O = 1 R = 9 M = 3 So WORM → 8193. Verification / Alternative check: Cross-check: R and M were obtained from FRAME, while W and O were obtained from TOWEL. Since all required letters exist in the mapping and E was consistent across samples, 8193 is reliable. Why Other Options Are Wrong: 9183: swaps W and R positions incorrectly. 9376: uses digits not mapped to WORM correctly. 1593: starts with O instead of W. 8139: misplaces R and M digits. Common Pitfalls: Reading digits in wrong order, mixing mappings between letters, or assuming digits represent positions rather than substitutions are common mistakes. Final Answer: 8193

Question 4

In a certain code language, symbols are interchanged as follows: '-' means multiplication (*), '÷' means addition (+), '+' means division (/), and 'x' means subtraction (-). Using this decoding, find the correct value of: 12 - 6 + 4 x 10 ÷ 16 = ?

Accepted Answer

Introduction / Context: This question evaluates your ability to decode swapped arithmetic operators and then compute the expression using normal precedence rules. The main trick is to avoid calculating before decoding the operators correctly. Given Data / Assumptions: '-' represents multiplication (*). '÷' represents addition (+). '+' represents division (/). 'x' represents subtraction (-). After decoding, use standard precedence. Concept / Approach: Rewrite the original expression by replacing each symbol with its true meaning, then evaluate normally. Multiplication and division are done before addition and subtraction. Step-by-Step Solution: Original: 12 - 6 + 4 x 10 ÷ 16 Decode each operator: 12 - 6 becomes 12 * 6 6 + 4 becomes 6 / 4 (because + means /) 4 x 10 becomes 4 - 10 10 ÷ 16 becomes 10 + 16 Correct decoded expression (by operator positions): 12 * 6 / 4 - 10 + 16 Now compute: 12 * 6 = 72 72 / 4 = 18 18 - 10 + 16 = 24 Verification / Alternative check: Once decoded, the first three terms simplify to 18. Then adding ( -10 + 16 ) = +6 gives 24, confirming consistency. Why Other Options Are Wrong: 14: from wrong precedence or wrong mapping of + and ÷. 5: from treating x as multiplication instead of subtraction. 2: from evaluating coded expression directly. 20: from arithmetic slip after correct decoding. Common Pitfalls: Decoding only some symbols, misreading operator positions, or doing addition before division/multiplication in the decoded expression are typical errors. Final Answer: 24

Question 5

The following equation is incorrect due to two operator signs being placed wrongly. Which two signs should be interchanged (swapped wherever they appear) to make the equation correct? 18 - 2 ÷ 20 + 5 x 16 = 69

Accepted Answer

Introduction / Context: This question tests operator-interchange correction. You must identify which two operators, when swapped throughout the expression, make the left-hand side equal the right-hand side. The challenge is systematic checking while respecting arithmetic precedence. Given Data / Assumptions: Equation: 18 - 2 ÷ 20 + 5 x 16 = 69 Exactly two operator signs must be interchanged. After swapping, evaluate using standard precedence: division and multiplication before addition and subtraction. Concept / Approach: Try each suggested pair-swap by replacing every occurrence of the first sign with the second and vice versa. Then compute the new left-hand side. The correct swap is the one that yields 69. Step-by-Step Solution: Test option: swap ÷ and -. Original: 18 - 2 ÷ 20 + 5 x 16 After swapping ÷ and -: 18 ÷ 2 - 20 + 5 x 16 Now evaluate: 18 ÷ 2 = 9 5 x 16 = 80 So LHS = 9 - 20 + 80 9 - 20 = -11 -11 + 80 = 69 This matches RHS = 69. Verification / Alternative check: Because the final computed value matches exactly, no further swaps are required. Also, the structure is sensible: a clean division at the start, then addition of a large product, which naturally can reach 69. Why Other Options Are Wrong: + and x: changes only one multiplication location and typically produces non-69 values. + and ÷: creates multiple divisions/additions that shift the result far from 69. - and +: mostly rearranges plus/minus but keeps 2 ÷ 20 small, not enough adjustment. x and ÷: disrupts the big 5 x 16 term, making it hard to reach 69. Common Pitfalls: Swapping only one occurrence of a sign, ignoring precedence, or doing swaps mentally without rewriting often leads to wrong conclusions. Final Answer: ÷ and -

Question 6

A custom operation @ is defined by the examples: -2@-4 = -8, -1@-8 = -8, and -1@6 = 6. Using the same rule (consistent across all examples), what is the value of -1@7 = ?

Accepted Answer

Introduction / Context: This problem tests your ability to infer a custom operator definition from examples. The symbol @ does not have a standard meaning, so you must identify a rule that fits all provided input-output pairs and then apply it to a new case. Given Data / Assumptions: -2@-4 = -8 -1@-8 = -8 -1@6 = 6 Find -1@7 using the same rule. Assume one consistent arithmetic rule applies to all cases. Concept / Approach: Test simple operations: addition, subtraction, multiplication, division, and sign modifications. A good rule must satisfy every example, including mixed signs (negative with positive). Step-by-Step Solution: Try multiplication first: -2 * -4 = 8, but output is -8. This suggests the result might be the negative of the product. Define: a@b = -(a * b). Verify with -2@-4: a * b = (-2) * (-4) = 8 -(a*b) = -8, matches. Verify with -1@-8: (-1) * (-8) = 8, negative gives -8, matches. Verify with -1@6: (-1) * 6 = -6, negative gives 6, matches. Now compute -1@7: (-1) * 7 = -7 Negative of that is 7. Verification / Alternative check: The rule a@b = -(a*b) is validated by all three examples. Since it fits both negative-negative and negative-positive cases, applying it to -1 and 7 is consistent, giving 7. Why Other Options Are Wrong: -7: would be the raw product, not the negative of the product. 8 or -8: comes from misusing the earlier examples or assuming the output copies the second number. 14: would be from adding magnitudes incorrectly. Common Pitfalls: Assuming @ means normal multiplication, ignoring the sign flip, or fitting a rule to only one example instead of all examples are common mistakes. Final Answer: 7

Question 7

A coding scheme assigns numerical values to letters based on their alphabetical positions (A=1, B=2, C=3, ..., Z=26). For example, HAT = 29. Using the same letter-position sum method, what is the value of PAN?

Accepted Answer

Introduction / Context: This question uses the standard alphabet-position coding system where each letter is replaced by its position in the alphabet, and the word value is the sum of those positions. You must apply the same method to a new word. Given Data / Assumptions: A=1, B=2, ..., Z=26. Example: HAT = 29. Find PAN using the same rule (sum of letter positions). Concept / Approach: Convert each letter in the word to its alphabetical position and add them. Validate the rule using HAT to confirm that the interpretation is correct. Step-by-Step Solution: First verify HAT: H = 8, A = 1, T = 20 Sum = 8 + 1 + 20 = 29 (matches). Now compute PAN: P = 16 A = 1 N = 14 Sum = 16 + 1 + 14 = 31 Verification / Alternative check: A quick mental check: P(16) and N(14) already total 30, plus A(1) gives 31. This is consistent with the same method used for HAT. Why Other Options Are Wrong: 28: would occur if N is mistaken as 11 or if a letter is skipped. 21: could come from counting letters rather than positions. 41: often from using A=0 or adding extra offsets incorrectly. 33: from misreading P as 18 or N as 16. Common Pitfalls: Using A=0, confusing letter positions, or applying reverse positions (A=26) instead of forward positions are common errors. Final Answer: 31

Question 8

In a certain coded arithmetic, the symbols represent different operations: 'X' means addition (+), '-' means division (/), '/' means subtraction (-), and '+' means multiplication (*). Based on this decoding, which of the following coded equations is…

Accepted Answer

Introduction / Context: This question tests operator substitution and equation validation. The expression uses symbols that do not represent their usual operations. You must decode each equation and check which one becomes true under standard arithmetic rules. Given Data / Assumptions: X means addition (+). - means division (/). / means subtraction (-). + means multiplication (*). After decoding, use standard precedence (*/ before + and -). Concept / Approach: Pick one option at a time, replace each operator with its decoded meaning, then compute the left-hand side. The correct coded equation is the one whose decoded left-hand side equals the right-hand side exactly. Step-by-Step Solution: Check option A: 25+10-5/10X3=43 Decode: + becomes *, - becomes /, / becomes -, X becomes + So LHS becomes: 25 * 10 / 5 - 10 + 3 Compute: 25 * 10 = 250 250 / 5 = 50 50 - 10 + 3 = 43 Decoded LHS equals RHS (43). So option A is correct. Verification / Alternative check: Notice that 25 * 10 / 5 simplifies neatly: it is (25/5)*10 = 5*10 = 50, then 50 - 10 + 3 = 43. This confirms the equality without lengthy work. Why Other Options Are Wrong: Option B: after decoding, the arithmetic does not evaluate to 72. Option C: decoding changes the structure; it will not match 12 under correct precedence. Option D: becomes a different numeric value than 18 when computed correctly. Option E: is a distractor and does not decode to 40. Common Pitfalls: Using the printed symbols as normal, decoding only one or two operators, or performing addition/subtraction before division/multiplication in the decoded equation leads to incorrect selection. Final Answer: 25+10-5/10X3=43

Question 9

In this coding system, two two-digit numbers are combined by interleaving their digits. For example: 53 34 becomes 5334, and 65 46 becomes 6456. Using the same digit-interleaving pattern, what will 75 24 become?

Accepted Answer

Introduction / Context: This question tests pattern recognition in number coding. Two two-digit numbers are being combined into a four-digit output using a consistent arrangement of digits. The goal is to identify that arrangement and apply it to a new pair. Given Data / Assumptions: 53 34 = 5334 65 46 = 6456 Find: 75 24 = ? Assume the same digit placement rule applies to all cases. Concept / Approach: Break each two-digit number into tens and ones digits. Check how the four digits appear in the output. A common pattern is interleaving: first tens digit, then tens digit of second, then ones digit of first, then ones digit of second. Step-by-Step Solution: Take 65 and 46: 65 has digits: 6 (tens), 5 (ones) 46 has digits: 4 (tens), 6 (ones) Output is 6456 = 6,4,5,6 So the rule is: (tens of first), (tens of second), (ones of first), (ones of second). Now apply to 75 and 24: 75 gives 7 (tens), 5 (ones) 24 gives 2 (tens), 4 (ones) Interleave: 7,2,5,4 → 7254 Verification / Alternative check: Check 53 and 34: tens digits 5 and 3, ones digits 3 and 4, giving 5,3,3,4 → 5334. This matches, confirming the same rule, so 7254 is correct. Why Other Options Are Wrong: 7542: keeps first number then reversed second, not interleaving. 7524: concatenates numbers directly. 7452: mixes tens/ones order incorrectly. 7245: swaps the last two digits incorrectly. Common Pitfalls: Concatenating without interleaving, reversing one number, or interleaving in the wrong sequence (ones first instead of tens first) are typical errors. Final Answer: 7254

Question 10

A coding scheme assigns each letter its alphabetical position (A=1, B=2, ..., Z=26) and the coded value of a word is the sum of those positions. For example, I=9 and SLIP=56. Using the same method, what is the value of FALL?

Accepted Answer

Introduction / Context: This question uses alphabet-position coding where each letter is replaced by its position in the alphabet and the word value is obtained by adding these positions. The examples confirm the mapping and the summation rule. Given Data / Assumptions: I = 9 implies alphabetical positions are used. SLIP = 56 is given as an example. Find FALL using the same letter-position sum rule. Concept / Approach: Compute the alphabetical position for each letter in FALL and add them. Use SLIP to verify the interpretation before applying it to the required word. Step-by-Step Solution: Verify SLIP: S=19, L=12, I=9, P=16 Sum = 19 + 12 + 9 + 16 = 56 (matches). Now compute FALL: F = 6 A = 1 L = 12 L = 12 Sum = 6 + 1 + 12 + 12 = 31 Verification / Alternative check: Since L appears twice, you can do 12*2 = 24, then add F and A: 24 + 6 + 1 = 31. This confirms the same result quickly. Why Other Options Are Wrong: 51: comes from using reverse coding or adding extra offsets. 41: often from misreading F as 16 or A as 11. 21: may come from counting letters or using A=0. 29: could come from treating one L incorrectly. Common Pitfalls: Using A=0, confusing positions (L=11 instead of 12), or applying reverse alphabet values can cause wrong sums. Final Answer: 31

Question 11

In a certain code language, the operators are interchanged as follows: '+' means division (/), '−' means multiplication (*), '÷' means addition (+), and '×' means subtraction (-). Using this decoding, find the correct value of: 36×12+4÷6+2−3 = ?

Accepted Answer

Introduction / Context: This question tests symbol interchanging in arithmetic expressions. The printed operators do not carry their usual meaning, so you must first decode them and then evaluate using standard precedence. Accuracy depends on correct replacement at each operator position. Given Data / Assumptions: '+' means division (/). '−' means multiplication (*). '÷' means addition (+). '×' means subtraction (-). After decoding, use normal precedence (*/ before + and -). Concept / Approach: Rewrite the expression by replacing each operator with its decoded operation, maintaining the original operator positions. Then compute the final value normally. Step-by-Step Solution: Original: 36×12+4÷6+2−3 Decode operator by operator: × becomes - : 36 - 12 ... + becomes / : ... 12 / 4 ... ÷ becomes + : ... 4 + 6 ... + becomes / : ... 6 / 2 ... − becomes * : ... 2 * 3 So decoded expression is: 36 - 12 / 4 + 6 / 2 * 3 Compute: 12 / 4 = 3 Compute: 6 / 2 = 3 Compute: 3 * 3 = 9 Now: 36 - 3 + 9 = 42 Verification / Alternative check: After decoding, the middle part becomes -3 + 9 = +6, so 36 + 6 = 42. This quick simplification confirms the computed result. Why Other Options Are Wrong: 18: often from treating + as + instead of /. 6: from reducing the expression incorrectly. 2: from decoding only one operator or ignoring precedence. 12: from incorrect handling of the final multiplication. Common Pitfalls: Mixing up which operator maps to which, evaluating before decoding fully, and ignoring multiplication/division precedence are common mistakes. Final Answer: 42

Question 12

Some equations have been solved using a specific coding pattern. For example: 8x7x6 = 765 and 5x3x2 = 421. Using the same pattern (applied consistently to each number), what will 9x6x4 be equal to?

Accepted Answer

Introduction / Context: This is a number coding pattern problem. The symbol x here is not multiplication; it simply separates three numbers. The output is formed by applying a consistent transformation to each of the three numbers and then writing the results together as a three-digit number. Given Data / Assumptions: 8x7x6 = 765 5x3x2 = 421 Find: 9x6x4 = ? Assume the same transformation is applied to each number individually. Concept / Approach: Compare each input triple with its output. A strong clue is that 8,7,6 become 7,6,5 which looks like each number is reduced by 1. Verify this rule using the second example before applying it to the target triple. Step-by-Step Solution: Check 8x7x6 = 765: 8 decreased by 1 gives 7 7 decreased by 1 gives 6 6 decreased by 1 gives 5 So output becomes 765. Matches. Verify with 5x3x2 = 421: 5-1 = 4, 3-1 = 2, 2-1 = 1 Output 421 matches. Now apply to 9x6x4: 9-1 = 8 6-1 = 5 4-1 = 3 So 9x6x4 = 853 Verification / Alternative check: Since both examples match the same simple decrement-by-1 rule, using it for 9,6,4 is consistent. The output must be 8,5,3 in the same order, giving 853. Why Other Options Are Wrong: 583: rearranges the order incorrectly. 841: uses wrong decrements or mixes digits. 481: looks like subtracting 5,2,3 randomly. 754: would correspond to 8,6,5 not to 9,6,4. Common Pitfalls: Treating x as multiplication, changing the order of numbers, or using different operations for each position rather than a uniform rule are frequent mistakes. Final Answer: 853

Question 13

In a certain code language, the word EXAMPLES is written as EMAXSEPL. This code is formed by rearranging letters in a fixed positional pattern. Using the same rearrangement rule, how will the word BUOYANCY be written in that code language?

Accepted Answer

Introduction / Context: This problem tests letter rearrangement coding-decoding. The letters are not shifted in the alphabet; instead, they are moved to different positions to form the coded output. The example EXAMPLES → EMAXSEPL reveals a consistent positional permutation that must be applied to BUOYANCY. Given Data / Assumptions: EXAMPLES is coded as EMAXSEPL. Both words have 8 letters. The coding rule is a fixed rearrangement of positions (a permutation). Apply the same position pattern to BUOYANCY. Concept / Approach: Label letters of EXAMPLES by position 1 to 8, and then map which original positions appear in the coded word. Once the position order is discovered, apply that same order to BUOYANCY (also 8 letters). Step-by-Step Solution: Write EXAMPLES with positions: 1E 2X 3A 4M 5P 6L 7E 8S Coded word: E M A X S E P L Match each coded letter to its original position: E comes from position 1 M comes from position 4 A comes from position 3 X comes from position 2 S comes from position 8 E comes from position 7 P comes from position 5 L comes from position 6 So the position order is: 1,4,3,2,8,7,5,6. Now write BUOYANCY with positions: 1B 2U 3O 4Y 5A 6N 7C 8Y Apply order 1,4,3,2,8,7,5,6: B, Y, O, U, Y, C, A, N → BYOUYCAN Verification / Alternative check: The same 8-position permutation derived from EXAMPLES must be used unchanged. Applying it cleanly to BUOYANCY yields BYOUYCAN, confirming a consistent positional code rather than any alphabet shift. Why Other Options Are Wrong: CYOUYBAN: begins with C (position 7) instead of position 1. CUYOYBAN: scrambles positions and drops the discovered order. YBANCYOU: resembles a rotation/reversal, not the exact permutation. CUOYYBAN: repeats Y incorrectly and misorders letters. Common Pitfalls: Assuming a reverse, assuming swapping adjacent letters only, or guessing without deriving the exact position order from the example are common errors. Final Answer: BYOUYCAN

Question 14

In a certain coded arithmetic, P denotes multiplication (*), T denotes subtraction (-), M denotes addition (+), and B denotes division (/). Using these meanings and standard arithmetic precedence, find the value of: 28B7P8T6M4 = ?

Accepted Answer

Introduction / Context: This question tests coded operators where letters represent arithmetic operations. The key steps are: translate each letter into its real operation, then evaluate the resulting expression using standard precedence rules. Given Data / Assumptions: P means multiplication (*). T means subtraction (-). M means addition (+). B means division (/). Use standard precedence: division and multiplication before addition and subtraction. Concept / Approach: Rewrite the expression by replacing B, P, T, M with /, *, -, + respectively. Then compute step-by-step, ensuring correct precedence so the result is accurate. Step-by-Step Solution: Expression: 28B7P8T6M4 Replace codes: B → /, P → *, T → -, M → + So it becomes: 28 / 7 * 8 - 6 + 4 Compute division first: 28 / 7 = 4 Then multiplication: 4 * 8 = 32 Now handle subtraction and addition left to right: 32 - 6 = 26 26 + 4 = 30 Verification / Alternative check: Another quick view: 28/7 is small (4), then 4*8 is 32, and (-6+4) is -2, so 32-2 = 30. This confirms the same final value. Why Other Options Are Wrong: 28: happens if you stop after 28/7*8 without finishing operations. 34 or 32: often from adding 6 instead of subtracting, or ignoring precedence. 26: from stopping at 32 - 6 and not adding 4. Common Pitfalls: Doing subtraction before multiplication, misreading B as minus, or calculating strictly left-to-right without precedence can lead to incorrect answers. Final Answer: 30

Question 15

Some equations are solved using a fixed arrangement pattern of the three numbers. For example: 7 x 5 x 6 is written as 576, and 4 x 2 x 5 is written as 245. Using the same number-ordering pattern, what will 8 x 2 x 5 be written as?

Accepted Answer

Introduction / Context: This coding-decoding question uses a rearrangement pattern of three numbers. The symbol x is only a separator, not multiplication. You must identify the order in which the three input numbers are placed to form the three-digit output. Given Data / Assumptions: 7 x 5 x 6 = 576 4 x 2 x 5 = 245 Find: 8 x 2 x 5 = ? Assume the same rearrangement rule applies to all cases. Concept / Approach: Compare the input order with the output digits. In 7,5,6 → 576, the output starts with the middle number 5, then the first number 7, then the last number 6. Verify this with 4,2,5 → 245 before applying it to 8,2,5. Step-by-Step Solution: From 7 x 5 x 6 = 576: Output order is: second, first, third → 5,7,6 Check with 4 x 2 x 5 = 245: Second, first, third → 2,4,5 which matches 245 So the rule is confirmed: write numbers in the order (2nd, 1st, 3rd). Now apply to 8 x 2 x 5: Second = 2, First = 8, Third = 5 So output is 285. Verification / Alternative check: Once the order is confirmed by both examples, no arithmetic is needed. Simply placing the digits as (2nd, 1st, 3rd) for 8,2,5 gives 285 reliably. Why Other Options Are Wrong: 258: keeps original order, not the coded order. 582: starts with third number, not second. 852: begins with first number, which contradicts examples. 528: mixes second and third incorrectly. Common Pitfalls: Treating x as multiplication, guessing a random rearrangement without verifying with both examples, or mixing the positions (like 1st-3rd-2nd) are frequent mistakes. Final Answer: 285

Question 16

If the word PROJECT is coded as KILQVXG using a fixed letter-substitution rule (each letter is replaced by its opposite letter in the alphabet, such as A↔Z, B↔Y, C↔X, etc.), then how will the word EGO be coded using the same opposite-letter (Atbash)…

Accepted Answer

Introduction / Context: This question tests a substitution cipher where each letter is replaced by its opposite letter in the alphabet. This is commonly known as the Atbash pattern: A↔Z, B↔Y, C↔X, ..., M↔N. The example PROJECT → KILQVXG matches this opposite-letter substitution. Given Data / Assumptions: PROJECT is coded as KILQVXG. Rule: each letter maps to its opposite in the alphabet (Atbash). Opposite pairs: A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N. Find the code for EGO. Concept / Approach: Identify that P→K, R→I, O→L, etc., corresponds to opposite-letter mapping. Then apply the same mapping to each letter of EGO in sequence to form the coded word. Step-by-Step Solution: Using opposite-letter mapping: E ↔ V (E is 5th letter, V is 22nd) G ↔ T O ↔ L Now encode EGO: E → V G → T O → L So EGO → VTL. Verification / Alternative check: Check consistency with the example: P becomes K, and O becomes L, which are known opposite pairs. Since the same mapping is used for all letters, EGO must become VTL without any shifting or reordering. Why Other Options Are Wrong: SGD: corresponds to different mapping (like shifting) not opposite-letter substitution. VPU: would imply G→P which is incorrect in Atbash. MJN: does not follow opposite pairs for E, G, O. ETL: keeps E unchanged, breaking the substitution rule. Common Pitfalls: Using + or - shifts instead of opposite mapping, reversing the word order, or mapping using A=0 style offsets can lead to wrong codes. Final Answer: VTL

Question 17

In a certain code language, the operator symbols are redefined as follows: '+' means multiplication (*), '-' means addition (+), 'x' means division (/), and '÷' means subtraction (-). Using this decoding and standard precedence, what is the correct …

Accepted Answer

Introduction / Context: This question checks your ability to decode operator substitutions and then correctly evaluate the resulting arithmetic expression. The symbols shown in the expression do not represent their usual operations, so decoding is mandatory before calculating. Given Data / Assumptions: '+' represents multiplication (*). '-' represents addition (+). 'x' represents division (/). '÷' represents subtraction (-). Use standard precedence after decoding. Concept / Approach: Replace each operator according to the mapping while keeping the operator positions the same. Then evaluate using standard precedence (multiplication/division before addition/subtraction). Step-by-Step Solution: Original: 75 - 5 + 25 ÷ 125 Decode each operator at its position: '-' becomes +, so: 75 + 5 ... '+' becomes *, so between 5 and 25 it becomes: * 25 '÷' becomes -, so between 25 and 125 it becomes: - 125 Decoded expression: 75 + 5 * 25 - 125 Compute multiplication: 5 * 25 = 125 Now: 75 + 125 - 125 = 75 Verification / Alternative check: After decoding, the expression becomes 75 + (125 - 125). Since (125 - 125) = 0, the result must be 75. This provides a quick confirmation. Why Other Options Are Wrong: 10 or 5: come from wrong decoding of + as + or ÷ as /. 3: typically from dividing 75 by something incorrectly. 80: comes from doing 75 + 5 without applying multiplication and subtraction correctly. Common Pitfalls: Evaluating before decoding, ignoring precedence (doing 75+5 first then multiplying), or mixing up which symbol maps to subtraction are common mistakes. Final Answer: 75

Question 18

In a certain coding pattern, the operator "@" acts on two numbers in such a way that 15@7 = 44, 5@4 = 18, and 6@17 = 46. Using the same hidden rule, what is the value of 17@4?

Accepted Answer

Introduction / Context: This verbal reasoning question tests your ability to identify a hidden numerical pattern expressed through a special operator symbol. Instead of using the familiar arithmetic operators like plus or minus, the expression uses the symbol "@", and you must decode the rule from the given examples. Such questions are very common in coding decoding and arithmetic reasoning sections of competitive exams. Given Data / Assumptions: - The operator "@" connects two numbers using a consistent rule. - We are told that 15@7 = 44, 5@4 = 18, and 6@17 = 46. - We must use the same rule to find the value of 17@4. - All calculations are assumed to follow normal arithmetic on whole numbers. Concept / Approach: The key idea is to look for a simple and consistent relationship between the two input numbers and the output. Common patterns include addition, subtraction, multiplication, division, or combinations such as 2 * (a + b), a + 2b, or similar forms. We test different patterns on all given examples and accept only the rule that works perfectly for each pair. Once identified, we apply that rule to the required pair 17 and 4. Step-by-Step Solution: Step 1: Check a simple sum: 15 + 7 = 22, but the result given is 44, which is exactly 2 * 22. Step 2: Test the same rule on the second example: 5 + 4 = 9. Then 2 * (5 + 4) = 2 * 9 = 18, which matches the given 18. Step 3: Test the rule on the third example: 6 + 17 = 23. Then 2 * (6 + 17) = 2 * 23 = 46, which matches the given 46. Step 4: Therefore, the rule is: a@b = 2 * (a + b). Step 5: Apply the rule to 17@4: 17 + 4 = 21, then 2 * 21 = 42. Verification / Alternative check: We have verified the rule against all three examples. Each pair of numbers follows the pattern a@b = 2 * (a + b) without any contradiction. Because three consistent examples support the same rule, it is highly reliable to apply this rule to 17 and 4. No other simple pattern such as a + 2b or 2a + b fits all examples so neatly. Why Other Options Are Wrong: - Option 36 would require 2 * (17 + 4) to be 36, but that would mean 2 * 21 = 36, which is incorrect. - Option 40 suggests a different pattern, but 2 * (17 + 4) is not 40, so it does not follow the deduced rule. - Option 49 does not arise from any simple combination of 17 and 4 that also matches the earlier examples, so it is inconsistent with the pattern. Common Pitfalls: Students often try patterns like a + b, a * b, or a + 2b and may abandon the problem too quickly if these first guesses do not work. Another mistake is to find a rule that fits only one or two examples but not all of them. Always verify your pattern against every given equation before using it to find the unknown value. Final Answer: Using the rule a@b = 2 * (a + b), we get 17@4 = 2 * (17 + 4) = 42. Therefore, the correct answer is 42.

Question 19

In a certain coded arithmetic system, "x" stands for minus, "+" stands for multiplication, "÷" stands for plus, and "-" stands for division. Using this coding, what is the correct value of the expression 175 - 25 ÷ 5 + 2 x 3 + 10?

Accepted Answer

Introduction / Context: This question checks your understanding of coded arithmetic operations, where familiar symbols are reassigned new meanings. Instead of directly using plus, minus, multiplication, and division, the expression uses a coded mapping that you must decode correctly before performing any calculation. Such problems are common in coding decoding and quantitative aptitude sections because they combine symbol interpretation with arithmetic skills. Given Data / Assumptions: - "x" stands for minus (subtraction). - "+" stands for multiplication. - "÷" stands for plus (addition). - "-" stands for division. - The expression to evaluate is 175 - 25 ÷ 5 + 2 x 3 + 10, interpreted using the coded meanings. - Normal arithmetic precedence applies after decoding: division and multiplication before addition and subtraction. Concept / Approach: The key approach is two step. First, rewrite the given expression by replacing each coded operator with its real arithmetic meaning. Second, once the decoded expression is obtained, evaluate it carefully using operator precedence. It is important not to mix up the original printed symbol and its actual mathematical role after decoding. Step-by-Step Solution: Step 1: Start with the given coded expression: 175 - 25 ÷ 5 + 2 x 3 + 10. Step 2: Replace "-" with division, "÷" with plus, "+" with multiplication, and "x" with minus. Step 3: After substitution, the expression becomes: 175 ÷ 25 + 5 * 2 - 3 * 10. Step 4: Apply operator precedence. First compute 175 ÷ 25 = 7. Step 5: Next compute 5 * 2 = 10 and 3 * 10 = 30. Step 6: Now handle addition and subtraction from left to right: 7 + 10 - 30 = 17 - 30 = -13. Verification / Alternative check: We can verify the decoding by rechecking each mapping carefully. Every symbol in the original expression has been replaced according to the statement of the question. Recomputing 175 ÷ 25, 5 * 2, and 3 * 10 clearly gives 7, 10, and 30. Combining them as 7 + 10 - 30 gives -13 consistently. No alternative decoding matches the given mappings, so the result is stable. Why Other Options Are Wrong: - Option 13 ignores the minus sign at the end and treats the result as positive, which is a sign error after 17 - 30. - Option -3 might come from partial calculation such as 7 + 10 - 20, but that does not follow the given expression correctly. - Option 3 is also a result of an incorrect order of operations or wrong decoding of one of the symbols. None of these alternatives respect both the mapping and proper precedence. Common Pitfalls: The most common errors include decoding only some of the symbols, using the printed symbol instead of the described meaning, or forgetting to apply standard operator precedence. Some learners also evaluate strictly from left to right without handling multiplication and division first, which leads to wrong answers. Always decode fully first and then compute carefully. Final Answer: After decoding the operators and evaluating with correct precedence, the value of 175 - 25 ÷ 5 + 2 x 3 + 10 in the coded system is -13.

Question 20

In a certain numerical code, 4 * 2 = 3 and 8 * 4 = 3. Using the same pattern, what is the value of 21 * 7?

Accepted Answer

Introduction / Context: This problem presents an unusual operator, written as "*", which does not follow normal multiplication. Instead, it encodes a special relationship between two numbers. By using the given examples, you must decode the rule and then apply it to a new pair of numbers. Such puzzles test pattern recognition and logical reasoning rather than rote arithmetic. Given Data / Assumptions: - We are given 4 * 2 = 3. - We are also given 8 * 4 = 3. - We must find the value of 21 * 7 under the same rule. - The operator "*" here represents some consistent arithmetic pattern involving the two numbers. Concept / Approach: The idea is to express the result as a function of the two given numbers. Since 4 * 2 and 8 * 4 both equal 3, we look for formulas such as (a + b) / b, (a + b) / a, or (a / b) plus or minus some adjustment. We then verify which expression gives the correct result for both known examples. Once we have a candidate rule that works for both, we apply it to the pair 21 and 7. Step-by-Step Solution: Step 1: Start with 4 * 2 = 3. Compute (4 + 2) / 2 = 6 / 2 = 3. This fits the given result. Step 2: Test the same expression on the second example: (8 + 4) / 4 = 12 / 4 = 3, which again matches the given value. Step 3: Therefore, we conclude that the rule is a * b = (a + b) / b. Step 4: Apply this rule to 21 * 7: (21 + 7) / 7 = 28 / 7 = 4. Step 5: So the correct value of 21 * 7 under this code is 4. Verification / Alternative check: To be sure, we can test other simple formulas. For example, (a + b) / a does not work, because (4 + 2) / 4 = 6 / 4 is not 3. Similarly, (a - b) or (a * b) divided by some number does not provide consistent results for both examples. The formula (a + b) / b is the only simple expression that correctly yields 3 in both given cases and therefore is the most reasonable coded rule. Why Other Options Are Wrong: - Option 3 would be the answer only if the pattern did not change with larger numbers, but (21 + 7) / 7 clearly equals 4, not 3. - Option 8 might come from using direct division 21 / 7 = 3 and then guessing incorrectly, or from mixing up the pattern with normal multiplication. - Option 16 cannot be constructed naturally from (21 + 7) using the pattern that fits the original examples, so it does not follow the consistent rule. Common Pitfalls: Many students assume that "*" always means multiplication and try to force the examples into that framework. Others guess a pattern after checking only one example rather than all of them. The safe strategy is to form a hypothesis from the first example and then rigorously test it on every other example given in the question. Final Answer: Using the decoded rule a * b = (a + b) / b, we obtain 21 * 7 = 4. Thus, the correct answer is 4.

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