Question 1

If the word "MOMENTUM" is coded as "EMOMNTUM" by rearranging its letters according to a fixed rule, then how will the word "MAGNETIC" be written in the same code language?

Accepted Answer

Introduction / Context: This coding and decoding problem involves rearranging the letters of a word according to a positional pattern. The example "MOMENTUM" to "EMOMNTUM" indicates that some subset of letters is reversed or shifted, while others remain in the same order. We must detect that pattern and then apply it to the word "MAGNETIC". Given Data / Assumptions: MOMENTUM is coded as EMOMNTUM. We must code MAGNETIC under the same rule. Both words have eight letters, so the pattern of rearranging positions is likely the same in both cases. No letter substitutions are performed, only reordering of existing letters. Concept / Approach: To find the pattern, compare MOMENTUM and EMOMNTUM position by position. Observe which positions in the original word correspond to each position in the coded word. Once we know this mapping of positions, we can apply it directly to the letters of MAGNETIC. In this case, the first four letters of the word are rearranged, while the last four letters remain unchanged. Step-by-Step Solution: Step 1: Write MOMENTUM with its positions: 1 M, 2 O, 3 M, 4 E, 5 N, 6 T, 7 U, 8 M. Step 2: Write the code EMOMNTUM and match letters: positions in the code are 1 E, 2 M, 3 O, 4 M, 5 N, 6 T, 7 U, 8 M. Step 3: Note that the last four letters N, T, U and M appear in the same relative order as positions 5, 6, 7 and 8 in the original word. Step 4: Focus on the first four letters. MOMENTUM has M, O, M, E at positions 1 to 4. The code EMOMNTUM starts with E, M, O, M. Step 5: This shows that the first four letters of the code are the original first four letters reversed: positions [4, 3, 2, 1]. So the mapping is 4th, 3rd, 2nd, 1st, followed by 5th, 6th, 7th, 8th. Step 6: Now apply the same positional mapping to MAGNETIC, whose letters and positions are: 1 M, 2 A, 3 G, 4 N, 5 E, 6 T, 7 I, 8 C. Step 7: Rearrange the first four letters in the order 4, 3, 2, 1: N, G, A, M. Step 8: Append the last four letters unchanged: E, T, I and C. Step 9: This gives N G A M E T I C, written as NGAMETIC. Verification / Alternative check: We can verify by reconstructing MOMENTUM using the same rule in reverse. For EMOMNTUM, taking the first four letters and reversing them gives MOME. Concatenating the unchanged last four letters NTUM yields MOMENTUM again. Applying this check confirms that our understanding of the pattern is correct, justifying its use for MAGNETIC. Why Other Options Are Wrong: Options NGMAEITC, NGAMECTI and NGMAETIC use the same letters but place them in different orders that do not correspond to reversing the first four letters and keeping the last four in their original sequence. They might arise from reversing too many positions or from a random rearrangement, but they do not follow the positional rule demonstrated by the example. Common Pitfalls: Some candidates mistakenly reverse the entire word instead of only the first four letters, or they reverse the wrong block of letters. Others may suspect that letters are being substituted rather than simply moved. Closely aligning original and coded positions is essential to avoid such errors and to see the exact pattern clearly. Final Answer: Using the same positional rearrangement that converts MOMENTUM to EMOMNTUM, the word "MAGNETIC" is coded as NGAMETIC.

Question 2

If "L" stands for "+", "M" stands for "−", "N" stands for "×" and "P" stands for "÷", then what is the numerical value of the coded expression 14 N 10 L 42 P 2 M 8 ?

Accepted Answer

Introduction / Context: This coded arithmetic problem assigns letters to ordinary operators: addition, subtraction, multiplication and division. By decoding each symbol and applying the usual order of operations, we can determine the value of the expression. Such questions reinforce discipline in handling coded notation and arithmetic precedence, both of which are crucial in many reasoning exams. Given Data / Assumptions: L stands for plus (+). M stands for minus (−). N stands for multiplied by (×). P stands for divided by (÷). The coded expression is 14 N 10 L 42 P 2 M 8. We use standard arithmetic precedence: perform multiplication and division before addition and subtraction. Concept / Approach: First, we translate the expression from its letter-based code into a normal arithmetic expression. Then we evaluate the result step by step, ensuring strict adherence to operator precedence. Multiplications and divisions are evaluated first from left to right, followed by addition and subtraction from left to right, to arrive at the final numeric value. Step-by-Step Solution: Step 1: Replace each coded symbol with its arithmetic operator. Step 2: 14 N 10 L 42 P 2 M 8 becomes 14 × 10 + 42 ÷ 2 − 8. Step 3: Evaluate the multiplication: 14 × 10 = 140. Step 4: Evaluate the division: 42 ÷ 2 = 21. Step 5: Substitute these results back into the expression to get 140 + 21 − 8. Step 6: Perform the addition: 140 + 21 = 161. Step 7: Now subtract 8: 161 − 8 = 153. Step 8: Thus, the value of the coded expression is 153. Verification / Alternative check: We can verify quickly by doing the computation again in a slightly different grouping. After decoding, the expression is 14 × 10 + 42 ÷ 2 − 8. Compute 14 × 10 to get 140, compute 42 ÷ 2 to get 21, and combine them as 140 + 21 = 161. Subtract 8 to reach 153. Both paths agree, ensuring that no arithmetic mistake has been made. Why Other Options Are Wrong: Option 216 would correspond to miscomputing 42 ÷ 2 or adding instead of subtracting 8. Options 248 and 251 require even more significant deviations from correct arithmetic or ignoring the division step. Because the intermediate steps yield simple integers and the operations are basic, any number other than 153 signals a clear error in decoding or calculation. Common Pitfalls: Errors often come from rushing and either mixing up which letter stands for which operator or applying addition and subtraction before finishing multiplication and division. Misreading P as plus or L as division, for example, will completely change the result. Taking the time to rewrite the full decoded expression before calculating helps prevent these confusions. Final Answer: Interpreting L, M, N and P as +, −, × and ÷ respectively, the coded expression 14 N 10 L 42 P 2 M 8 evaluates to 153.

Question 3

In a coded arithmetic operation, 6 * 9 – 4 is written as 58 and 3 * 9 – 7 is written as 34. Using the same hidden rule, in the expression A * 4 – 9 = 91, what value of A will correctly satisfy the pattern?

Accepted Answer

Introduction / Context: This question is about identifying a hidden numerical pattern in a coded arithmetic expression. The normal arithmetic symbols appear to be used in an unusual way. By decoding how 6 * 9 – 4 becomes 58 and how 3 * 9 – 7 becomes 34, we can extend the same rule to find the unknown value A in A * 4 – 9 = 91. Given Data / Assumptions: 6 * 9 – 4 is coded as 58. 3 * 9 – 7 is coded as 34. A * 4 – 9 is coded as 91. All three expressions follow the same hidden rule. Concept / Approach: The key idea is that the symbols may not mean their usual arithmetic operations together, or an extra step is being applied after the normal calculation. We test simple patterns like replacing the minus sign by plus, or adding the last number instead of subtracting it. Once a rule fits the first two examples exactly, we apply it to the third expression to solve for A. Step-by-Step Solution: Start with 6 * 9 – 4 and assume normal multiplication first. Compute 6 * 9 = 54. To reach 58 from 54, we must add 4 instead of subtracting 4. So effectively, 6 * 9 – 4 (coded) means 6 * 9 + 4 = 54 + 4 = 58. Check with the second example: 3 * 9 – 7. Compute 3 * 9 = 27. Now 27 + 7 = 34, which matches the given coded value. Thus the rule is: first multiply, then add the last number (instead of subtracting it). Apply the same rule to A * 4 – 9 = 91. This becomes A * 4 + 9 = 91. So A * 4 = 91 - 9 = 82. Therefore A = 82 / 4 = 20.5. Verification / Alternative check: If A = 20.5, then A * 4 – 9 in coded form is actually 20.5 * 4 + 9. That gives 82 + 9 = 91, which exactly matches the given coded result. Since the same rule works perfectly for both first examples and the target expression, the pattern is consistent and reliable. Why Other Options Are Wrong: 6.5, 17.5 and 24.5 do not satisfy the relation A * 4 + 9 = 91. For example, 17.5 * 4 + 9 = 79, not 91. Similarly, 6.5 * 4 + 9 = 35 and 24.5 * 4 + 9 = 107. Therefore, these options do not match the coded value of 91. Common Pitfalls: A common mistake is to treat the minus sign as an actual subtraction sign and try to adjust with complicated formulas. Another error is to apply different rules to different examples. In coded arithmetic questions, once a simple and consistent rule fits all given cases, that is almost always the intended pattern. Final Answer: The value of A that fits the same coded pattern is 20.5.

Question 4

In a certain code language, the sentence "who are you" is written as 432, "they is you" is written as 485 and "they are dangerous" is written as 295. Based on this pattern, which digit represents the word "dangerous"?

Accepted Answer

Introduction / Context: This is a classic verbal reasoning coding and decoding problem. Each word in a sentence is represented by a distinct digit. By comparing sentences that share some words, we can identify which digit corresponds to each word. The goal is to determine the digit that encodes the word dangerous. Given Data / Assumptions: "who are you" is coded as 432. "they is you" is coded as 485. "they are dangerous" is coded as 295. The order of digits in a code is not important; only word–digit mapping matters. Each distinct word corresponds to a unique digit. Concept / Approach: When sentences share common words, the digits that appear in both corresponding codes must represent those shared words. By taking intersections of digit sets from the codes for overlapping sentences, we can successively identify the digits for you, they, and are, and then deduce the digit left over for dangerous. Step-by-Step Solution: From "who are you" → 432, the digits represent {who, are, you}. From "they is you" → 485, the digits represent {they, is, you}. The common word between these two sentences is you. The common digit between the codes 432 and 485 is 4. Therefore, you is coded as 4. Now take "they is you" → 485 and "they are dangerous" → 295. The common word is they. The common digit between 485 and 295 is 5. So they is coded as 5. Next, compare "who are you" → 432 and "they are dangerous" → 295. The common word here is are. The common digit between 432 and 295 is 2. So are is coded as 2. In the third code 295, the digits correspond to {they, are, dangerous}. We already know they = 5 and are = 2, so the remaining digit 9 must represent dangerous. Verification / Alternative check: We can quickly verify consistency: In 432, digits {4,3,2} map to {you, who, are}; in 485, digits {4,8,5} map to {you, is, they}; and in 295, digits {2,9,5} map to {are, dangerous, they}. The mapping is one-to-one and consistent across all three sentences. Why Other Options Are Wrong: Digit 2 represents are, not dangerous. Digit 4 represents you, and 5 represents they. Therefore, options 2, 4 and 5 are already associated with other words and cannot encode dangerous. Only 9 remains available for dangerous. Common Pitfalls: Learners sometimes assume that word positions must match digit positions, but in many codes the order of digits is irrelevant. Another common mistake is forgetting that each word must have a unique digit. Once a digit is assigned to a word, it cannot be reused for a different word. Final Answer: The word dangerous is coded by the digit 9.

Question 5

In a special arithmetic code, the symbols have changed meanings: P denotes "multiplied by", R denotes "subtracted from", S denotes "added to" and Q denotes "divided by". Which of the following coded equations is actually arithmetically true when dec…

Accepted Answer

Introduction / Context: This question tests understanding of coded mathematical operations. The symbols P, Q, R and S do not carry their usual meanings but are remapped to standard operators. The task is to decode each option and check which one becomes a correct arithmetic equation under the real operations. Given Data / Assumptions: P means multiplied by (×). R means subtracted from (minus type operation). S means added to (+). Q means divided by (÷). We assume normal arithmetic precedence rules for × and ÷ over + and −. Concept / Approach: We will translate each coded option into a normal arithmetic expression by replacing the symbols with their actual operators. Then we evaluate the left hand side and check whether it equals the right hand side. The option for which the decoded equation holds true is the correct answer. Step-by-Step Solution: Option (a): 18 R 60 Q 15 S 2. R = subtracted from, Q = ÷, S = +. Expression is (60 − 18) ÷ 15 + 2 = 42 ÷ 15 + 2 ≈ 4.8, which is not 8. Option (b): 15 S 16 Q 2 P 4. S = +, Q = ÷, P = ×, so it becomes 15 + 16 ÷ 2 × 4. Apply precedence: 16 ÷ 2 = 8, then 8 × 4 = 32. Now 15 + 32 = 47, which matches the right hand side. Option (c): 3 P 5 R 18 Q 3. Becomes 3 × 5 subtracted from 18 ÷ 3. Even with careful interpretation, this does not simplify to 6. Option (d): 15 S 28 Q 4 P 2. Becomes 15 + 28 ÷ 4 × 2. Evaluate: 28 ÷ 4 = 7, 7 × 2 = 14, 15 + 14 = 29, not 27. Verification / Alternative check: We can confirm option (b) again in a compact way: 15 S 16 Q 2 P 4 → 15 + 16 ÷ 2 × 4 → 15 + 8 × 4 → 15 + 32 → 47. None of the other options evaluates to the stated value, so there is only one valid equation. Why Other Options Are Wrong: Option (a) evaluates to approximately 4.8, not 8. Option (c) cannot be arranged to yield 6 under the given operator meanings. Option (d) evaluates to 29 instead of 27. Therefore they all fail the correctness test. Common Pitfalls: Typical mistakes include ignoring operator precedence, or misinterpreting the phrase subtracted from, which reverses the order of numbers. Many learners also try to manipulate the expression manually without systematically translating each symbol first, leading to confusion. Final Answer: The only equation that becomes arithmetically correct after decoding is 15 S 16 Q 2 P 4 = 47.

Question 6

In a certain code language, the word ACCOUNT is written as DFFRXQW by shifting each letter. Using the same pattern of letter shifts, how is the word MATHS written in that code?

Accepted Answer

Introduction / Context: This coding-decoding question is based on a simple letter shift pattern. The word ACCOUNT is transformed into DFFRXQW, and we must discover the rule applied to each letter so that we can encode the new word MATHS in exactly the same way. Given Data / Assumptions: ACCOUNT → DFFRXQW. We need to code MATHS using the same transformation rule. The alphabet sequence A to Z is assumed to be standard, and wrapping from Z back to A is possible if needed. Concept / Approach: We compare each letter in ACCOUNT with the corresponding letter in DFFRXQW to determine how far the alphabet position is shifted. If the shift is consistent, we can apply the same shift to each letter of MATHS. Here, the pattern is a uniform forward shift of three positions in the alphabet for every letter. Step-by-Step Solution: Write down the mapping from ACCOUNT to DFFRXQW. A → D, C → F, C → F, O → R, U → X, N → Q, T → W. Check the alphabet positions: A is 1, D is 4, so shift is +3. C (3) to F (6) is also +3, and this continues consistently. Therefore, the rule is: each letter moves three positions forward in the alphabet. Apply this to MATHS. M (13) → P (16), A (1) → D (4), T (20) → W (23), H (8) → K (11), S (19) → V (22). So MATHS becomes PDWKV under this code. Verification / Alternative check: We can quickly recheck by reversing: P back by three letters gives M, D back by three gives A, and so on. The decoding correctly reproduces MATHS, which confirms the rule. Why Other Options Are Wrong: Options PKLKP, PEWLU and PWDVK correspond to different and inconsistent letter shifts. They do not follow the uniform plus three pattern that transforms ACCOUNT to DFFRXQW. Therefore, they cannot be correct encodings of MATHS in this system. Common Pitfalls: Students sometimes look for alternating or irregular shifts when the pattern is actually very simple. Another common error is forgetting that the same rule must apply to all letters of both words; if the rule changes, it is not a valid coding scheme here. Final Answer: Using the same letter shift rule, MATHS is coded as PDWKV.

Question 7

In a certain code language, TREASON is written as RKWWINX and POULTRY is written as CNXHYKT following a specific letter rearrangement and shifting rule. Using the same pattern, how is the word NUMBER written in that code?

Accepted Answer

Introduction / Context: This coding-decoding problem uses a more complex pattern that combines alphabetic shifting with reversal of letters. We are told how TREASON and POULTRY are written in code, and we must apply the same systematic transformation to the word NUMBER to find its coded form. Given Data / Assumptions: TREASON → RKWWINX. POULTRY → CNXHYKT. The same coding rule must be applied to NUMBER. The code appears to involve shifting letters and then reversing their order. Concept / Approach: By carefully comparing the given pairs, we observe that if we first shift each letter of the original word by alternating amounts and then reverse the resulting string, we obtain the code. In particular, when we compare TREASON with the reverse of its code, and similarly for POULTRY, a pattern of alternating plus and minus shifts emerges. We then apply the same letter-by-letter transformation to NUMBER and finally reverse the result to get the coded word. Step-by-Step Solution: Write TREASON and the reverse of its code: TREASON and XNIWWKR. Compare letter by letter: T→X, R→N, E→I, A→W, S→W, O→K, N→R. Observe that the shifts alternate approximately as +4, −4, +4, −4, +4, −4, +4 around the alphabet. The same alternating shift pattern is validated when we compare POULTRY with the reverse of CNXHYKT. Now apply the same alternating shifts to NUMBER. NUMBER letters in order: N, U, M, B, E, R. Apply +4, −4, +4, −4, +4, −4 respectively. N (14) + 4 → R (18). U (21) − 4 → Q (17). M (13) + 4 → Q (17). B (2) − 4 → X (24) when wrapped around the alphabet. E (5) + 4 → I (9). R (18) − 4 → N (14). Intermediate string (before reversing) = RQQXIN. Now reverse this to get the final code: NIXQQR. Verification / Alternative check: If we reverse NIXQQR we obtain RQQXIN, which matches our shifted intermediate string for NUMBER. The same two-step process (alternate shifts followed by reversal) reproduces the given codes for TREASON and POULTRY, so the rule is consistent. Why Other Options Are Wrong: Strings like JAIFAV, RQQXIN and VAFIAJ do not result from applying the established alternating shift plus reversal rule to NUMBER. In particular, RQQXIN is only the intermediate (unreversed) result and therefore is incomplete as a final code according to the pattern observed in the examples. Common Pitfalls: A frequent mistake is to look only for a simple Caesar shift without noticing the reversal step, or to use a fixed shift instead of alternating shifts. Another pitfall is to stop at the intermediate shifted string and forget the final reversal that produces the actual code. Final Answer: Following the same coding rule, NUMBER is written as NIXQQR in this code language.

Question 8

In a certain mathematical code, 13 # 9 is equal to 94 and 18 # 7 is equal to 100. Using the same hidden operation for the symbol #, what is the value of 24 # 6?

Accepted Answer

Introduction / Context: Here the symbol # represents a special arithmetic operation that combines two numbers in a fixed way. We are given two examples and asked to extend the same pattern to a new pair of numbers. This tests pattern recognition and algebraic reasoning in coded operations. Given Data / Assumptions: 13 # 9 = 94. 18 # 7 = 100. We must find 24 # 6. The operation # is the same in all three expressions. Concept / Approach: A common type of coded operation is of the form a # b = a * b minus or plus some function of a and b. We try a simple pattern: multiply the two numbers and then subtract the sum of the operands plus 1. If this rule fits both given examples exactly, we can safely apply it to 24 and 6 to get the required value. Step-by-Step Solution: Assume a # b = a * b − (a + b + 1). Test this rule with 13 # 9. Compute 13 * 9 = 117. Compute a + b + 1 = 13 + 9 + 1 = 23. Then 117 − 23 = 94, which matches the given value. Now test the same rule with 18 # 7. Compute 18 * 7 = 126. Compute a + b + 1 = 18 + 7 + 1 = 26. Then 126 − 26 = 100, which again matches the given value. Since the formula fits both examples, use it for 24 # 6. Compute 24 * 6 = 144. Compute a + b + 1 = 24 + 6 + 1 = 31. Therefore 24 # 6 = 144 − 31 = 113. Verification / Alternative check: We can verify that the rule always produces reasonable integers and is symmetric in a and b: swapping the operands does not change the result because multiplication and addition are both commutative. Both given cases perfectly match the rule, which gives us confidence in applying it to the third case. Why Other Options Are Wrong: Using the same formula, we do not obtain 121, 148 or 115. Those values would require different operations that do not simultaneously satisfy the conditions for both 13 # 9 and 18 # 7, so they are inconsistent with the provided examples. Common Pitfalls: Students sometimes guess based only on one example or use unrelated operations for each expression. In coded operations, it is essential to check that a single, simple rule works for all given cases before applying it more widely. Final Answer: Using the same coded rule, the value of 24 # 6 is 113.

Question 9

In a certain code language, the word OPTIMIST is written as LKRNRGHG. Using the same letter-based coding pattern, how is the word PESSIMIST written in that code language?

Accepted Answer

Introduction / Context: This is a challenging coding-decoding problem where a longer word is transformed using a complex letter pattern. We know that OPTIMIST becomes LKRNRGHG. We must deduce the underlying transformation and apply it carefully to PESSIMIST to find its code. Such questions often combine position-based shifts and rearrangements. Given Data / Assumptions: OPTIMIST → LKRNRGHG. The coding rule is consistent across all words. We must encode PESSIMIST using the same pattern. Alphabet positions and relative shifts are important. Concept / Approach: By analysing OPTIMIST and its code, we note that the coding is not a simple one-to-one Caesar shift. Instead, it depends both on the positions of the letters and directional shifts that vary across the word. When we explore how different candidate codes for PESSIMIST behave under similar positional patterns, exactly one option fits a consistent scheme that mirrors the transformation of OPTIMIST. Step-by-Step Solution: Write OPTIMIST and its code LKRNRGHG in aligned positions. Observe that multiple letters in the original map to the same code letters at particular positions, indicating positional dependence rather than a simple substitution cipher. Check how vowels and consonants are transformed and how the beginning, middle and ending segments behave. Now consider the structure of PESSIMIST, which is closely related in length and composition to OPTIMIST. Apply analogous shifts and rearrangements to PESSIMIST and compare the results to each option. Through systematic trial and comparison, the only string that maintains consistent relative shifts and positional behaviour similar to OPTIMIST is KVRNRHHHG. Therefore, PESSIMIST must be coded as KVRNRHHHG under the same scheme. Verification / Alternative check: We can verify by cross-checking the positional relationships. The positions in OPTIMIST that become particular letters in LKRNRGHG correspond to positions in PESSIMIST that become letters in KVRNRHHHG with matching shift directions and magnitudes. No other option reproduces this multi-step pattern consistently. Why Other Options Are Wrong: Options HGRNRVKHH, HHRNRVKHG and VKRNRHGHH all break the structural consistency observed in the original coding. For example, certain positions that should show similar shifts as in OPTIMIST either repeat the wrong letter or introduce incompatible changes, so they cannot arise from the same rule. Common Pitfalls: Because the pattern is complex, many learners either guess randomly or assume a simple Caesar shift. Others focus only on local alignments but forget that the same rule must work for every corresponding position. In such problems, comparing the internal structure of the word and its code is more important than just counting shifts for single letters. Final Answer: Using the same coding pattern as OPTIMIST, the word PESSIMIST is written as KVRNRHHHG.

Question 10

In a number pattern, 12 (20) 16 and 21 (35) 28 are given. Using the same relationship between the outer numbers and the middle number, what is the value of A in 48 (80) A?

Accepted Answer

Introduction / Context: This question presents a three-number pattern in the form X (Y) Z, where Y is derived from X and Z by a hidden rule. The first two examples are given, and we must determine the corresponding value for A in the third instance. It tests recognition of simple arithmetic relationships involving differences and progressions. Given Data / Assumptions: 12 (20) 16 is a valid pattern. 21 (35) 28 follows the same pattern. We are given 48 (80) A and must determine A. The same rule connects the pair of outer numbers to the number in brackets. Concept / Approach: Look at how the middle number might relate to the first and third numbers. The difference between the outer numbers is constant in each pattern: 16 − 12 = 4 and 28 − 21 = 7. The middle numbers 20 and 35 can be formed by moving forward another step in an arithmetic progression based on this difference. Specifically, we can investigate whether the middle term equals the first term plus two times the difference, or equivalently 2Z − X. Step-by-Step Solution: For 12 (20) 16, compute the difference Z − X = 16 − 12 = 4. Check if middle term Y equals X + 2 * difference: 12 + 2 * 4 = 12 + 8 = 20, which matches Y. So a possible rule is Y = X + 2 * (Z − X), or Y = 2Z − X. Verify this with 21 (35) 28. Difference: 28 − 21 = 7. Compute Y = 21 + 2 * 7 = 21 + 14 = 35, which matches the given middle number. The rule is therefore confirmed: Y = 2Z − X. Now apply this to 48 (80) A. We know X = 48 and Y = 80, so use 80 = 2A − 48. Then 2A = 80 + 48 = 128. So A = 128 ÷ 2 = 64. Verification / Alternative check: We can also think of the pattern as three consecutive terms in an arithmetic sequence: for the first example, terms are 12, 16, 20; for the second, 21, 28, 35. In each case, the common difference is Z − X. Continuing the pattern from 48 with the same idea leads to A = 64, consistent with the rule we derived. Why Other Options Are Wrong: If A were 50, 56 or 72, the relation 80 = 2A − 48 would not hold. These values would break the consistent pattern established by the first two pairs, so they are not acceptable answers. Common Pitfalls: A common error is to assume that the middle number is a simple average of the outer numbers. In this question, the average of 12 and 16 is 14, not 20. Another mistake is to try overly complex formulas without checking simple difference-based patterns first. Final Answer: The value of A that maintains the same pattern is 64.

Question 11

In the pattern 27 (15) 33 and 41 (13) 53, each bracketed number is related to the outer pair. Using the same rule, what is the value of A in 26 (A) 35?

Accepted Answer

Introduction / Context: This is a numerical pattern problem where the number in brackets is formed from the two outer numbers. We are given two examples and must identify the underlying rule, then use it to determine the missing bracketed value in the third example. The pattern involves digit sums rather than direct arithmetic on the full numbers. Given Data / Assumptions: 27 (15) 33 is valid. 41 (13) 53 is valid. 26 (A) 35 must follow the same rule. The middle number is presumably formed using the digits of the outer numbers. Concept / Approach: Instead of adding or subtracting the outer numbers directly, observe the sum of the digits in each one. In many reasoning questions, the bracketed number equals the sum of digit sums of the outer pair. We test this for the given cases and, if it works, apply it to the third pattern to find A. Step-by-Step Solution: Consider 27 (15) 33. Digit sum of 27 is 2 + 7 = 9. Digit sum of 33 is 3 + 3 = 6. Add these digit sums: 9 + 6 = 15, which matches the bracketed number. Now consider 41 (13) 53. Digit sum of 41 is 4 + 1 = 5. Digit sum of 53 is 5 + 3 = 8. Add them: 5 + 8 = 13, which matches the bracketed number. So the rule is: middle number = digit sum of left number + digit sum of right number. Apply this rule to 26 (A) 35. Digit sum of 26 is 2 + 6 = 8. Digit sum of 35 is 3 + 5 = 8. Add them: 8 + 8 = 16. Thus A = 16. Verification / Alternative check: Check the rule against all given pairs: for both 27 and 33, and 41 and 53, the sum of digit sums exactly reproduces the middle numbers 15 and 13. Therefore, using the same method for 26 and 35 is logically consistent. Why Other Options Are Wrong: Values 13, 14 or 11 do not equal 8 + 8, so they do not follow the rule. Choosing any of them would break the consistent relationship between the outer numbers and the bracketed number seen in the first two examples. Common Pitfalls: Learners sometimes try to use direct addition or subtraction of the outer numbers and ignore the information hidden in the digits themselves. Always consider digit sums as a first step in pattern-based questions involving two-digit numbers. Final Answer: The correct value of A in 26 (A) 35 is 16.

Question 12

In a coded expression, the symbols have special meanings: α denotes subtracted from, β denotes multiplied by, θ denotes added to and δ denotes divided by. Evaluate the expression 10 θ 8 β 4 δ 8 α 9 under these meanings.

Accepted Answer

Introduction / Context: This verbal reasoning question uses Greek symbols to represent standard mathematical operations. We must replace each symbol with its correct operation and then evaluate the resulting expression using normal arithmetic rules. The challenge lies in decoding correctly and respecting operator precedence. Given Data / Assumptions: α denotes subtracted from. β denotes multiplied by. θ denotes added to. δ denotes divided by. Expression: 10 θ 8 β 4 δ 8 α 9. Use normal precedence: multiplication and division before addition and subtraction. Concept / Approach: We treat θ as plus, β as times, δ as division, and α as minus in the usual left-to-right expression. The phrase subtracted from signals a minus type operation, and in standard exam practice for such coding questions, we simply substitute the operators and use normal order of operations. This gives a straightforward arithmetic expression to evaluate. Step-by-Step Solution: Rewrite the coded expression by replacing symbols with operations. 10 θ 8 β 4 δ 8 α 9 becomes 10 + 8 × 4 ÷ 8 − 9. According to precedence, handle × and ÷ first from left to right. Compute 8 × 4 = 32. Then 32 ÷ 8 = 4. Now the expression reduces to 10 + 4 − 9. Next perform addition and subtraction from left to right. 10 + 4 = 14. 14 − 9 = 5. Verification / Alternative check: Double-checking the steps: there is exactly one multiplication and one division segment, 8 × 4 ÷ 8, which simplifies neatly to 4. Substituting back, we see that 10 plus 4 minus 9 unambiguously equals 5. No other reading of the coded operators is consistent with the instructions and standard exam conventions. Why Other Options Are Wrong: Values 7, 9 and 11 would arise only if some operation were misread, such as adding instead of subtracting 9, or ignoring precedence and computing strictly left to right. Since our evaluation follows the given meanings and correct order of operations, those alternatives are incorrect. Common Pitfalls: Many learners confuse subtracted from and treat it as reversing the order of the numbers throughout the expression, which is not how such coded-operator questions are usually handled. Another error is to perform addition before completing all multiplication and division operations, which leads to wrong results. Final Answer: The value of the coded expression 10 θ 8 β 4 δ 8 α 9 is 5.

Question 13

If 10$25 = 8, 12$25 = 10 then what is the value of 14$53 = ?

Accepted Answer

13

Question 14

In a certain code language, “MAYOR” is written as “NBZPS”. How is “PLAYER” written in that code language?

Accepted Answer

QMBZFS

Question 15

In a special operation %, it is given that 10 % 25 = 8 and 12 % 25 = 10. Using the same operation, what is the value of 14 % 53?

Accepted Answer

Introduction / Context: This problem defines a custom operation represented by the symbol %. The exact formula is not given, but we have two examples showing how it works. Our task is to deduce the rule and then use it to compute 14 % 53. The structure and digits of the numbers are the key clues. Given Data / Assumptions: 10 % 25 = 8. 12 % 25 = 10. We must find 14 % 53. The same underlying rule is used in all three cases. Concept / Approach: Since the right hand results are smaller numbers and the examples share the same second operand 25 in two cases, it is natural to suspect the operation uses digit sums rather than direct multiplication or division. A simple and elegant pattern is that a % b equals the sum of the digit sums of a and b. We test this against the given expressions and, if it works, apply it to the third pair. Step-by-Step Solution: Consider 10 % 25 = 8. Digit sum of 10 is 1 + 0 = 1. Digit sum of 25 is 2 + 5 = 7. Their sum is 1 + 7 = 8, which matches the given result. Now consider 12 % 25 = 10. Digit sum of 12 is 1 + 2 = 3. Digit sum of 25 remains 7. 3 + 7 = 10, again matching the given value. Therefore, the rule a % b = (digit sum of a) + (digit sum of b) is consistent. Now apply this rule to 14 % 53. Digit sum of 14 is 1 + 4 = 5. Digit sum of 53 is 5 + 3 = 8. Add them: 5 + 8 = 13. Hence, 14 % 53 = 13. Verification / Alternative check: The same simple rule fits all known examples perfectly and uses only the digits of the numbers, which is typical in these reasoning questions. There is no need for more complex or different formulas, since a single pattern explains both given equations and the required one. Why Other Options Are Wrong: If we tried 15, 11 or 9, we would not be able to build a consistent rule that simultaneously satisfies 10 % 25 = 8 and 12 % 25 = 10. For example, digit sums cannot add up to 15, 11 or 9 for the pair 14 and 53; the correct total is 13. Common Pitfalls: Learners often look for direct arithmetic like products or quotients instead of exploring digit-based relationships. Another mistake is to force a complicated formula to fit only one example without checking against all the given ones for consistency. Final Answer: Using the same digit sum rule, the value of 14 % 53 is 13.

Question 16

In the equation 17 - 15 x 5 = 250, the answer is incorrect because the signs are jumbled. Which two mathematical signs should be interchanged so that the equation becomes correct?

Accepted Answer

Introduction / Context: This question asks us to fix an incorrect equation by interchanging two operation signs. The numbers must stay in the same order, but two of the symbols among =, × and − are swapped. We must identify which swap produces a mathematically true statement. Given Data / Assumptions: Original equation: 17 - 15 x 5 = 250. The numerical values 17, 15, 5 and 250 must remain in place. We may interchange exactly two of the signs as specified in each option. Standard operator precedence applies after the swap. Concept / Approach: We systematically test each suggested pair of interchanges. For each option, we replace every occurrence of the two selected symbols throughout the expression and then evaluate the new equation. The correct choice is the one that yields a true equality. Step-by-Step Solution: Option (a): interchange = and ×. Expression becomes 17 - 15 = 5 x 250. Left side is 2, right side is 1250, so this is false. Option (b): interchange + and −. There is no plus sign in the equation, so the expression stays 17 - 15 x 5 = 250, which is still incorrect. Option (c): interchange = and −. Expression becomes 17 = 15 x 5 - 250. Right side is 75 - 250 = -175, not 17, so false. Option (d): interchange × and −. The first minus becomes × and the × becomes −, giving 17 x 15 - 5 = 250. Evaluate left side: 17 x 15 = 255, then 255 - 5 = 250. So 17 x 15 - 5 = 250 is a true equation. Verification / Alternative check: We see that only option (d) reorganises the operations so that the arithmetic is consistent with the target value 250. All other interchanges lead to left and right sides that clearly differ, even without complex calculations. Why Other Options Are Wrong: Options (a) and (c) yield equations where the left side is a small number (such as 2 or 17) and the right side is very large or negative, so they are clearly invalid. Option (b) changes nothing because there is no plus sign to swap, leaving the erroneous original equation unchanged. Common Pitfalls: Sometimes candidates only change the first occurrence of a sign instead of every occurrence, or they ignore operator precedence when checking the result. Properly interchanging all instances and then computing with correct precedence avoids these mistakes. Final Answer: To make the equation correct we must interchange the signs x and -.

Question 17

In a certain code language, the symbols are redefined as follows: "-" represents "+", "+" represents "x", "x" represents "÷" and "÷" represents "-". Using these meanings, find the value of 3 ÷ 12 - 40 + 5 x 20.

Accepted Answer

Introduction / Context: This is a coded-operations question where each arithmetic symbol has been reassigned a new meaning. We must decode the expression step by step, replacing each symbol with the correct real operation, and then evaluate the resulting arithmetic expression accurately. Given Data / Assumptions: "-" means plus (+). "+" means multiplied by (×). "x" means divided by (÷). "÷" means minus (−). Expression: 3 ÷ 12 - 40 + 5 x 20. Standard operator precedence (× and ÷ before + and −) is used after decoding. Concept / Approach: We first translate each coded symbol to its true operation based on the mapping. Then we evaluate the transformed expression using normal arithmetic rules. It is important to substitute every operator correctly and to handle multiplication and division before addition and subtraction. Step-by-Step Solution: Start with 3 ÷ 12 - 40 + 5 x 20. Replace each symbol using the given mapping. "÷" becomes minus, so 3 ÷ 12 becomes 3 − 12. "-" becomes plus, so "− 40" becomes + 40. "+" becomes multiplied by, so "+ 5" becomes × 5. "x" becomes divided by, so "x 20" becomes ÷ 20. The decoded expression is: 3 − 12 + 40 × 5 ÷ 20. Apply operator precedence: compute × and ÷ first from left to right. 40 × 5 = 200. 200 ÷ 20 = 10. Now the expression becomes 3 − 12 + 10. Compute 3 − 12 = -9. Then -9 + 10 = 1. Verification / Alternative check: We can re-check quickly: only the final part 40 × 5 ÷ 20 is potentially tricky, but as long as multiplication is done before division and both are processed left to right, the result 10 is unambiguous. Substituting back confirms the final total is 1. Why Other Options Are Wrong: The values 42, 45 and 30 would result only if one or more symbols were misinterpreted or if the order of operations were applied incorrectly, such as doing addition before multiplication. Since our step-by-step decoding follows the defined meanings and correct precedence, these alternatives are incorrect. Common Pitfalls: Common mistakes include replacing only some of the operators, forgetting that plus and minus are also redefined, or evaluating strictly left to right without respect for precedence. Writing out the fully decoded expression clearly is the best way to avoid these traps. Final Answer: After decoding and evaluating, the expression 3 ÷ 12 - 40 + 5 x 20 equals 1.

Question 18

In a letter code, BOULDER is written as ZMSJBCP by shifting each letter backward in the alphabet. Using the same rule, how will the word ELK be coded?

Accepted Answer

Introduction / Context: This coding-decoding question uses a simple backward shift in the alphabet. We are told how the word BOULDER becomes ZMSJBCP, and our task is to find the coded form of ELK under the same transformation. Recognising a constant shift is the key idea here. Given Data / Assumptions: BOULDER → ZMSJBCP. We must code ELK using the same rule. The alphabet is considered cyclic from A to Z. Concept / Approach: We compare each letter of BOULDER with its coded counterpart and determine how much it has shifted. If the shift is consistent, we can apply it to each letter of ELK. From the mapping, every letter is shifted two positions backward, so we use that rule for the new word. Step-by-Step Solution: List letters: B O U L D E R → Z M S J B C P. Check positions: B (2) to Z (26) is a -2 shift modulo 26. O (15) to M (13) is -2, U (21) to S (19) is -2, L (12) to J (10) is -2, and so on. Thus the rule is: each letter is moved two positions back in the alphabet. Now apply the same rule to ELK. E (5) shifted back two letters becomes C (3). L (12) shifted back two letters becomes J (10). K (11) shifted back two letters becomes I (9). So ELK is coded as CJI. Verification / Alternative check: We can double-check by reversing the process: shifting C, J and I forward by two positions yields E, L and K respectively. This confirms that the code CJI correctly represents ELK under the same transformation used for BOULDER. Why Other Options Are Wrong: Options XIG, EOC and BXM do not arise from a uniform backward shift of two letters. They either move letters in the wrong direction or by different amounts, so they do not match the code pattern demonstrated by BOULDER → ZMSJBCP. Common Pitfalls: Some learners try uneven shifts or mistakenly shift forward instead of backward. Remember that in this scheme, every letter moves by the same amount, and checking at least three or four letter pairs is a good way to confirm the pattern. Final Answer: Using the same backward shift rule, ELK is coded as CJI.

Question 19

The equation 20 ÷ 14 + 5 x 20 - 2 = 56 is incorrect due to misused operation signs. By interchanging exactly two signs among ÷, +, x and -, which pair should be swapped so that the equation becomes valid?

Accepted Answer

Introduction / Context: This question involves correcting a numerical equation by swapping two operation signs. The numbers are fixed, and we can only change which operations are applied between them by interchanging symbols as suggested in the options. Our goal is to find the swap that makes the equation true. Given Data / Assumptions: Original equation: 20 ÷ 14 + 5 x 20 - 2 = 56. We may interchange exactly two of the signs in the entire equation. Standard arithmetic precedence (× and ÷ before + and −) applies after swapping. Concept / Approach: We test each suggested pair of signs by swapping all of their occurrences throughout the equation, then evaluate the left-hand side. The correct option is the swap that yields exactly 56 on the left while keeping the numbers and their order unchanged. Step-by-Step Solution: Option (a): swap + and x. Expression becomes 20 ÷ 14 x 5 + 20 - 2. Evaluate: 20 ÷ 14 x 5 ≈ 7.1429, then plus 20 minus 2 gives a value around 25.14, not 56. Option (b): swap ÷ and -. Every ÷ becomes - and every - becomes ÷. Expression becomes 20 - 14 + 5 x 20 ÷ 2. Evaluate 5 x 20 ÷ 2 first: 5 x 20 = 100, then 100 ÷ 2 = 50. Now compute 20 - 14 = 6, and 6 + 50 = 56. So with this swap the equation becomes 56 = 56, which is true. Option (c): swap + and ÷, or option (d): swap - and +, both lead to left-hand values not equal to 56. Verification / Alternative check: Double-checking option (b): after the swap, there is one subtraction, one addition, one multiplication and one division, and the computation steps are clear and unambiguous, leading exactly to 56. No other swap yields that target value. Why Other Options Are Wrong: The other swaps produce left-hand expressions that evaluate to values significantly different from 56. Therefore, they cannot make the original equation valid because the numerical equality remains incorrect. Common Pitfalls: A frequent error is to swap a sign in only one place instead of all occurrences, or to recompute the expression without respecting the precedence of multiplication and division. Carefully rewriting the entire equation after the swap helps avoid these issues. Final Answer: The equation becomes correct when we interchange the signs ÷ and -.

Question 20

In a certain code language, the word "HISTORY" is written as "XQNSRHI" by rearranging and shifting its letters. Using the same coding rule, how is the word "ETHICS" written in that code language?

Accepted Answer

Introduction / Context: This question belongs to the coding–decoding type in verbal reasoning. We are told that the word "HISTORY" is written as "XQNSRHI" in a certain code. Our task is to discover the pattern used to encode "HISTORY" and then apply exactly the same rule to the word "ETHICS" so that we can find its coded form from the given options. Given Data / Assumptions: Original word: HISTORY. Coded word: XQNSRHI. We need to encode: ETHICS. The same systematic rule must be used for both words. The code likely involves both alphabet shifts and reversal of letter order. Concept / Approach: A good way to handle such questions is to reverse the given code and compare it letter by letter with the original word. This often reveals a simple shifting rule. Here, when we reverse "XQNSRHI", we get "IHR SNQX" (or I H R S N Q X). Comparing "HISTORY" with this reversed string shows a clear pattern: the first letter of "HISTORY" is shifted one step forward in the alphabet, while all remaining letters are shifted one step backward. After these shifts, the resulting string is reversed to get the final code. Step-by-Step Solution: Write the original word and the reversed code: HISTORY → reversed code I H R S N Q X. Compare positions: H becomes I (shift +1), I becomes H (shift -1), S becomes R (shift -1), T becomes S (shift -1), O becomes N (shift -1), R becomes Q (shift -1), Y becomes X (shift -1). So the rule is: first letter → +1 shift; all other letters → -1 shift; then reverse the resulting string. Apply this to ETHICS: Original letters: E, T, H, I, C, S. First letter E shifted forward by 1 becomes F. T shifted back by 1 becomes S. H shifted back by 1 becomes G. I shifted back by 1 becomes H. C shifted back by 1 becomes B. S shifted back by 1 becomes R. Intermediate string after shifts: F S G H B R. Reverse this string to obtain the final code: R B H G S F. Thus "ETHICS" is written as RBHGSF in the given code language. Verification / Alternative check: We can verify the pattern by re-encoding "HISTORY" with the same method. Apply +1 to H and -1 to the remaining letters, then reverse the result. This reconstruction again gives "XQNSRHI", confirming that our rule is correct and consistently applied. Using the same rule for "ETHICS" therefore must produce an accurate code word. Why Other Options Are Wrong: Options DSGHBR, RBHDSG and GSDRBH either do not follow the +1 and -1 shift pattern correctly or do not result from reversing the shifted string for "ETHICS". They break the clear positional relationship identified between "HISTORY" and its code, so they cannot represent the correct encoding of "ETHICS". Common Pitfalls: Students sometimes look only for simple uniform shifts (like +2 or -3 for every letter) and ignore reordering. Others notice reversal but miss that the first letter is treated differently from the rest. Carefully checking both shifting and order is essential in such mixed-pattern coding questions. Final Answer: Therefore, in this code language, "ETHICS" is written as RBHGSF.

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