Question 1

In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 50 + 5 - 7…

Accepted Answer

Introduction: This problem again challenges us with redefined arithmetic operators in a coded language. Familiar symbols +, -, x, and ÷ no longer carry their usual meanings. We must translate each symbol according to the given rule and then compute the value of 50 + 5 - 700 x 28 correctly with ordinary precedence. This blends careful reading with basic arithmetic skills. Given Data / Assumptions: The code language uses the following interpretations: 1) "+" stands for multiplication. 2) "-" stands for addition. 3) "x" stands for division. 4) "÷" stands for subtraction. The expression to be evaluated is 50 + 5 - 700 x 28. Once decoded, we carry out the operations using the standard order: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: We start by systematically replacing each coded symbol with its true operator. This gives a standard arithmetic expression. After that, we apply familiar rules of BODMAS or PEMDAS. The most frequent sources of error are forgetting to translate one symbol or unconsciously using its normal meaning rather than the new one. Step-by-Step Solution: Step 1: Convert 50 + 5 using the new meaning of "+", which is multiplication. So 50 + 5 becomes 50 * 5.Step 2: Convert "- 700" using the fact that "-" means addition. So "- 700" becomes + 700.Step 3: Convert "x 28" using the fact that "x" means division. So "x 28" becomes / 28.Step 4: The fully decoded expression is 50 * 5 + 700 / 28.Step 5: Apply precedence: evaluate the multiplication and division before the addition.Step 6: Compute 50 * 5 = 250.Step 7: Compute 700 / 28. Since 28 * 25 = 700, we have 700 / 28 = 25.Step 8: Now add the results: 250 + 25 = 275.Step 9: Therefore, the value of 50 + 5 - 700 x 28 in the coded system is 275. Verification / Alternative check: We can verbally re phrase the decoded expression as "50 multiplied by 5 plus 700 divided by 28". That clearly yields 250 plus 25, again giving 275. There are no hidden brackets or secondary rules that alter the order of operations, so this answer is secure. Why Other Options Are Wrong: The values 94, 100, 90, and 255 might result from treating one or more symbols with their original meanings or from performing the operations strictly left to right without precedence. None of these incorrect methods respects both the reassigned meanings and the standard evaluation rules. Common Pitfalls: Students sometimes forget to convert the minus sign in the middle and still treat it as subtraction. Others may convert correctly but then handle 50 * 5 + 700 / 28 as (50 * 5 + 700) / 28, which is not implied by the expression. Always decode first, then apply the usual step by step calculation rules. Final Answer: Using the coded meanings of the operators, the expression evaluates to 275.

Question 2

In a certain numerical code, the symbol "%" represents a special operation between two numbers. It is given that 3 % 2 = 50 and 2 % 4 = 60. Using the same rule, what is the value of 5 % 4?

Accepted Answer

Introduction: This question defines a custom operation using the "%" symbol, distinct from its usual use in percentages. Two sample equations involving small integers are provided, and we must deduce the common rule that produces results 50 and 60. After discovering this rule, we apply it to the new pair 5 and 4 to find the value of 5 % 4. It is a simple arithmetic pattern recognition exercise. Given Data / Assumptions: The code gives the following: 1) 3 % 2 = 50 2) 2 % 4 = 60 We need to determine 5 % 4. We assume: 1) The same operation % is applied consistently in all three cases. 2) The outputs are closely related to basic combinations of the two input numbers, probably through sums or products scaled by a constant. Concept / Approach: Since the answer values 50 and 60 end in zero, it is natural to suspect that the underlying operation involves multiplication by 10. We test whether taking the sum of the two numbers and multiplying by 10 matches the results in both examples. If this rule fits all given cases, we then use it directly to compute the new value. Step-by-Step Solution: Step 1: For 3 % 2, test the sum based rule: compute (3 + 2) * 10.Step 2: The sum 3 + 2 is 5, and 5 * 10 = 50, which matches the given value exactly.Step 3: For 2 % 4, compute (2 + 4) * 10.Step 4: The sum 2 + 4 is 6, and 6 * 10 = 60, again matching the given value.Step 5: Since the formula (a + b) * 10 explains both examples, we adopt it as the definition of a % b.Step 6: Apply this formula to 5 % 4: compute (5 + 4) * 10.Step 7: The sum 5 + 4 is 9, and 9 * 10 = 90.Step 8: Therefore, the value of 5 % 4 is 90. Verification / Alternative check: Check that no simpler common rule fits both examples. The plain sum gives 5 and 6, not 50 and 60. The product, 3 * 2 = 6 and 2 * 4 = 8, also does not match. Only the scaled sum formula (a + b) * 10 explains both given equations. Hence, the derived rule is consistent and appropriate. Why Other Options Are Wrong: The values 16, 9, 20, and 45 appear unrelated to the pattern used in the examples. They might arise by squaring, simple addition, or partial multiplication, but none of those schemes produce both 50 and 60 from the first two pairs. Therefore, they cannot be correct if we insist on a single consistent operation definition. Common Pitfalls: Students may focus on more complicated operations such as squares or cubes without first trying simple linear relationships involving sums and constants. Another common mistake is to find a rule that works for one example but fails to validate against the second. Always ensure that all given samples fit the same formula before answering. Final Answer: According to the pattern, the value of 5 % 4 is 90.

Question 3

In a certain number code, the symbol "#" denotes a special operation between two numbers. It is known that 6 # 30 = 5, 8 # 24 = 3 and 7 # 28 = 4. Using the same rule, what is the value of 8 # 40?

Accepted Answer

Introduction: This question introduces a custom operator "#" applied to ordered pairs of numbers. Instead of its usual use as a symbol in programming or text, it represents a simple hidden arithmetic operation. We are given three examples and asked to determine the value of 8 # 40 under the same rule. This is a direct test of pattern recognition in numerical reasoning. Given Data / Assumptions: The provided relationships are: 1) 6 # 30 = 5 2) 8 # 24 = 3 3) 7 # 28 = 4 We need 8 # 40. We assume: 1) The operation # is the same in all four cases. 2) The rule likely involves a straightforward combination, such as division, between the second and first numbers. Concept / Approach: Looking at each pair, the results 5, 3, and 4 are small compared with the second numbers 30, 24, and 28. A good first guess is that the result might be obtained by dividing the second number by the first. If this hypothesis works consistently for all given examples, we will then apply it to the new pair 8 and 40. Step-by-Step Solution: Step 1: For 6 # 30, compute 30 / 6. The result is 5, matching the given answer.Step 2: For 8 # 24, compute 24 / 8. The result is 3, again matching the given value.Step 3: For 7 # 28, compute 28 / 7. The result is 4, which also matches the given output.Step 4: Since in each example the result is the second number divided by the first number, we define a # b = b / a.Step 5: Apply this rule to 8 # 40. Here a = 8 and b = 40.Step 6: Compute 40 / 8 = 5.Step 7: Therefore, the value of 8 # 40 is 5. Verification / Alternative check: We can double check that no alternative simple pattern is needed. For example, if we tried a / b instead, we would obtain fractions less than 1, clearly not matching the given integer outputs. Products and sums give much larger numbers, so they are unsuitable. The division b / a is the only natural and consistent explanation for all three examples. Why Other Options Are Wrong: The value 47 or 24 or 6 cannot be generated by simply dividing the second number by the first for any of the examples. The value 4 would be correct for 7 # 28, but not for 8 # 40. Thus, the only option that matches the pattern consistently for the new pair is 5. Common Pitfalls: One common mistake is to test only the first example and prematurely conclude a rule, such as subtracting or adding a constant, without checking the other two examples. Another pitfall is accidentally reversing the order of division and computing a / b instead of b / a. Always verify your rule on every example provided before using it on the unknown case. Final Answer: Under the given pattern, the value of 8 # 40 is 5.

Question 4

In a certain code language, the English word "SQUALOR" is written as "USWCNQT". Using the same letter shifting pattern, how will the word "WHY" be written in that code language?

Accepted Answer

Introduction: This coding and decoding problem involves a consistent alphabetic shift applied to letters of English words. The word SQUALOR is coded as USWCNQT, and we must apply the same transformation to the word WHY. The question checks familiarity with alphabet positions and careful mapping of letter shifts. Given Data / Assumptions: The mapping given is SQUALOR → USWCNQT. We assume: 1) Each letter of the original word is replaced by a single letter in the coded word. 2) The same shift is applied to every letter of the alphabet. 3) The alphabet is treated cyclically, so after Z we wrap around to A if needed. Concept / Approach: To discover the rule, we compare the positions of corresponding letters from SQUALOR and USWCNQT. If the difference between each original and coded letter is constant, then we have a simple Caesar shift. Once we know the magnitude and direction of the shift, we apply it to the letters W, H, and Y in WHY. Step-by-Step Solution: Step 1: Determine positions: S=19, Q=17, U=21, A=1, L=12, O=15, R=18.Step 2: For the coded form USWCNQT, positions are U=21, S=19, W=23, C=3, N=14, Q=17, T=20.Step 3: Calculate the shift for each pair: S to U is 19 to 21 (plus 2), Q to S is 17 to 19 (plus 2), U to W is 21 to 23 (plus 2), and similarly for all other letters.Step 4: Since each original letter is shifted forward by 2 positions, the rule is: coded letter = original letter shifted forward by 2 places in the alphabet.Step 5: Apply this rule to WHY. W is 23 and becomes Y, H is 8 and becomes J, Y is 25 and becomes A, wrapping around after Z (since 25 plus 2 equals 27, which corresponds to 1, the position of A).Step 6: Thus, WHY is coded as YJA. Verification / Alternative check: If we reverse the operation by shifting each letter of YJA backward by 2 positions, we should return to WHY. Y becomes W, J becomes H, and A becomes Y. This confirms that we have applied the correct Caesar shift in the correct direction. Why Other Options Are Wrong: The options CZR, SGY, YPT, and WJA cannot all be generated by a uniform forward shift of 2 places starting from W, H, and Y. Each of them would require a different shift for at least one letter or a different direction of movement along the alphabet, which contradicts the uniform rule observed in SQUALOR → USWCNQT. Common Pitfalls: Learners sometimes forget to handle wrap around correctly when letters near the end of the alphabet are shifted forward. Another mistake is to miscalculate the alphabet positions or to assume a shift of 1 or 3 without checking all letter pairs. Careful checking of each mapping ensures a reliable solution. Final Answer: The word "WHY" is written as YJA in the given code language.

Question 5

In a certain code language, the symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 9 + 3 - 72 x 6 ÷ 3?

Accepted Answer

Introduction: Here we again encounter an expression where familiar arithmetic symbols have been assigned new meanings. The challenge is to decode each symbol according to the new definitions and then evaluate the resulting numerical expression correctly. This tests attention to detail and understanding of operation precedence. Given Data / Assumptions: The special meanings are: 1) "+" represents multiplication. 2) "-" represents addition. 3) "x" represents division. 4) "÷" represents subtraction. The coded expression to evaluate is 9 + 3 - 72 x 6 ÷ 3. After decoding, we apply the usual arithmetic precedence rules: division and multiplication before addition and subtraction. Concept / Approach: The safe strategy is to ignore the usual meanings of the symbols and wholly rely on the given code. We rewrite the entire expression with the true operations first, and only then proceed to calculate. This avoids mixing interpretations and reduces logical mistakes, especially in more complex expressions that contain several different coded operators. Step-by-Step Solution: Step 1: Replace "+" with its coded meaning multiplication. Thus 9 + 3 becomes 9 * 3.Step 2: Replace "-" with addition. Therefore "- 72" becomes + 72.Step 3: Replace "x" with division. So "72 x 6" becomes 72 / 6.Step 4: Replace "÷" with subtraction. So "6 ÷ 3" means 6 - 3, but note it is part of the coded structure in the original expression as 72 x 6 ÷ 3. After full decoding, the expression becomes 9 * 3 + 72 / 6 - 3.Step 5: Apply operation precedence. First compute 9 * 3 = 27.Step 6: Compute 72 / 6 = 12.Step 7: Substitute these results into the expression, giving 27 + 12 - 3.Step 8: Evaluate addition and subtraction from left to right: 27 + 12 = 39, then 39 - 3 = 36.Step 9: Hence, the value of the coded expression is 36. Verification / Alternative check: We can rephrase the decoded expression verbally: "nine multiplied by three plus seventy two divided by six minus three." Clearly this is 27 plus 12 minus 3, which equals 36. There are no additional brackets or special rules that modify this order, so the computation is stable. Why Other Options Are Wrong: The value 46 or 30 could appear if someone miscalculates 72 / 6 or fails to perform the final subtraction. The value 21 or 9 might come from treating one or more operators with their original meanings or from evaluating strictly left to right. Such interpretations contradict the given symbol definitions and correct precedence rules. Common Pitfalls: Learners may forget to translate all operators before starting the computation, especially when many different symbols are present together. Others ignore precedence and compute 9 * 3 + 72 then divide by 6 and subtract 3, which is not intended. Carefully translating and then working step by step prevents these common mistakes. Final Answer: According to the coded definitions of the operators, the expression evaluates to 36.

Question 6

In a certain code language, the English word "REGAINS" is written as "QDFZHMR". Using the same letter shifting pattern, how will the word "PRY" be written in that code language?

Accepted Answer

Introduction: This coding and decoding question uses a simple alphabetic shift applied consistently to all letters. The word REGAINS is written as QDFZHMR. We must recognise the underlying shift and then apply it to the word PRY. This type of question checks your ability to handle basic Caesar cipher style transformations. Given Data / Assumptions: The provided mapping is REGAINS → QDFZHMR. We assume: 1) Each letter in the original word is replaced with exactly one letter in the coded word. 2) The same shift is applied to every letter of any word. 3) The alphabet is cyclic, so shifting backward from A leads to Z if needed. Concept / Approach: To uncover the rule, we compare each letter of REGAINS with the corresponding letter in QDFZHMR and compute the difference in terms of alphabet positions. If the difference is constant and negative, we have a fixed backward shift. Once the shift amount is confirmed, we apply it to the letters P, R, and Y in PRY. Step-by-Step Solution: Step 1: Determine the positions of letters in REGAINS: R=18, E=5, G=7, A=1, I=9, N=14, S=19.Step 2: Determine the positions of letters in QDFZHMR: Q=17, D=4, F=6, Z=26, H=8, M=13, R=18.Step 3: Compare each pair: R to Q is 18 to 17 (minus 1), E to D is 5 to 4 (minus 1), G to F is 7 to 6 (minus 1), A to Z is 1 to 26, which is effectively minus 1 with wrap around, and the same minus 1 shift holds for the remaining letters.Step 4: The rule is therefore: coded letter = original letter shifted backward by 1 position.Step 5: Apply this rule to PRY. P is 16 and becomes O (15), R is 18 and becomes Q (17), Y is 25 and becomes X (24).Step 6: So PRY is written as OQX in the code language. Verification / Alternative check: If we shift each letter of OQX forward by one position, we should recover PRY. O becomes P, Q becomes R, and X becomes Y. This confirms that the shift of minus 1 has been applied correctly in generating the code word OQX. Why Other Options Are Wrong: The options BJX, LFT, PSU, and OQY cannot consistently be obtained by shifting each letter of PRY backward by exactly 1 position. Some of these options involve either a different shift magnitude or movement in the wrong direction in the alphabet. Hence, they do not obey the uniform rule verified from REGAINS → QDFZHMR. Common Pitfalls: Students sometimes miscalculate the position of letters near the ends of the alphabet, especially when wrapping around from A to Z or Z to A. Others assume a forward shift without checking all pairs. Carefully computing positions and verifying the same shift for every letter in the example avoids these errors. Final Answer: The word "PRY" is written as OQX in the given code language.

Question 7

In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 45 x 5 + 2…

Accepted Answer

Introduction: This operator coding problem asks us to evaluate an arithmetic expression in which each familiar symbol has been reassigned a new meaning. The correct solution requires decoding every operator in the expression 45 x 5 + 2 - 20 and then applying normal arithmetic precedence rules. The question checks both symbol translation skills and basic calculation accuracy. Given Data / Assumptions: The redefined meanings are: 1) "+" represents multiplication. 2) "-" represents addition. 3) "x" represents division. 4) "÷" represents subtraction (not used directly here). The coded expression is 45 x 5 + 2 - 20. After decoding, we apply standard precedence: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: The most robust approach is a two step process: first, convert the coded symbols into actual operations; second, compute the final value carefully. It is important not to mix the visual symbol with its usual arithmetic meaning but to always use the provided mapping. Once rewritten, the expression looks familiar and can be evaluated as usual. Step-by-Step Solution: Step 1: Replace the "x" symbol with division. Thus 45 x 5 becomes 45 / 5.Step 2: Replace the "+" symbol with multiplication. So + 2 becomes * 2.Step 3: Replace the "-" symbol with addition. So - 20 becomes + 20.Step 4: The decoded expression becomes 45 / 5 * 2 + 20.Step 5: Apply arithmetic precedence. First evaluate 45 / 5 = 9.Step 6: Then evaluate 9 * 2 = 18.Step 7: Now the expression is 18 + 20.Step 8: Add the numbers: 18 + 20 = 38.Step 9: Therefore, the value of the given coded expression is 38. Verification / Alternative check: We can rephrase the decoded expression as "forty five divided by five multiplied by two plus twenty". This clearly evaluates to 9 times 2 plus 20, or 18 plus 20, which is 38. No extra brackets or alternative interpretations are implicit, so the answer is consistent. Why Other Options Are Wrong: The value 17 or 28 could arise from treating one of the operations as subtraction instead of multiplication or addition. The value 81 might come from mistakenly doing 45 * 5 then combining with 2 and 20 in an ad hoc manner. The value 64 would require ignoring division or misapplying operator precedence. None of these approaches respects both the redefined operators and standard evaluation order. Common Pitfalls: Common mistakes include leaving one operator untranslated, such as still reading "-" as minus, or performing operations strictly left to right without handling division and multiplication first. Writing the fully translated expression before starting the calculation helps maintain clarity and avoid confusion. Final Answer: Using the given coded meanings of the operators, the expression evaluates to 38.

Question 8

In a certain numerical code, the symbol "@" denotes a special operation between two numbers. It is known that 5 @ 1 = 60, 12 @ 8 = 200 and 16 @ 2 = 180. Using the same rule, what is the value of 16 @ 10?

Accepted Answer

Introduction: This question introduces a custom numeric operator "@". Instead of having a standard mathematical meaning, the operator is defined implicitly by several example equations. By analysing those examples, we must infer the general rule for a @ b and then apply that rule to compute 16 @ 10. It is a straightforward test of pattern discovery in number puzzles. Given Data / Assumptions: The three given relationships are: 1) 5 @ 1 = 60 2) 12 @ 8 = 200 3) 16 @ 2 = 180 We must find 16 @ 10. We assume: 1) The operation @ is defined consistently across all these equations. 2) The result is obtained through simple arithmetic combinations involving the sum of the two numbers, possibly scaled by a constant. Concept / Approach: Since the results 60, 200, and 180 end with a zero or are round numbers, a natural guess is that the operation involves multiplying a sum by 10 or by another fixed constant. We test whether (a + b) * 10 matches each given example. If this rule works for all, we can confidently apply it to 16 and 10. Step-by-Step Solution: Step 1: Test the first example: 5 @ 1. Compute (5 + 1) * 10.Step 2: The sum is 6, and 6 * 10 = 60, matching the given value.Step 3: Test the second example: 12 @ 8. Compute (12 + 8) * 10.Step 4: The sum is 20, and 20 * 10 = 200, again matching the given value.Step 5: Test the third example: 16 @ 2. Compute (16 + 2) * 10 = 18 * 10 = 180, which also matches.Step 6: Since the pattern (a + b) * 10 fits all three equations, we accept this as the definition of a @ b.Step 7: Apply the rule to 16 @ 10: compute (16 + 10) * 10.Step 8: The sum is 26, and 26 * 10 = 260.Step 9: Therefore, 16 @ 10 equals 260. Verification / Alternative check: We can consider other simple possibilities, such as a * b, a * b + 10, or (a - b) * 10, but none of these produce 60, 200, and 180 together from the given input pairs. Only the rule (a + b) * 10 matches all three cases simultaneously, so it is the most credible and consistent interpretation. Why Other Options Are Wrong: The values 32, 11, and 9 are much smaller and cannot be obtained by the discovered rule. The value 180 corresponds to 16 @ 2 and not to 16 @ 10. Thus, 260 is the only option consistent with the pattern already confirmed by the examples. Common Pitfalls: A frequent mistake is to fixate on multiplication of the two numbers and add or subtract arbitrary constants until the first example fits, without checking the subsequent examples. Another error is to overlook the common factor of 10 in the answers, which is a strong clue towards (a + b) * 10. Always ensure that the same simple rule holds for all given equations before using it on the unknown case. Final Answer: Using the established pattern, the value of 16 @ 10 is 260.

Question 9

In a certain code language, the English word "QUICKLY" is written as "OSGAIJW". Using the same systematic shift of letters, how will the word "HUE" be written in that code language?

Accepted Answer

Introduction: This coding and decoding question uses a consistent shift of letters in the alphabet. The word QUICKLY is coded as OSGAIJW. Our task is to determine the rule that maps each original letter to its coded partner, and then apply that rule to the letters of HUE. This tests comfort with basic Caesar shift style ciphers in the alphabet. Given Data / Assumptions: The mapping is QUICKLY → OSGAIJW. We assume: 1) Each letter is replaced by exactly one other letter. 2) A fixed shift (forward or backward) is applied to all letters. 3) The alphabet wraps around cyclically from A to Z and from Z to A if needed. Concept / Approach: To find the shift, we compare the positions of corresponding letters from QUICKLY and OSGAIJW. If the difference in positions is constant across every pair, we have identified a Caesar shift. Once we know whether the shift is forward or backward and by how many positions, we can apply it to H, U, and E in the word HUE. Step-by-Step Solution: Step 1: List positions for QUICKLY: Q=17, U=21, I=9, C=3, K=11, L=12, Y=25.Step 2: List positions for OSGAIJW: O=15, S=19, G=7, A=1, I=9, J=10, W=23.Step 3: Find the shift: Q to O is 17 to 15 (minus 2), U to S is 21 to 19 (minus 2), I to G is 9 to 7 (minus 2), C to A is 3 to 1 (minus 2), K to I is 11 to 9 (minus 2), L to J is 12 to 10 (minus 2), and Y to W is 25 to 23 (minus 2).Step 4: Since each letter is shifted back by 2 positions, the code rule is: coded letter = original letter shifted backward by 2.Step 5: Apply this shift to HUE. H is 8 and becomes F (6), U is 21 and becomes S (19), E is 5 and becomes C (3).Step 6: Therefore, HUE is written as FSC in the code language. Verification / Alternative check: If we shift each letter of FSC forward by 2 positions, we should obtain HUE. F becomes H, S becomes U, and C becomes E. This confirms that the shift has been applied correctly, and the cipher is internally consistent for this word as well as for QUICKLY. Why Other Options Are Wrong: The options ZMA, HZK, HNI, and GTC do not result from a uniform backward shift of 2 applied to H, U, and E. Each of these options would require different shifts for different letters or a forward shift, which contradicts the pattern derived from QUICKLY → OSGAIJW. Common Pitfalls: One common mistake is miscounting when shifting backward, especially near the start of the alphabet. Another is to identify the wrong shift magnitude because only the first pair of letters was checked. Always validate the hypothesised shift by testing it against every letter pair in the given example word. Final Answer: The word "HUE" is written as FSC in the given code language.

Question 10

In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 42 x 7 ÷ 7…

Accepted Answer

Introduction: This question again tests our ability to work with redefined arithmetic symbols. Operators +, -, x and ÷ have been assigned new meanings, and we must carefully decode the expression 42 x 7 ÷ 7 + 9 - 62 before computing its value. This is a blend of symbolic translation and standard arithmetic practice. Given Data / Assumptions: The coded meanings are: 1) "+" represents multiplication. 2) "-" represents addition. 3) "x" represents division. 4) "÷" represents subtraction. The coded expression is 42 x 7 ÷ 7 + 9 - 62. After decoding, we apply normal precedence: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: We first translate each symbol into its true operation according to the code. Only after this translation do we attempt any calculation. This prevents us from accidentally using the familiar but incorrect meanings of the symbols. Once the expression is rewritten, we evaluate it step by step using standard arithmetic rules. Step-by-Step Solution: Step 1: Replace "x" by division, so 42 x 7 becomes 42 / 7.Step 2: Replace "÷" by subtraction, so "÷ 7" becomes - 7.Step 3: Replace "+" by multiplication, so "+ 9" becomes * 9.Step 4: Replace "-" by addition, so "- 62" becomes + 62.Step 5: The fully decoded expression is 42 / 7 - 7 * 9 + 62.Step 6: Apply precedence rules: first compute division and multiplication from left to right.Step 7: Evaluate 42 / 7 = 6.Step 8: Evaluate 7 * 9 = 63.Step 9: Substitute these values to obtain 6 - 63 + 62.Step 10: Now evaluate from left to right: 6 - 63 = -57.Step 11: Then -57 + 62 = 5.Step 12: Thus, the value of the coded expression is 5. Verification / Alternative check: We can state the decoded expression in words as "forty two divided by seven minus seven multiplied by nine plus sixty two". That is clearly 6 minus 63 plus 62, which equals 5. Since operator precedence is standard after decoding, there is no alternate correct evaluation path that yields a different result. Why Other Options Are Wrong: The values 87, 22, 2, and 11 would require misinterpreting at least one operator or changing the order of operations by inserting brackets not present in the expression. For example, treating "-" as subtraction instead of addition or forgetting the multiplication 7 * 9 would give misleading intermediate results and a wrong final answer. Common Pitfalls: Learners sometimes translate only some of the operators and inadvertently mix coded and normal meanings. Others neglect precedence and attempt to compute strictly left to right. To avoid errors, always rewrite the entire expression with standard operators first, then compute according to normal rules. Final Answer: With the given coded meanings, the expression evaluates to 5.

Question 11

In a certain numerical code, the symbol "@" denotes a special operation between two numbers. It is known that 17 @ 1 = 8, 9 @ 1 = 4 and 6 @ 4 = 1. Using the same rule, what is the value of 8 @ 2?

Accepted Answer

Introduction: This question introduces another custom numeric operator, written as "@". Several example equations involving pairs of numbers and small integer results are given. We must identify the rule that connects each pair to its result and then apply that rule to the pair 8 and 2. This type of problem is common in reasoning tests to check comfort with basic arithmetic patterns. Given Data / Assumptions: The relationships are: 1) 17 @ 1 = 8 2) 9 @ 1 = 4 3) 6 @ 4 = 1 We must find 8 @ 2. We assume: 1) The operator @ is defined consistently for all input pairs. 2) The results are derived through a simple arithmetic expression, likely involving differences, sums, or averages of the two numbers. Concept / Approach: Because the results 8, 4, and 1 are noticeably smaller than the first numbers in each pair, it is natural to examine the difference between the two numbers. A convenient pattern to test is whether the result equals half of the difference between the first and second numbers. If this pattern works for all three examples, we can reasonably apply it to 8 and 2. Step-by-Step Solution: Step 1: For 17 @ 1, compute the difference 17 - 1 = 16.Step 2: Half of this difference is 16 / 2 = 8, which matches the given result.Step 3: For 9 @ 1, compute 9 - 1 = 8, and half of this is 8 / 2 = 4, again matching the given result.Step 4: For 6 @ 4, compute 6 - 4 = 2, and half is 2 / 2 = 1, which also matches the given result.Step 5: Since in each case the result equals half of the difference between the first and second numbers, we define a @ b = (a - b) / 2.Step 6: Apply this rule to 8 @ 2: compute (8 - 2) / 2.Step 7: The difference is 6, and 6 / 2 = 3.Step 8: Therefore, 8 @ 2 equals 3. Verification / Alternative check: We can rule out alternative simple patterns. The sum based rule (a + b) or (a + b) / 2 does not produce the results 8, 4, and 1. Products or ratios get even further from these small integers. The half difference rule is the only simple arithmetic expression that matches all three sample equations precisely. Why Other Options Are Wrong: The values 26, 23, and 47 are far larger than expected from a rule that generates 8, 4, and 1 for reasonably small inputs. The value 5 would require a different operation or an added constant. None of these alternative values are consistent with the pattern confirmed by all three examples, so they cannot be correct for 8 @ 2. Common Pitfalls: Some learners try to force a sum based or product based rule because those are more familiar, but these do not fit all the data. Another mistake is to test a rule on a single example and then apply it without checking the others, which can lead to incorrect generalisation. Always verify a hypothesised rule with every example provided. Final Answer: Under the defined pattern, the value of 8 @ 2 is 3.

Question 12

In a certain code language, the English word "CHANTED" is written as "ZEXKQBA". Using the same letter shifting pattern, how will the word "MAY" be written in that code language?

Accepted Answer

Introduction: This coding and decoding problem is based on a uniform shift of letters in the alphabet. The word CHANTED is coded as ZEXKQBA. We must deduce the rule relating each original letter to its coded counterpart and then apply this rule to the word MAY. This question checks comfort with simple backward shifts in the alphabet and careful handling of wrap around at the beginning and end of the sequence. Given Data / Assumptions: The mapping is CHANTED → ZEXKQBA. We assume: 1) Each letter of the original word is replaced by one letter in the coded word. 2) The transformation is consistent and involves the same shift for all letters. 3) The alphabet is cyclic, so shifting backward from A leads to Z, and so on. Concept / Approach: To find the shift pattern, we compare the positions of corresponding letters from the original and coded word. If each letter has moved the same number of steps in the same direction (forward or backward), then a simple Caesar shift is in use. Once we know the shift, we can quickly code the letters M, A, and Y in the word MAY. Step-by-Step Solution: Step 1: Determine positions for CHANTED: C=3, H=8, A=1, N=14, T=20, E=5, D=4.Step 2: Determine positions for ZEXKQBA: Z=26, E=5, X=24, K=11, Q=17, B=2, A=1.Step 3: Compute the differences: C to Z is 3 to 26, effectively minus 3; H to E is 8 to 5 (minus 3); A to X is 1 to 24 (minus 3 with wrap); N to K is 14 to 11 (minus 3); and the same minus 3 shift appears for T to Q, E to B, and D to A.Step 4: The rule is therefore: coded letter = original letter shifted backward by 3 positions.Step 5: Apply this rule to MAY. M is 13 and becomes J (10), A is 1 and becomes X (24), Y is 25 and becomes V (22).Step 6: Hence, MAY is written as JXV in this code language. Verification / Alternative check: We can verify the correctness by shifting JXV forward by 3 positions. J becomes M, X becomes A, and V becomes Y. That returns us to the original word MAY, confirming that the backward shift of 3 is accurate and consistently applied. Why Other Options Are Wrong: The options XIG, OBI, XAV, and JXU are not obtained by shifting each letter of MAY backward by exactly 3 positions. Each of them would require a different shift amount or direction for at least one letter, which would contradict the pattern deduced from CHANTED → ZEXKQBA. Common Pitfalls: Students sometimes miscalculate backward shifts when wrapping around from A to the end of the alphabet, or they guess a forward shift because it feels more intuitive. Another common error is checking the shift for only one letter pair and assuming it holds everywhere without verification. Always compute positions and differences for several letters to ensure consistency. Final Answer: According to the coding pattern, the word "MAY" is written as JXV in this code language.

Question 13

In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 12 x 6 ÷ 5…

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Introduction: Once again we are given an arithmetic expression in which each familiar operator symbol has a new coded meaning. Our job is to interpret 12 x 6 ÷ 5 + 4 according to the redefined meanings of +, -, x and ÷, and then evaluate the resulting standard arithmetic expression. This problem checks both precise translation and correct use of operation precedence. Given Data / Assumptions: The symbol meanings are: 1) "+" represents multiplication. 2) "-" represents addition. 3) "x" represents division. 4) "÷" represents subtraction. The coded expression we must evaluate is 12 x 6 ÷ 5 + 4. After decoding, we follow normal arithmetic rules where division and multiplication take precedence over addition and subtraction. Concept / Approach: The recommended approach is to perform the translation step carefully and only then proceed with the arithmetic. Each coded symbol is replaced by its actual operation, giving us a standard expression in terms of /, *, + and -. We then compute that expression step by step, ensuring that division and multiplication are processed before subtraction. Step-by-Step Solution: Step 1: Replace "x" with division: 12 x 6 becomes 12 / 6.Step 2: Replace "÷" with subtraction: "÷ 5" becomes - 5.Step 3: Replace "+" with multiplication: "+ 4" becomes * 4.Step 4: The decoded expression is therefore 12 / 6 - 5 * 4.Step 5: Apply operation precedence: first perform the division and multiplication from left to right.Step 6: Evaluate 12 / 6 = 2.Step 7: Evaluate 5 * 4 = 20.Step 8: Now substitute into the expression: 2 - 20.Step 9: Compute the result: 2 - 20 = -18.Step 10: Thus, the value of the coded expression is -18. Verification / Alternative check: We can restate the decoded expression in words: "twelve divided by six minus five multiplied by four". This is clearly 2 minus 20, which equals -18. There are no additional brackets in the original expression that would change the grouping, so the calculation is unambiguous once the operators are decoded. Why Other Options Are Wrong: The values 8, 42, 18, and 2 would arise only if we misinterpreted at least one symbol or ignored operator precedence. For example, interpreting "+" as addition instead of multiplication would change the result dramatically. Similarly, performing subtraction before multiplication would produce an incorrect intermediate value and an incorrect final answer. Common Pitfalls: A common error is to forget to change the meaning of the plus sign and still treat it as addition. Another frequent mistake is to perform operations in the written order rather than respecting the standard precedence of division and multiplication over addition and subtraction. A careful translation and stepwise, rule based evaluation keep these mistakes in check. Final Answer: When correctly decoded and evaluated, the expression has the value -18.

Question 14

In a certain number pattern, pairs of outer numbers are written with a middle number in brackets as follows: 14 (16) 18 and 33 (64) 25. Using the same rule, 25 (49) A is also written in this form. What is the correct value of A that fits this patter…

Accepted Answer

Introduction: This problem features a numerical pattern where two outer numbers are linked to a middle number written in brackets. The given examples are 14 (16) 18 and 33 (64) 25. We must observe the relationship among the three numbers in each case and then apply the same rule to determine the possible value or values of A in 25 (49) A. The question tests pattern discovery and careful handling of absolute differences. Given Data / Assumptions: The pairs and middle numbers given are: 1) 14 (16) 18 2) 33 (64) 25 We are told that 25 (49) A follows the same pattern. We assume: 1) The middle number in brackets is determined solely by the two outer numbers. 2) The same rule applies consistently to both examples and to the unknown case. Concept / Approach: On inspection, 16 and 64 in the middle look like perfect squares: 16 is 4^2 and 64 is 8^2. This suggests that the middle number might be the square of the difference between the outer numbers. We check whether this rule holds for both examples. If it does, then in 25 (49) A, the middle number 49 should similarly be the square of the absolute difference between 25 and A. Step-by-Step Solution: Step 1: Examine 14 (16) 18. Compute the difference of the outer numbers: |18 - 14| = 4. The square of this difference is 4^2 = 16, which matches the middle number.Step 2: Examine 33 (64) 25. Compute the difference: |33 - 25| = 8. The square of this difference is 8^2 = 64, which again matches the middle number.Step 3: The confirmed rule is: for outer numbers X and Y, the middle number equals (|X - Y|)^2.Step 4: Apply this to 25 (49) A. Here the middle number 49 must equal the square of the absolute difference between 25 and A.Step 5: So we have (|25 - A|)^2 = 49. Taking the positive square root gives |25 - A| = 7.Step 6: Solve the absolute value equation: 25 - A = 7 or 25 - A = -7.Step 7: From 25 - A = 7, we get A = 18. From 25 - A = -7, we get 25 + 7 = A, so A = 32.Step 8: Therefore, both A = 18 and A = 32 satisfy the pattern, meaning either value is mathematically valid. Verification / Alternative check: Check both candidates explicitly. For A = 18, the pair 25 and 18 yields |25 - 18| = 7, and 7^2 = 49. For A = 32, the pair 25 and 32 also yields |25 - 32| = 7, and again 7^2 = 49. In each case, the middle number remains 49 and the same rule holds, so both outer values are acceptable within this pattern. Why Other Options Are Wrong: The values 24 and 14 do not satisfy the equation (|25 - A|)^2 = 49, because |25 - 24| = 1 and |25 - 14| = 11, whose squares are 1 and 121, not 49. Choosing only 32 or only 18 would ignore the fact that the difference is taken in absolute value, allowing two symmetric solutions. The only option that correctly reflects all valid values is the combined choice "32 or 18". Common Pitfalls: Some learners forget that the absolute difference between two numbers can be realised in two ways, leading to two distinct outer values that fit the same square. Others may recognise only one solution and ignore the mirror case. It is important to treat |X - Y| as a distance, not an ordered subtraction, and to solve for all possible values that satisfy the relationship. Final Answer: Both A = 32 and A = 18 satisfy the given pattern, so the correct choice is 32 or 18.

Question 15

If, in a certain code language, the word HEROISM is written as SVILRHN, then according to the same coding rule how will the word ALP be written?

Accepted Answer

Introduction / Context: This question tests coding and decoding based on a letter transformation rule applied consistently to all letters of a word. The example shows how the word HEROISM is converted into a coded form, and we are asked to apply the same rule to the shorter word ALP. Such questions build comfort with alphabet positions and symmetric patterns in verbal reasoning, and they are frequently used in many aptitude tests. Given Data / Assumptions: Original word: HEROISM. Coded word: SVILRHN. Target word: ALP. The same rule that converts HEROISM to SVILRHN must be used for ALP. All letters are from the English alphabet, and their relative positions are important. Concept / Approach: The key idea is to understand how each letter of HEROISM transforms into the corresponding letter in SVILRHN. If we look at the alphabet positions, we notice that H and S, E and V, R and I, O and L, I and R, S and H, M and N form reflective pairs around the middle of the alphabet. This is known as an Atbash type mapping, where A pairs with Z, B with Y, C with X, and so on. Once we recognise that HEROISM and SVILRHN are Atbash counterparts, we can apply the same reflection rule directly to each letter of ALP to find its coded form. Step-by-Step Solution: Step 1: Write the alphabet from A to Z and pair A with Z, B with Y, C with X, continuing until M with N.Step 2: Check the mapping for the example: H pairs with S, E with V, R with I, O with L, I with R, S with H, M with N. This confirms the Atbash style reflection.Step 3: For the target word ALP, find Atbash pairs. A pairs with Z, L pairs with O, and P pairs with K.Step 4: Therefore ALP is encoded as ZOK.Step 5: Compare ZOK with the given answer options and select the matching option. Verification / Alternative check: As a quick check, take any other letter pair from the example such as M and N. M is the 13th letter and N is the 14th, and in the Atbash mapping 13 pairs with 14, which matches the transformation from M to N. Similarly, S maps back to H, again consistent with reflection around the centre of the alphabet. Applying the same rule to A, L, and P gives Z, O, and K respectively, so ZOK is fully consistent with the established pattern and therefore the code for ALP is correct. Why Other Options Are Wrong: LTV, ZSX, and SGD do not follow the Atbash mapping for ALP. For example, if A mapped to L as in option LTV, that would contradict the mapping that sends A to Z in the HEROISM example. The option XQO is also inconsistent because it does not match the standard reflected partners of A, L, or P. Only ZOK preserves the reflection rule for all three letters, so the other options must be rejected as incorrect decodings. Common Pitfalls: A common error is to look for simple forward or backward shifts in the alphabet, such as plus two or minus three, rather than checking for a full reflection around the alphabet centre. Another mistake is to guess based on visual similarity of options instead of systematically verifying the mapping against the example. Learners may also wrongly assume that each letter moves by a fixed number of positions, which fails here because the pattern is symmetric rather than a constant shift. Working with explicit alphabet positions and checking at least three or four letter pairs helps to avoid such mistakes. Final Answer: The correct code for the word ALP, using the same Atbash style reflection rule that maps HEROISM to SVILRHN, is ZOK, which corresponds to the correct option given in the problem.

Question 16

In a certain code language, plus means multiplication, minus means addition, multiplication means division and division means subtraction. What is the value of the expression 15 - 5 + 25 ÷ 10 under this coding scheme?

Accepted Answer

Introduction / Context: This question belongs to the verbal reasoning topic of coding and decoding of mathematical operators. Instead of using the normal meaning of symbols such as plus, minus, multiply, and divide, the symbols are reassigned new meanings. The objective is to decode the expression by replacing each symbol with its correct operation and then evaluate the expression using standard arithmetic rules. It checks both understanding of operator precedence and the careful reading of symbol definitions. Given Data / Assumptions: The symbol plus represents multiplication. The symbol minus represents addition. The symbol multiplication represents division. The symbol division represents subtraction. The expression to decode is 15 - 5 + 25 ÷ 10, and normal arithmetic precedence rules apply after decoding. Concept / Approach: The key is to translate the encoded expression into a standard arithmetic expression. Every symbol in the given expression must be replaced with the operation it represents. After decoding, we must apply the usual order of operations: perform multiplication and division first, followed by addition and subtraction from left to right. Many errors occur when candidates either decode incorrectly or ignore operator precedence and simply compute from left to right without regard for multiplication and division priority. Step-by-Step Solution: Step 1: Note that minus stands for addition, plus stands for multiplication, and division stands for subtraction in this specific code.Step 2: The given coded expression is 15 - 5 + 25 ÷ 10.Step 3: Replace each symbol with its real operation: minus becomes plus, plus becomes multiplication, and division becomes subtraction. So the expression becomes 15 + 5 * 25 - 10.Step 4: Apply operator precedence. First evaluate the multiplication: 5 * 25 = 125.Step 5: Substitute this result: 15 + 125 - 10.Step 6: Perform the addition and subtraction from left to right: 15 + 125 = 140, then 140 - 10 = 130.Step 7: Therefore the decoded value of the original coded expression is 130. Verification / Alternative check: As a quick verification, we can plug the answer back and mentally confirm each step. The original coded form 15 - 5 + 25 ÷ 10, once translated, becomes 15 plus 5 times 25 minus 10. There is only one multiplication and one subtraction after decoding. No brackets are involved, so the only potential source of variance is operator precedence. Recomputing 5 times 25 gives 125, then adding 15 and subtracting 10 yields exactly 130, confirming that the final answer is consistent. Why Other Options Are Wrong: The option 22 could result from incorrectly replacing symbols and then simply performing addition and subtraction without multiplication precedence. The value minus 4 may arise if division is performed first as 25 divided by 10 and then misapplied with incorrect symbolic meanings. The option 17 can come from evaluating strictly left to right without performing the multiplication first, which is not mathematically correct. The distractor 40 is another possible miscalculation where the intermediate multiplication or subtraction step is handled wrongly. None of these match the correctly decoded and evaluated value of 130. Common Pitfalls: Many learners rush and forget to decode all the symbols consistently, leaving one or more operations with their original meaning. Another frequent issue is ignoring the standard hierarchy of operations, especially in questions where multiplication appears after addition or subtraction. Writing the translated expression explicitly and underlining multiplication and division before computing helps avoid mistakes. It is also wise to recheck the mapping rules at least once before final evaluation. Final Answer: After decoding the operators and applying normal arithmetic precedence, the value of the coded expression 15 - 5 + 25 ÷ 10 is 130.

Question 17

In a certain code language, the word STYLE is written as ELTYS. According to the same rearrangement rule, how is the word FRUIT written in that code language?

Accepted Answer

Introduction / Context: This item tests coding and decoding where letters of a word are rearranged according to a pattern, rather than replaced individually by other symbols. We are told how STYLE becomes ELTYS and asked to apply the same rearrangement to FRUIT. This reinforces the idea that coding questions can use permutations of letter positions, not only alphabet shifts, and encourages systematic observation of letter order. Given Data / Assumptions: Original word: STYLE. Coded word: ELTYS. Target word to code: FRUIT. The coding rule involves changing the order of letters, and the same ordering must be applied to the new word. No letter substitution or numeric conversion is mentioned, so only position changes are assumed. Concept / Approach: The main idea is to compare the positions of letters in STYLE with their positions in ELTYS. If we label the original letters as positions 1 to 5, we can map which original position moves to which coded position. Once we know the mapping of indices, we apply that pattern to any other word of the same length. This is a pure position permutation, so the actual letter values do not matter, only their order in the sequence. Step-by-Step Solution: Step 1: Write STYLE with position numbers: S(1), T(2), Y(3), L(4), E(5).Step 2: Write ELTYS with position numbers relative to the original word: E is original position 5, L is 4, T is 2, Y is 3, and S is 1.Step 3: Conclude that the coding rule reorders the letters in the sequence of positions 5, 4, 2, 3, 1.Step 4: Apply the same position mapping to FRUIT, whose letters at positions are F(1), R(2), U(3), I(4), T(5).Step 5: Take the letters in the order 5, 4, 2, 3, 1: 5 gives T, 4 gives I, 2 gives R, 3 gives U, and 1 gives F.Step 6: Combine these letters to form the coded word TIRUF. Verification / Alternative check: To verify, we can check that applying the reverse permutation to ELTYS restores STYLE. If we map coded positions 1 to 5 back to original positions 3, 4, 2, 5, 1 respectively, we recover S, T, Y, L, E. Similarly, mapping FRUIT to TIRUF is consistent with using the same index pattern. Because the pattern depends only on positions, this check confirms the method is correct and the answer TIRUF is reliable. Why Other Options Are Wrong: The options TIUFR and TIURF involve mixing letters of FRUIT in different orders that do not follow the exact 5, 4, 2, 3, 1 sequence derived from the example. The option GSVJU is completely unrelated to the letters of FRUIT and suggests a different type of substitution cipher, which is not supported by the question statement. The additional distractor TRUF I does not even present the letters as a clean contiguous code word. Only TIRUF exactly respects the positional mapping illustrated by STYLE and ELTYS. Common Pitfalls: Many candidates attempt to find alphabetic shifts between S and E, T and L, and so on, but quickly discover that the differences are inconsistent. This often leads to confusion. The correct approach is to track positions, not letter distances. Another common mistake is to mislabel positions and inadvertently use a slightly different ordering like 5, 4, 3, 2, 1, which would give a simple reversal but not match the example. Carefully writing indices under each letter avoids these pitfalls. Final Answer: Using the same position rearrangement rule that maps STYLE to ELTYS, the word FRUIT is coded as TIRUF.

Question 18

In a certain code language, the word CERTAIN is written as DFSTBJO. Using the same coding rule, how is the word CRICKET written in that language?

Accepted Answer

Introduction / Context: This question is about a simple substitution code where each letter of a word is replaced by another letter according to a fixed algebraic rule on alphabet positions. The example shows how CERTAIN becomes DFSTBJO. We must detect the underlying transformation and then apply it to the new word CRICKET. Such questions usually involve adding or subtracting a constant from the alphabet index of each letter. Given Data / Assumptions: Original word: CERTAIN. Coded word: DFSTBJO. Target word: CRICKET. The same coding rule applies to both words. We work with the standard English alphabet A to Z and their positions from 1 to 26. Concept / Approach: By pairing letters from CERTAIN and DFSTBJO, we can check how many positions each letter is shifted. For most pairs, C to D, E to F, R to S, A to B, I to J, and N to O, the transformation is a shift of plus one in the alphabet. The letter T remains T, which is a slight irregularity but does not affect the general pattern. Since exam questions usually target a simple rule, we adopt the basic pattern that each letter shifts to the next letter in the alphabet. We then apply this uniform plus one shift to each letter of CRICKET. Step-by-Step Solution: Step 1: Assign positions: C is 3, E is 5, R is 18, T is 20, A is 1, I is 9, and N is 14.Step 2: Check the coded letters: D is 4, F is 6, S is 19, T is 20, B is 2, J is 10, and O is 15.Step 3: The pattern is that most letters increase by one position: C to D, E to F, R to S, A to B, I to J, N to O, with T remaining unchanged.Step 4: Apply this rule to CRICKET. C, R, I, C, K, E, T become D, S, J, D, L, F, U respectively by shifting each letter one step forward.Step 5: Thus CRICKET is coded as DSJDLFU. Verification / Alternative check: We can verify by reversing the shift. Taking DSJDLFU and shifting each letter back by one, D to C, S to R, J to I, D to C, L to K, F to E, and U to T, we recover CRICKET. Similarly, reversing DFSTBJO by one gives CERTAIN, except for the unchanged T case, which still maps correctly. This confirms that the intended rule is a plus one shift and that DSJDLFU is the only option consistent with this mapping. Why Other Options Are Wrong: The option DSJBLFU differs in the middle letters and would not revert to CRICKET when shifted back. The options DSJCLFU and DSJCLFV similarly introduce letters that do not match the plus one pattern at all positions and would encode some different word. The extra distractor DTKDMSG is not consistent with a uniform single step shift from CRICKET and therefore cannot represent the same coding rule. Only DSJDLFU exactly follows the shift pattern derived from the CERTAIN example. Common Pitfalls: Candidates sometimes mix up plus one and minus one shifts, or they calculate the shift correctly for a few letters but make a small mistake in the middle of the word. Another issue is ignoring an irregular letter like T in the example and assuming a more complicated rule than needed. Focusing on the majority pattern and checking the reverse transformation helps avoid overcomplication and small arithmetic errors. Final Answer: Using the same plus one alphabet shift used to code CERTAIN, the word CRICKET is written as DSJDLFU.

Question 19

In a certain code language, the word RINKS is written as SKOMT. Using the same letter shift pattern, how is the word FRIED written in that language?

Accepted Answer

Introduction / Context: This question involves a positional pattern where different letters of the word are shifted by different amounts. The example RINKS becomes SKOMT. We must decode the transformation by examining each letter pair and then apply the same alternating shifts to the new word FRIED. The task combines knowledge of alphabet positions with the ability to recognise repeating patterns across positions in a word. Given Data / Assumptions: Original example: RINKS is coded as SKOMT. Target word: FRIED. The coding rule depends on the position of each letter in the word. Alphabet positions A to Z are considered from 1 to 26. The same pattern of shifts is applied consistently to any five letter word. Concept / Approach: We begin by converting each letter of RINKS and SKOMT into their alphabetic positions and computing the differences. For the first letter, R becomes S, which is a forward shift of one. I becomes K, which is a forward shift of two. N becomes O, a forward shift of one. K becomes M, a forward shift of two. S becomes T, another forward shift of one. So the pattern is an alternating sequence of plus one, plus two, plus one, plus two, plus one across the five positions. We then apply exactly this alternation to FRIED: position one plus one, position two plus two, position three plus one, and so on. Step-by-Step Solution: Step 1: Convert RINKS to positions: R(18), I(9), N(14), K(11), S(19).Step 2: Convert SKOMT to positions: S(19), K(11), O(15), M(13), T(20).Step 3: Compute differences: 18 to 19 is plus one, 9 to 11 is plus two, 14 to 15 is plus one, 11 to 13 is plus two, and 19 to 20 is plus one. The pattern is +1, +2, +1, +2, +1.Step 4: Write FRIED and note positions: F(6), R(18), I(9), E(5), D(4).Step 5: Apply the pattern. Position one: F plus one becomes G. Position two: R plus two becomes T. Position three: I plus one becomes J. Position four: E plus two becomes G. Position five: D plus one becomes E.Step 6: Combine the coded letters to obtain GTJGE. Verification / Alternative check: To verify, we can reverse the process on GTJGE using minus one, minus two, minus one, minus two, minus one. Starting from G, T, J, G, E and applying the opposite shifts we get back F, R, I, E, D, which confirms that GTJGE is correctly derived from FRIED under the same pattern. Likewise, reversing the pattern on SKOMT reconstructs RINKS, so the transformation is self consistent and the answer is reliable. Why Other Options Are Wrong: The options PQGHJ, HUKHD, and KOTGJ show different shift magnitudes that do not match the alternating plus one and plus two pattern when checked letter by letter. For instance, if the second letter of FRIED, R, does not become T under the candidate code, that option is immediately inconsistent. The distractor GSJGF also uses letters from near the same region of the alphabet but fails to follow the precise alternation, so it does not reconstruct FRIED under the reverse shift rule. Only GTJGE obeys the exact coded sequence at all positions. Common Pitfalls: Many candidates wrongly assume a constant shift across all letters, such as plus two throughout, which would not match the example. Another typical mistake is to miscalculate a single alphabetic step, for instance counting E to H as two steps instead of three. Keeping a written list of alphabet positions and marking each forward shift explicitly helps prevent these off by one errors and ensures the alternating pattern is captured correctly. Final Answer: Using the same alternating shifts of plus one and plus two applied to RINKS, the coded form of FRIED is GTJGE.

Question 20

The following equation with coded operators is incorrect: 18 x 12 - 3 ÷ 10 + 2 = 64. If exactly two mathematical signs are interchanged to make the equation correct, which two signs must be swapped?

Accepted Answer

Introduction / Context: This question checks understanding of arithmetic equations with incorrect operator placements. We are given an equation that does not hold true and asked to correct it by interchanging exactly two types of operators everywhere they appear. Such problems test attention to detail, operator precedence, and the ability to reason systematically through multiple possibilities, rather than relying on guesswork. Given Data / Assumptions: The intended full equation is 18 x 12 - 3 ÷ 10 + 2 = 64, with the usual multiplication and division symbols. Exactly two different signs among plus, minus, multiplication, and division must be interchanged. Interchanging means that wherever one of these two signs appears, it is replaced with the other, and this swap is global across the equation. The final corrected equation must be numerically true when evaluated with standard operator precedence. Concept / Approach: We should treat each option as a candidate pair of operators to swap and then check whether the resulting equation evaluates to 64. Because the equation contains multiplication, subtraction, division, and addition, changing any pair may significantly alter the result. The systematic way is to translate the expression into a compact form, test each swap option step by step, and compute the value using normal precedence: multiplication and division first, then addition and subtraction from left to right. Step-by-Step Solution: Step 1: Rewrite the original equation in symbolic form as 18 * 12 - 3 / 10 + 2.Step 2: Consider the option of interchanging the division and minus signs. This means every division sign becomes minus and every minus sign becomes division.Step 3: Apply this swap: 18 * 12 / 3 - 10 + 2 becomes 18 * 12 / 3 - 10 + 2 after replacement, which simplifies to 18 * 12 / 3 - 10 + 2 using standard symbols.Step 4: Evaluate with precedence. First compute 18 * 12 = 216. Then 216 / 3 = 72. The equation now reads 72 - 10 + 2.Step 5: Perform the remaining operations from left to right: 72 - 10 = 62 and 62 + 2 = 64.Step 6: The final left hand side equals 64, which matches the right hand side, so swapping division and minus corrects the equation. Verification / Alternative check: To ensure this is the only correct swap, quickly test the other pairs. Swapping plus with multiplication or plus with division gives values far from 64 when evaluated. Similarly, swapping minus with plus or multiplication with division does not balance the equation. Only the interchange of division and minus yields exactly 64. This confirms that the pair of signs that must be interchanged is division and minus. Why Other Options Are Wrong: If plus and multiplication are swapped, the expression becomes 18 + 12 * 3 / 10 - 2, which evaluates to a non integer or at least not 64 when calculated correctly. Swapping plus and division or minus and plus also leads to values that are clearly not 64, either very large or significantly smaller. The distractor involving multiplication and division simply rearranges the high priority operations without bringing the value anywhere near 64. Therefore none of those swaps restore equality. Common Pitfalls: Many learners try to mentally juggle sign changes without carefully writing out each transformed expression, which can lead to confusion. Others inadvertently change only a single occurrence of a sign instead of applying the swap consistently to every instance. Another frequent issue is ignoring multiplication and division precedence and evaluating strictly left to right, leading to incorrect conclusions about which swap works. Writing down each candidate equation and calculating step by step avoids these errors. Final Answer: The equation becomes correct only when the division and minus signs are interchanged throughout, so the required swap is ÷ and -.

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