Question 1

In a certain code language, the digits of numbers stand for letters. If 3456 is coded as ROPE and 15526 is coded as APPLE, then what word is represented by the code 54613?

Accepted Answer

Introduction / Context: This coding decoding question presents a digit to letter substitution. Each distinct digit corresponds to exactly one letter, and the same mapping is used across several codes. You are given two known number word pairs and asked to decode a third numeric string into a meaningful arrangement of letters. This type of question tests your ability to notice consistent symbol to letter mappings. Given Data / Assumptions: - 3456 is coded as ROPE. - 15526 is coded as APPLE. - We need to decode 54613 using the same digit to letter mapping. - Each digit always represents the same letter whenever it appears. Concept / Approach: The strategy is to align the positions of digits with the positions of letters in the known codes. This allows us to deduce which digit corresponds to which letter. Once we know the mapping for all digits that appear in the unknown code 54613, we simply substitute the corresponding letters in the same order to obtain the required word. No arithmetic operations are involved, only symbolic substitution. Step-by-Step Solution: Step 1: From 3456 = ROPE, match each position: 3 → R, 4 → O, 5 → P, 6 → E. Step 2: From 15526 = APPLE, match each position: 1 → A, 5 → P, 5 → P, 2 → L, 6 → E. Step 3: Combine information from both words to get the full mapping: 1 → A, 2 → L, 3 → R, 4 → O, 5 → P, 6 → E. Step 4: Now decode 54613 digit by digit using this mapping. Step 5: 5 → P, 4 → O, 6 → E, 1 → A, 3 → R. Thus 54613 corresponds to POEAR. Verification / Alternative check: We can verify the mapping by reconfirming the original codes. Using our mapping, 3456 becomes R (3), O (4), P (5), E (6), which is ROPE. Similarly, 15526 becomes A (1), P (5), P (5), L (2), E (6), which reconstructs APPLE perfectly. Because it is consistent, the same mapping must apply to 54613 as well. Why Other Options Are Wrong: - Option RPPEO misplaces several letters and does not follow the precise digit to letter order we deduced. - Option ROPEA incorrectly attaches A to the end, which does not match the sequence 54613. - Option PAREO corresponds to a completely different digit sequence; it is not the correct translation of 54613 under the established mapping. Common Pitfalls: A common mistake is to focus only on part of the code or to assume that the letters must form an existing English word. In many coding decoding questions, the resulting string may not be a meaningful word, but the mapping must still be strictly followed. Always base your answer on consistent positional mapping rather than guesswork about English vocabulary. Final Answer: Using the digit to letter mapping derived from the given information, 54613 decodes to POEAR.

Question 2

Some equations are solved according to a special system. If 5 x 4 x 3 = 70 and 6 x 5 x 4 = 140 under this rule, then what is the correct value of 7 x 6 x 5 in the same pattern?

Accepted Answer

Introduction / Context: This question involves a nonstandard way of evaluating expressions with three numbers and the multiplication symbol. The expressions 5 x 4 x 3 and 6 x 5 x 4 do not equal their usual arithmetic products but instead follow a special rule that transforms the product into a different value. Your task is to identify this rule and then apply it to 7 x 6 x 5. Given Data / Assumptions: - According to the special system, 5 x 4 x 3 = 70. - Also, 6 x 5 x 4 = 140. - We must determine the value of 7 x 6 x 5 under the same rule. - The pattern should work consistently for both given examples. Concept / Approach: The natural starting point is the ordinary product of the three numbers. For 5, 4, and 3, the normal product is 5 * 4 * 3 = 60, which is close to 70. For 6, 5, and 4, the product is 6 * 5 * 4 = 120, which is close to 140. This suggests that a constant extra term, perhaps increasing in a simple way, is being added to the product. We then look at the differences between the standard product and the given result to find a clear pattern. Step-by-Step Solution: Step 1: Compute the ordinary product for the first expression: 5 * 4 * 3 = 60. Step 2: Compare with the given result 70. The difference is 70 - 60 = 10. Step 3: For the second expression, compute 6 * 5 * 4 = 120. Step 4: Compare with the given result 140. The difference is 140 - 120 = 20. Step 5: Notice that the additional term increases by 10 when the first number increases from 5 to 6. Step 6: For 7 x 6 x 5, compute the normal product: 7 * 6 * 5 = 210, and then add 30 as the next step in the pattern 10, 20, 30. So 210 + 30 = 240. Verification / Alternative check: The pattern of differences 10 and 20 is simple and arithmetic. It is natural to extend it to 30 for the third case, because the first factor increases from 5 to 6 to 7. Any other choice of extra term would break the regular progression. Also, attempts to express 70 and 140 as more complicated functions of the three numbers do not give such a simple and consistent result. Why Other Options Are Wrong: - Option 210 equals the plain product 7 * 6 * 5 but ignores the observed extra addition used in the previous equations. - Option 220 would require an increase of only 10 over 210, which would not match the established pattern of adding 10, then 20, then 30. - Option 230 would correspond to adding 20, which again fails to continue the increasing sequence of additional terms. Common Pitfalls: A common error is to assume that the same number is always added to the product or to try to use overly complex formulas. Another mistake is to overlook the simple arithmetic sequence in the differences between the real products and the coded results. Always examine both the primary arithmetic relationship and the differences to uncover such patterns. Final Answer: Using the observed rule of adding 10, 20, and then 30 to successive products, we find that 7 x 6 x 5 = 210 + 30 = 240 under the given system.

Question 3

In a certain letter code, the word HUMBLED is written as JWODNGF by shifting each letter forward in the alphabet. Using the same pattern, how will the word WAX be coded?

Accepted Answer

Introduction / Context: This is a straightforward letter coding question where each letter of a word is transformed according to a consistent rule. The transformation from HUMBLED to JWODNGF suggests a positional shift in the alphabet. Identifying the size and direction of this shift allows us to apply the same pattern to another word, WAX, and determine its coded form. Given Data / Assumptions: - The word HUMBLED is coded as JWODNGF. - We must find the code for the word WAX using the same rule. - The alphabet is treated cyclically, so if necessary letters near the end can wrap around, although this particular mapping does not require wraparound for WAX. Concept / Approach: The approach is to compare each letter of HUMBLED with the corresponding letter in JWODNGF. We check how many positions forward or backward in the alphabet each letter has moved. If the same shift applies to all letters, we conclude that the code is a uniform Caesar style shift. We then apply this shift to all letters in the new word WAX to get its code. Step-by-Step Solution: Step 1: Write the pairs of letters: H → J, U → W, M → O, B → D, L → N, E → G, D → F. Step 2: Count the shift for H → J. H is the 8th letter, J is the 10th letter. The shift is +2. Step 3: Check U → W. U is 21st, W is 23rd, again a shift of +2. Step 4: Similarly, M → O (13 to 15), B → D (2 to 4), L → N (12 to 14), E → G (5 to 7), and D → F (4 to 6) all represent a +2 shift. Step 5: Apply the same +2 shift to WAX. W (23rd) goes to Y (25th), A (1st) goes to C (3rd), and X (24th) goes to Z (26th). So WAX becomes YCZ. Verification / Alternative check: Rechecking each pair confirms that the shift is consistently +2 for all letters in HUMBLED. Because a single uniform shift works for the entire word, it is reasonable to apply it to WAX. There is no evidence of a more complicated pattern like reversing the word or using alternating shifts, so the simplest consistent rule is the correct one. Why Other Options Are Wrong: - Option DHP would involve a completely different set of shifts, not matching the +2 pattern. - Option VIS does not correspond to a +2 shift from WAX and cannot be generated from a uniform Caesar shift. - Option JMH again fails to follow the consistent rule derived from HUMBLED and JWODNGF. Common Pitfalls: Learners sometimes look for an unnecessarily complex rule when a simple shift is enough. Others forget to verify the shift on every letter, which is crucial to avoid incorrect patterns that only fit some positions. Always confirm that the same shift works for all letters in the example before applying it to a new word. Final Answer: Using a uniform shift of two positions forward in the alphabet, the word WAX is coded as YCZ.

Question 4

In a certain numerical code, the operator "@" transforms two numbers as follows: 9@3 = 12, 15@4 = 22, and 16@14 = 4. Using the same rule, what is the value of 6@2?

Accepted Answer

Introduction / Context: This question belongs to the coding decoding category for numbers. The operator "@" does not represent a standard arithmetic operation. Instead, it encodes a simple but hidden numerical relationship between its two arguments. Your task is to deduce this relationship from the given examples and then apply it to a new pair of numbers, 6 and 2. Given Data / Assumptions: - We have 9@3 = 12. - We also have 15@4 = 22. - We further have 16@14 = 4. - We must compute 6@2 according to the same rule. - The rule is assumed to be consistent across all these examples. Concept / Approach: A natural idea is to look at differences or sums between the two numbers, as these often produce simple patterns. Observing the examples suggests that the difference between the first and second numbers may be important. Therefore we experiment with expressions like a - b, 2 * (a - b), a + b, or combinations. We then check which formula exactly reproduces all given results. Step-by-Step Solution: Step 1: Examine 9@3 = 12. The difference 9 - 3 = 6, and 2 * (9 - 3) = 2 * 6 = 12, which matches the result. Step 2: Check the same rule on 15@4. Here 15 - 4 = 11, and 2 * (15 - 4) = 2 * 11 = 22, which matches. Step 3: Test the rule on 16@14. The difference 16 - 14 = 2, and 2 * (16 - 14) = 2 * 2 = 4, which again matches. Step 4: Therefore, the rule is a@b = 2 * (a - b). Step 5: Apply this rule to 6@2. Compute 6 - 2 = 4, then 2 * 4 = 8. Verification / Alternative check: The formula a@b = 2 * (a - b) fits all three given examples exactly, without any exceptions. Other candidate patterns, such as a + b or a - 2b, do not work consistently across all three equations. Because we have three independent confirmations, we can confidently use this rule to evaluate 6@2 as 8. Why Other Options Are Wrong: - Option 26 would require 2 * (6 - 2) or some other simple expression to equal 26, which is impossible without breaking the pattern seen in the examples. - Option 1 does not arise from any natural expression such as difference or sum when we follow the established rule. - Option 30 might come from multiplying 6 and 5 or misreading the operation, but it does not match the decoded rule. Common Pitfalls: Students sometimes guess a rule that fits only one or two of the given equations and move on without checking the remaining ones. Others focus only on sums and products, ignoring the possibility of scaled differences like 2 * (a - b). The safe technique is to systematically test each candidate rule against all examples before using it. Final Answer: Using the decoded pattern a@b = 2 * (a - b), the value of 6@2 is 8.

Question 5

Two motorcyclists P and Q start from the same point. P rides 11 km west, then turns south and rides 16 km, then turns to his right and rides 14 km. Q rides 30 km south, then turns to his right and rides 25 km. Where is Q with respect to P now?

Accepted Answer

Introduction / Context: This question tests your understanding of direction sense and relative position in two dimensional space. Two riders move in different directions and distances from the same starting point. You are asked to determine where one rider is located relative to the other at the end of their journeys. Such questions combine basic coordinate geometry ideas with careful reading of directions like north, south, east, and west. Given Data / Assumptions: - P starts at the origin point and rides 11 km west, then 16 km south, then 14 km further after turning right from south. - Q starts at the same origin, rides 30 km south, then turns right and rides 25 km. - Directions follow the standard convention: north up, south down, east right, west left on an imaginary map. - We must find Q’s position relative to P, not relative to the original starting point. Concept / Approach: A convenient way to solve such problems is to place the starting point at the origin of a coordinate system. We can treat east as the positive x direction, west as negative x, north as positive y, and south as negative y. Then each segment of motion becomes a change in coordinates. After computing the final coordinates of P and Q, we subtract them to find the relative displacement of Q from P and interpret that displacement as a direction and distance. Step-by-Step Solution: Step 1: Let the starting point be (0, 0). West is negative x, south is negative y. Step 2: P rides 11 km west to (-11, 0). Step 3: P then rides 16 km south to (-11, -16). Step 4: From facing south, a right turn leads to west, so P rides 14 km west to (-25, -16). Step 5: Q rides 30 km south from (0, 0) to (0, -30). Step 6: From facing south, Q turns right, which again is towards west, and rides 25 km to (-25, -30). Verification / Alternative check: Now compare the coordinates. P ends at (-25, -16) and Q ends at (-25, -30). The x coordinates are equal, so they are vertically aligned. The difference in y is -30 minus (-16) = -14. This means Q is 14 km further south along the same vertical line. Hence, with respect to P, Q is 14 km to the south. The result is consistent with a diagram drawn to scale and with the interpretation of right turns from a southward direction. Why Other Options Are Wrong: - Option 14 km North reverses the direction; the calculations clearly show that Q is below P, not above. - Option 44 km South incorrectly combines distances without paying attention to the actual relative displacement. - Option 44 km North is both the wrong distance and the wrong direction. Common Pitfalls: Students often confuse left and right turns when they imagine the rider facing south or west instead of north. Another typical error is to add distances directly without working through coordinates or drawing a sketch. To avoid these mistakes, always track direction changes step by step and, if needed, sketch the path on paper with axes marked. Final Answer: After following their respective routes, Q is located 14 km directly south of P. Therefore, the correct answer is 14 km South.

Question 6

In a certain code language, the word GIVE is written as VIEG and the word OVER is written as EVRO. Following the same coding pattern, how will the word DISK be written?

Accepted Answer

Introduction / Context: This is a letter coding question where the letters of each word are rearranged in a fixed positional pattern. Two examples, GIVE → VIEG and OVER → EVRO, are provided. You must analyze how the positions of letters change from the original word to the coded word and then apply the same reordering to the new word DISK. Given Data / Assumptions: - GIVE is coded as VIEG. - OVER is coded as EVRO. - We need the code for DISK. - The lengths of the words are the same and the encoding is based on rearranging letter positions, not changing letters themselves. Concept / Approach: When the code uses the same letters but in a different order, the pattern is usually positional. We compare the positions of letters in the original word with those in the coded word. If we can describe a consistent order like "third, second, fourth, first," and see that it holds for both examples, then we apply exactly that ordering to the new word DISK to get its code. Step-by-Step Solution: Step 1: Write GIVE with positions: G(1), I(2), V(3), E(4). Step 2: The code VIEG can be written by positions as 3rd letter (V), 2nd letter (I), 4th letter (E), 1st letter (G). So the pattern is 3, 2, 4, 1. Step 3: Check OVER. O(1), V(2), E(3), R(4). Applying the pattern 3, 2, 4, 1 gives E(3), V(2), R(4), O(1), which is EVRO, matching the given code. Step 4: Now apply the same pattern to DISK. D(1), I(2), S(3), K(4). Step 5: Taking letters in the order 3, 2, 4, 1 gives S(3), I(2), K(4), D(1), so the coded form is SIKD. Verification / Alternative check: We have confirmed that the 3, 2, 4, 1 reordering pattern works for both given pairs. No other simple rearrangement, such as reversing the word or rotating by one position, fits both examples. Since the pattern is position based and consistent, applying it to DISK must be correct. Therefore, SIKD is the only valid encoding of DISK under this system. Why Other Options Are Wrong: - Option SIDK would correspond to 3, 1, 2, 4 or another inconsistent order and does not match the pattern 3, 2, 4, 1. - Option KISD rearranges the letters incorrectly and does not follow the same positional mapping used in the examples. - Option KDSI is another arbitrary order and is not derived from the established coding rule. Common Pitfalls: Learners sometimes focus on letter identities rather than positions and attempt to guess at an alphabetical shift, which is not used here. Others forget to check that a pattern works for all examples, not just one. The reliable method is always to map positions and confirm the same pattern across all given coded words. Final Answer: Using the positional pattern 3, 2, 4, 1, the word DISK is coded as SIKD.

Question 7

If BAPTISM is coded as DCRVKUO by shifting each letter two places forward in the alphabet, then using the same rule, how will the word TIN be coded?

Accepted Answer

Introduction / Context: This question involves a simple letter shifting code. The word BAPTISM is transformed into DCRVKUO, which suggests that each letter has been moved a fixed number of positions forward in the alphabet. Once we determine this shift, we can apply the same shift to the letters of TIN to obtain its coded form. Such Caesar style shifts are very common in coding decoding questions. Given Data / Assumptions: - BAPTISM is coded as DCRVKUO. - We must find the code for TIN using the same pattern. - The mapping is letter to letter with no change in word length. Concept / Approach: The method is to examine one or more letter pairs from the given example and compute how many positions forward in the alphabet each letter has moved. If the same shift is found for all letters, then we have a uniform shift code. Afterward, we apply this uniform shift to each letter in TIN. If any wraparound from Z back to A were needed, we would handle it, but in this case, the letters remain within the standard range. Step-by-Step Solution: Step 1: Match letters from BAPTISM → DCRVKUO. B → D, A → C, P → R, T → V, I → K, S → U, M → O. Step 2: Compute the shift for B → D. B is 2nd letter, D is 4th, so the shift is +2. Step 3: For A → C, the shift is again +2 (1 to 3). P → R is +2 (16 to 18), T → V is +2 (20 to 22), I → K is +2 (9 to 11), S → U is +2 (19 to 21), and M → O is +2 (13 to 15). Step 4: Since every letter is shifted by +2, we apply the same rule to TIN. Step 5: T is 20th, so T + 2 gives V (22nd). I is 9th, so I + 2 gives K (11th). N is 14th, so N + 2 gives P (16th). Hence, TIN is coded as VKP. Verification / Alternative check: We have verified that the shift is consistently +2 for all letters of BAPTISM, making it a standard Caesar shift. No alternating pattern or position dependent shift is required to explain the given code. Therefore, shifting each letter of TIN by +2 is the simplest and correct application of the rule, resulting in VKP. Why Other Options Are Wrong: - Option EBC reflects a different pattern that does not correspond to a uniform +2 shift from TIN. - Option FDF does not match the letter positions that result from adding 2 to T, I, and N. - Option CLS would require irregular shifts and is not consistent with the code used for BAPTISM. Common Pitfalls: Sometimes learners mistakenly use a -2 shift or mix forward and backward shifts without verifying all letter pairs. Others may guess codes that form meaningful words in English but do not respect the given pattern. The correct strategy is to rely on consistent positional changes, not on whether the resulting code itself is a real word. Final Answer: Using a uniform shift of two positions forward in the alphabet, the word TIN is coded as VKP.

Question 8

In a certain code language, "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. What is the value of the expression 45 x 5 - 24 + 3 ÷ 80 when evaluated using these coded operations?

Accepted Answer

Introduction / Context: This coded arithmetic problem replaces standard operation symbols with new meanings. Rather than evaluating the expression 45 x 5 - 24 + 3 ÷ 80 directly, you must first decode each symbol to its true operation and then apply normal arithmetic precedence rules. It checks both your ability to follow symbol substitution and your care in performing multi step arithmetic. Given Data / Assumptions: - "+" represents multiplication. - "-" represents addition. - "x" represents division. - "÷" represents subtraction. - The expression to evaluate is 45 x 5 - 24 + 3 ÷ 80. - After decoding, we apply the usual order of operations: division and multiplication before addition and subtraction. Concept / Approach: The solution proceeds in two clear phases. First, interpret each symbol according to the given mapping and rewrite the entire expression in terms of the real operations. Second, evaluate this decoded expression step by step, respecting operator precedence. Any mistake in decoding or precedence leads to an incorrect answer, so discipline in both stages is essential. Step-by-Step Solution: Step 1: Original coded expression is 45 x 5 - 24 + 3 ÷ 80. Step 2: Replace "x" by division, "-" by addition, "+" by multiplication, and "÷" by subtraction. Step 3: After substitution, we get: 45 ÷ 5 + 24 * 3 - 80. Step 4: Apply operator precedence. First compute 45 ÷ 5 = 9. Step 5: Then compute 24 * 3 = 72. Step 6: Now perform the remaining operations from left to right: 9 + 72 - 80 = 81 - 80 = 1. Verification / Alternative check: To verify, we can quickly redo the substitution and arithmetic. The decoded expression is 45 ÷ 5 + 24 * 3 - 80. Double checking the calculations, 45 ÷ 5 is clearly 9, 24 * 3 is 72, and 9 + 72 = 81. Subtracting 80 gives 1. Since each symbol has been correctly replaced and the calculations are straightforward, the result is stable and trustworthy. Why Other Options Are Wrong: - Option 100 would result from incorrect arithmetic such as 9 + 72 + 19 or similar careless combinations. - Option 52 might appear if someone computed 45 ÷ 5 = 9, then 24 * 3 = 72, but mishandled subtraction or addition. - Option 82 could come from adding 9 and 72 and then forgetting to subtract 80 properly. Common Pitfalls: Many students forget to decode every symbol or accidentally use the printed meaning of the symbol instead of the described one. Another frequent error is to perform operations strictly left to right without prioritizing division and multiplication. Whenever you face such coded arithmetic, always rewrite the whole expression in standard notation first and then calculate carefully. Final Answer: After decoding the operators and evaluating with the correct order of operations, the value of the expression is 1.

Question 9

In a certain numerical code, the operation "$" between two numbers is defined so that 5$125 = 25 and 12$48 = 4. Using the same rule, what is the value of 4$24?

Accepted Answer

Introduction / Context: This numerical coding question defines a special operation "$" between two numbers. The expressions 5$125 and 12$48 do not represent usual arithmetic symbols but instead follow a specific relationship. You must detect the rule from the examples and then apply it to compute 4$24. Such problems are popular in reasoning tests because they reward pattern recognition and logical thinking. Given Data / Assumptions: - 5$125 = 25. - 12$48 = 4. - We need to find 4$24. - The operation "$" is assumed to be consistent across these examples. Concept / Approach: We look for a simple relationship involving division or multiplication, since the results 25 and 4 are smaller than the second numbers 125 and 48. A natural guess is that the result could be the second number divided by the first number, or some variant of that idea. Once a candidate rule is identified, it must be checked against all given examples before using it to evaluate the new expression. Step-by-Step Solution: Step 1: For 5$125 = 25, notice that 125 ÷ 5 = 25, which matches the result. Step 2: For 12$48, compute 48 ÷ 12 = 4, which also matches the given result. Step 3: This suggests that a$b = b ÷ a for the "$" operation. Step 4: Apply this rule to 4$24. Here, a = 4 and b = 24. Step 5: Compute 24 ÷ 4 = 6. Verification / Alternative check: We can quickly check if any other simple rule might also work, such as a * b or b - a, but these do not produce 25 from 5 and 125 or 4 from 12 and 48. The division based rule b ÷ a is the only obvious and consistent one that fits both examples. Therefore we confidently apply it to 4 and 24 to get 6. Why Other Options Are Wrong: - Option 34 and option 35 are much larger than 24 and cannot be produced by dividing 24 by 4. - Option 5 might be guessed by mistake using 24 ÷ 4 plus or minus 1, but such an adjustment would break the consistency with the original examples. Common Pitfalls: A common error is to try to use both numbers symmetrically, for example averaging them or multiplying them in some fashion, even though the smaller result strongly suggests division of the larger by the smaller. Another mistake is to test a rule on only one of the two examples and not on both, which can lead to an incorrect final answer. Final Answer: Using the rule a$b = b ÷ a, we obtain 4$24 = 24 ÷ 4 = 6.

Question 10

In a certain code language, the word MIGRANT is written as LHFQZMS by shifting each letter one place backward in the alphabet. Using the same rule, how will the word GEL be coded?

Accepted Answer

Introduction / Context: This is another letter shift coding problem, but this time the letters are shifted backward rather than forward. The mapping MIGRANT → LHFQZMS strongly suggests that each letter has been moved by a fixed number of positions in the reverse direction through the alphabet. Once that shift is understood, we can apply the same transformation to the letters of GEL to find its coded form. Given Data / Assumptions: - MIGRANT is coded as LHFQZMS. - We must determine the code for the word GEL. - The code uses a consistent letter to letter mapping, likely a uniform shift. Concept / Approach: To solve this, we compare the positions of each letter in MIGRANT with the corresponding letter in LHFQZMS and measure the shift. If each letter is shifted by the same amount, we have a uniform backward shift. We then apply this same shift to each letter of GEL. If any letter reaches before A, we would wrap around, but in this particular case all letters stay within the standard range after shifting. Step-by-Step Solution: Step 1: Match the pairs: M → L, I → H, G → F, R → Q, A → Z, N → M, T → S. Step 2: Compute the shift for M → L. M is 13th, L is 12th, so the shift is -1. Step 3: Check I → H (9th to 8th), G → F (7th to 6th), R → Q (18th to 17th), N → M (14th to 13th), and T → S (20th to 19th). Each is also a -1 shift. Step 4: For A → Z, shifting backward by one from 1st letter A gives 26th letter Z, showing a wraparound. Step 5: Apply the same -1 shift to GEL. G (7th) becomes F (6th), E (5th) becomes D (4th), L (12th) becomes K (11th). So the code for GEL is FDK. Verification / Alternative check: Since all letters of MIGRANT show the same backward shift of one position, the coding rule is clearly a uniform -1 shift. No alternating pattern is needed to explain the given mapping. Applying this to GEL yields FDK without ambiguity. Rechecking the individual letter positions confirms that the shifts for G, E, and L are consistent with the rule. Why Other Options Are Wrong: - Option QXK uses letters that are far away and not reachable by a simple -1 shift from G, E, and L. - Option IXZ again fails to follow a consistent one step backward pattern from the original letters. - Option IFG scrambles different shifts and does not match the systematic one step backward rule demonstrated by MIGRANT. Common Pitfalls: Learners sometimes check only one or two letter pairs and then assume a forward shift when the actual mapping is backward. Another mistake is to forget the wraparound behavior illustrated by A → Z, which clearly indicates a backward movement. Always compute the position differences carefully and verify the shift across all given letters before applying it to a new word. Final Answer: Using a uniform shift of one position backward in the alphabet, the word GEL is coded as FDK.

Question 11

In a certain code language, "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. What is the value of 27 x 3 ÷ 30 + 5 - 125 when evaluated according to these coded operations?

Accepted Answer

Introduction / Context: This question is very similar in structure to other coded arithmetic problems. Each familiar symbol in the expression represents a different operation from its usual meaning. To obtain the correct value of the expression 27 x 3 ÷ 30 + 5 - 125, you must first translate each symbol into its true operation and then evaluate the resulting expression with standard precedence rules. Given Data / Assumptions: - "+" represents multiplication. - "-" represents addition. - "x" represents division. - "÷" represents subtraction. - The coded expression is 27 x 3 ÷ 30 + 5 - 125. - After decoding, we respect the usual arithmetic order: division and multiplication before addition and subtraction. Concept / Approach: The process again follows two phases. First, decode each symbol using the mapping provided by the question. Second, evaluate the decoded numeric expression carefully. Because the operators are reassigned, reading the expression without decoding leads to a completely different and incorrect result. Strict attention to the new meanings and to operator precedence is needed. Step-by-Step Solution: Step 1: Original coded expression: 27 x 3 ÷ 30 + 5 - 125. Step 2: According to the mapping, "x" becomes division, "÷" becomes subtraction, "+" becomes multiplication, and "-" becomes addition. Step 3: Rewrite the expression with true operations: 27 ÷ 3 - 30 * 5 + 125. Step 4: Apply operator precedence. First compute 27 ÷ 3 = 9. Step 5: Next compute 30 * 5 = 150. Step 6: Now process the remaining operations left to right: 9 - 150 + 125 = (9 - 150) + 125 = -141 + 125 = -16. Verification / Alternative check: We can quickly re verify each substitution. The symbol between 27 and 3 is "x", so we use division. The symbol between 3 and 30 is "÷", so we use subtraction. Between 30 and 5 is "+", so we use multiplication. Finally, between 5 and 125 is "-", so we use addition. Plugging these into the numeric calculation consistently gives -16. No alternative reading of the symbols matches the mappings from the question. Why Other Options Are Wrong: - Option 69 might arise if someone mistakenly treats some operations as ordinary plus or minus without decoding correctly. - Option 67 is another example of calculation error or misapplied precedence when combining 9, 150, and 125. - Option -15 suggests an arithmetic slip such as miscalculating -141 + 125. Common Pitfalls: Typical errors include decoding only part of the expression, forgetting to use multiplication where required, or not applying the standard operation order. A few candidates also attempt to evaluate the coded expression directly as it appears, which completely ignores the intended trick of the question. The safe habit is always to rewrite the entire expression with true operators before touching the numbers. Final Answer: After decoding each symbol and evaluating carefully, the value of the expression is -16.

Question 12

In a certain numerical code, the operation "$" between two numbers is defined so that 11$25 = 18 and 12$20 = 16. Using the same pattern, what is the value of 4$50?

Accepted Answer

Introduction / Context: This numerical reasoning problem defines a custom operation "$" that combines two numbers in a special way. The examples 11$25 = 18 and 12$20 = 16 hint that the operation may involve an average or similar combination of the two numbers. Your objective is to uncover the underlying rule and then apply it to 4$50. Given Data / Assumptions: - 11$25 = 18. - 12$20 = 16. - We must compute 4$50 using the same rule. - The operation is consistent across all examples and involves both numbers in a simple arithmetic fashion. Concept / Approach: Because the outputs 18 and 16 lie between the two numbers in each pair (11 and 25, 12 and 20), it is natural to suspect that the operation involves averaging. Therefore, we test the arithmetic mean (a + b) / 2 for both examples. If this matches, then we apply the same formula to 4 and 50 to find the required value. Step-by-Step Solution: Step 1: For 11$25 = 18, compute the arithmetic mean (11 + 25) / 2. Step 2: 11 + 25 = 36, and 36 / 2 = 18, which matches the given result. Step 3: For 12$20 = 16, compute (12 + 20) / 2. Step 4: 12 + 20 = 32, and 32 / 2 = 16, again matching the given result. Step 5: This confirms the rule a$b = (a + b) / 2. Step 6: Apply this rule to 4$50: (4 + 50) / 2 = 54 / 2 = 27. Verification / Alternative check: Alternative possibilities like a + b or b - a do not produce the results 18 and 16 for the given examples. The arithmetic mean works perfectly for both and is an intuitive and simple symmetric function of a and b. Checking the final calculation for 4 and 50 confirms that (4 + 50) / 2 is 27, so the rule applies cleanly to the new pair as well. Why Other Options Are Wrong: - Option 42 or 37 do not fall exactly halfway between 4 and 50, contradicting the average based rule. - Option 17 does not match any simple symmetric pattern of 4 and 50 and cannot be justified using the confirmed operation definition. Common Pitfalls: An error some students make is to try to construct a very complicated formula when a simple average explains the data perfectly. Others check the rule on only one example and then assume it holds without testing the second example. Always validate your rule on all given pairs to avoid incorrect generalizations. Final Answer: Using the rule a$b = (a + b) / 2, the value of 4$50 is 27.

Question 13

In a certain code language, the sentences "book is tough", "tough can easy" and "easy not book" are written as "fu la mi", "fu muk po" and "ti po la" respectively. What is the code for the word "tough" in that language?

Accepted Answer

Introduction / Context: This coding decoding question uses a word code language where each English word is represented by a unique code word. You are given three coded sentences and must determine which code corresponds to the word "tough". This kind of problem tests logical deduction by comparing overlapping information from multiple coded statements. Given Data / Assumptions: - "book is tough" is written as "fu la mi". - "tough can easy" is written as "fu muk po". - "easy not book" is written as "ti po la". - Each English word has a unique code word, and vice versa. - The order of words and codes is not necessarily the same, only the set membership matters. Concept / Approach: The method is to use set intersections of code words for sentences that share common English words. If two sentences contain the same English word, then their code sets must share a common code word. By comparing different pairs of sentences, we can map out which code stands for "book", which for "tough", and which for "easy". Once the mapping is clear, answering the question is straightforward. Step-by-Step Solution: Step 1: From "book is tough" → "fu la mi", we know that the words book, is, tough correspond to the code set {fu, la, mi}. Step 2: From "tough can easy" → "fu muk po", the words tough, can, easy correspond to {fu, muk, po}. Step 3: From "easy not book" → "ti po la", the words easy, not, book correspond to {ti, po, la}. Step 4: Consider the word "book", which appears in the first and third sentences. The common code between {fu, la, mi} and {ti, po, la} is "la", so "book" corresponds to "la". Step 5: Consider the word "easy", which appears in the second and third sentences. The common code between {fu, muk, po} and {ti, po, la} is "po", so "easy" corresponds to "po". Step 6: Now in the first and second sentences, the common English word left in both is "tough". The common code between {fu, la, mi} and {fu, muk, po} is "fu". Therefore, "tough" corresponds to "fu". Verification / Alternative check: With the mapping book → la, easy → po, tough → fu, we can verify the sentences. For "book is tough", the code set {fu, la, mi} must include la and fu for book and tough, which it does. For "tough can easy", the code set {fu, muk, po} includes fu for tough and po for easy. Finally, "easy not book" has {ti, po, la}, containing po for easy and la for book. All are consistent, confirming the mapping. Why Other Options Are Wrong: - Option mi is unused in the overlaps and does not uniquely correspond to "tough". - Option po has been shown to represent "easy", not "tough". - Option la has been determined to represent "book". Common Pitfalls: A common mistake is to assume a one to one mapping without checking all overlapping sentences, leading to incorrect associations. Another is to rely on the order of words instead of treating codes and words as unordered sets. Always use intersections of code sets for sentences sharing the same English word and confirm consistency across all sentences. Final Answer: The code word that represents "tough" in this language is fu.

Question 14

In a certain code language, "-" represents "+", "+" represents "x", "x" represents "÷" and "÷" represents "-". What is the value of the expression 2 - 12 + 10 x 5 ÷ 12 when evaluated using these coded operations?

Accepted Answer

Introduction / Context: This is yet another coded arithmetic problem in which each familiar operation symbol is reassigned a new meaning. The expression 2 - 12 + 10 x 5 ÷ 12 cannot be read with ordinary operator meanings. Instead, we must decode each symbol, rewrite the expression in true arithmetic form, and then evaluate it carefully following the correct precedence rules. Given Data / Assumptions: - "-" represents "+". - "+" represents "x" (multiplication). - "x" represents "÷" (division). - "÷" represents "-". - The coded expression is 2 - 12 + 10 x 5 ÷ 12. - After decoding, we apply the usual arithmetic precedence. Concept / Approach: The procedure is to substitute each coded symbol with its real meaning, then simplify step by step. Because the same symbols are used with nonstandard meanings, it is easy to slip back into reading them normally, so attention to the mapping is crucial. Once the expression is decoded, the rest of the work is straightforward arithmetic with division and multiplication first, followed by addition and subtraction. Step-by-Step Solution: Step 1: Start with the coded expression: 2 - 12 + 10 x 5 ÷ 12. Step 2: According to the mapping, "-" becomes "+", "+" becomes multiplication, "x" becomes division, and "÷" becomes subtraction. Step 3: Rewrite the expression in true operations: 2 + 12 * 10 ÷ 5 - 12. Step 4: Evaluate multiplication and division from left to right. First compute 12 * 10 = 120. Step 5: Then compute 120 ÷ 5 = 24. Step 6: Now the expression becomes 2 + 24 - 12. Perform addition and subtraction left to right: 2 + 24 = 26, then 26 - 12 = 14. Verification / Alternative check: Rechecking the mapping and substitution confirms that each symbol has been correctly replaced. There is no ambiguity in the arithmetic steps, and the intermediate results 120 and 24 are easy to verify. Therefore, the final answer 14 is reliable. Any alternative reading that ignores the symbol mapping would produce a different and incorrect value. Why Other Options Are Wrong: - Option 32 might result from performing 2 + 12 + 10 + 5 + 3 or some other incorrect combination without proper precedence. - Option 8 could come from mishandling the subtraction or forgetting to multiply before dividing. - Option 4 suggests an arithmetic mistake in combining 2, 24, and 12. Common Pitfalls: Students sometimes decode only part of the expression or forget to apply true operator precedence after decoding. Another frequent mistake is to treat the operators as if they still had their standard meanings. To avoid this, always write out the fully decoded expression before evaluating and double check each substitution step. Final Answer: After decoding all operators and evaluating with the correct order, the value of the expression is 14.

Question 15

The following equation is incorrect: 1 ÷ 14 x 30 + 20 - 10 = 12. By interchanging exactly two operation signs among "+", "-", "x" and "÷", which pair of signs must be swapped to make the equation correct?

Accepted Answer

Introduction / Context: This problem involves correcting an arithmetic equation by interchanging two operation signs. The left hand side expression 1 ÷ 14 x 30 + 20 - 10 does not equal 12 when evaluated with standard operator meanings and precedence. Your task is to identify which pair of signs, when swapped throughout the expression, will make the equation valid. Given Data / Assumptions: - Original incorrect equation: 1 ÷ 14 x 30 + 20 - 10 = 12. - We may interchange exactly two operation signs from the set {"+", "-", "x", "÷"}. - All other signs and numbers remain unchanged. - Standard operator precedence holds: division and multiplication before addition and subtraction. Concept / Approach: We systematically test the given options, each representing a specific pair of signs to interchange wherever they occur in the expression. For each candidate pair, we swap the signs, recompute the left hand side using correct precedence, and check whether the result equals 12. The pair that produces a true equality is the required answer. Step-by-Step Solution: Step 1: Focus on option "+ and ÷". If we interchange "+" and "÷", then every "+" becomes "÷" and every "÷" becomes "+". Step 2: Original expression is 1 ÷ 14 x 30 + 20 - 10. Step 3: After swapping "+" and "÷", the expression becomes 1 + 14 x 30 ÷ 20 - 10. Step 4: Evaluate using precedence. First compute 14 x 30 = 420. Step 5: Next compute 420 ÷ 20 = 21. Step 6: Now compute the full expression: 1 + 21 - 10 = 22 - 10 = 12, which matches the right hand side. Verification / Alternative check: We can briefly check that the other options do not work. Swapping "-" and "+" changes the balance of positive and negative terms but leaves the division and multiplication untouched, leading to a value different from 12. Similarly, swapping "÷ and x" or "x and -" produces expressions whose evaluated values are not 12 under standard precedence. Only interchanging "+" and "÷" yields the correct result of 12. Why Other Options Are Wrong: - Swapping "- and +" changes the addition and subtraction, but the resulting expression does not simplify to 12. - Swapping "÷ and x" distorts the relative size of the terms involving 14 and 30, making it impossible to reach 12 with the remaining additions and subtractions. - Swapping "x and -" similarly disrupts the expression and does not lead to the target value. Common Pitfalls: A typical mistake is to ignore operator precedence and evaluate expressions strictly from left to right while testing sign changes, which may suggest incorrect pairs work. Another error is to change more than two signs or to alter numbers, which is not allowed. The correct strategy is to follow the rules strictly and recompute carefully for each candidate pair. Final Answer: The equation becomes correct if we interchange the "+" and "÷" signs. Therefore, the required pair of signs is + and ÷.

Question 16

In a certain numerical code, the operation "*" between two numbers is defined so that 8*2 = 3, 14*18 = -2 and 18*2 = 8. Using the same rule, find the value of 14*10.

Accepted Answer

Introduction / Context: In this coding decoding problem, the symbol "*" represents a special numerical operation that combines two numbers in a nonstandard way. The examples 8*2 = 3, 14*18 = -2, and 18*2 = 8 all follow the same hidden rule. You must decode that rule and then apply it to the new expression 14*10 to find the correct value. Given Data / Assumptions: - 8*2 = 3. - 14*18 = -2. - 18*2 = 8. - We must evaluate 14*10 using the same operation. - The rule is algebraic and consistent for all given examples. Concept / Approach: Observing that some outputs are positive and some negative suggests that the operation might involve differences between the two numbers, possibly divided by a constant factor. A natural attempt is to compute (a - b) or (b - a) and then see whether halving the result matches the given outputs. Once a simple expression is found that fits all three cases, we can apply it confidently to 14 and 10. Step-by-Step Solution: Step 1: Test the expression (a - b) / 2 for 8 and 2. Compute (8 - 2) / 2 = 6 / 2 = 3, which matches 8*2 = 3. Step 2: Test the same expression for 14 and 18. Compute (14 - 18) / 2 = (-4) / 2 = -2, which matches 14*18 = -2. Step 3: Test it for 18 and 2. Compute (18 - 2) / 2 = 16 / 2 = 8, which matches 18*2 = 8. Step 4: Therefore the rule is a*b = (a - b) / 2. Step 5: Apply this rule to 14 and 10: (14 - 10) / 2 = 4 / 2 = 2. Verification / Alternative check: Having three consistent examples strongly supports the formula a*b = (a - b) / 2. If we attempted other expressions such as (b - a) / 2, (a + b) / 2, or a + b, they would not simultaneously reproduce all three given results. Recomputing each example confirms that we have the correct and unique simple rule. Therefore, using it for 14*10 is appropriate. Why Other Options Are Wrong: - Option -5 would require (14 - 10) / 2 to be -5 or a different rule altogether, which breaks consistency with earlier equations. - Option -2 corresponds to the specific case (14 - 18) / 2, not to 14 and 10. - Option 6 could result from 14 - 8 or 3 * 2 in a mistaken pattern, but it does not align with the established formula. Common Pitfalls: A frequent mistake is to focus on sums or products rather than differences when negative outputs are involved. Others may try several unrelated rules for different examples instead of searching for a single formula that fits all. The reliable strategy is to look for patterns that work uniformly across every given example and only then apply them to new inputs. Final Answer: Using the decoded rule a*b = (a - b) / 2, the value of 14*10 is 2.

Question 17

Consider the following sequence of seven letter strings formed using the letters X and x: XxXXXXX, XXxXXXX, XXXxXXX, XXXXxXX, XXXXXxX. In each successive term, the single lowercase x appears to shift one position to the right. Which of the following…

Accepted Answer

Introduction / Context: This question tests your ability to observe a visual pattern in a sequence of coded terms that use only the letters X and x. In coding and series based reasoning, the position of a particular symbol or letter often moves in a predictable way. Here, the lowercase x is the key element, and your task is to determine how it shifts through the sequence and then predict the next term that continues the same trend. Given Data / Assumptions: • Given terms: XxXXXXX, XXxXXXX, XXXxXXX, XXXXxXX, XXXXXxX. • Each term has seven letters in total. • Each term contains exactly one lowercase x and six uppercase X letters. • The next term must follow exactly the same positional pattern of the lowercase x. Concept / Approach: The core idea is to track the position of the lowercase x from left to right. In many sequence problems, an element moves step by step across positions. Once we map the exact position index of x in every term, we can predict its next position. After identifying this shift, we simply construct the term with x in the new position and X in all remaining positions. Step-by-Step Solution: Step 1: Mark positions from left to right as 1, 2, 3, 4, 5, 6, 7. Step 2: In the first term XxXXXXX, the lowercase x is at position 2. Step 3: In the second term XXxXXXX, the lowercase x is at position 3. Step 4: In the third term XXXxXXX, the lowercase x is at position 4. Step 5: In the fourth term XXXXxXX, the lowercase x is at position 5. Step 6: In the fifth term XXXXXxX, the lowercase x is at position 6. Step 7: The pattern is clear: the x moves one step to the right in each new term, so in the next (sixth) term it must be at position 7. Step 8: A term with x at position 7 and X elsewhere is XXXXXXx. Verification / Alternative check: You can confirm the pattern by counting positions again. From term one to term five the positions of x are 2, 3, 4, 5 and 6 respectively. This is an arithmetic progression with common difference 1. The next value in this progression is 7, which exactly matches the position of x in XXXXXXx. No other option moves the lowercase x to a new position consistent with the established pattern. Why Other Options Are Wrong: Option xXXXXXX places x at position 1, which would move it backwards instead of forward. Option XxXXXXX repeats the first term and does not continue the sequence. Option XXxXXXX repeats the second term and again fails to progress the pattern. Option XXXxXXX repeats the third term rather than giving the sixth distinct term. Common Pitfalls: Some learners focus only on the number of X and x letters and overlook the precise position of the lowercase x. Others mistakenly assume the sequence might restart after a few terms. It is important to track the exact index of the special character and not be distracted by terms that just look familiar. Another pitfall is to treat the pattern as alternating randomly, instead of a simple left to right shift. Final Answer: The lowercase x continues moving one step to the right and therefore occupies the seventh position in the next term. The correct continuation of the series is XXXXXXx.

Question 18

In a certain letter coding system, each word is assigned a numerical value based on its letters. For example, the single letter S has the value 19, the word SUN has the value 54, and the word CAKE has the value 20. Using the same coding pattern, wha…

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Introduction / Context: This problem is a classic example of a letter to number coding question, where each letter of the English alphabet is associated with its position number, and then those values are combined to obtain the code for a word. Such questions test your familiarity with alphabet positions and your ability to quickly add several numbers. Understanding this pattern makes it easy to handle many similar verbal reasoning questions. Given Data / Assumptions: • The letter S is coded as 19. • The word SUN is coded as 54. • The word CAKE is coded as 20. • We assume standard alphabet positions: A = 1, B = 2, C = 3, …, Z = 26. • The same rule must be applied to find the code for MISTAKE. Concept / Approach: The most natural approach is to check whether the codes are obtained by summing alphabet positions of each letter in the word. If this works for the given examples, we can safely apply the same rule to the target word. We therefore convert each letter into its positional value, add those values, and match the total with one of the options. Step-by-Step Solution: Step 1: Check S = 19. In the alphabet, S is the 19th letter, so this fits the pattern directly. Step 2: Check SUN = 54. Positions: S = 19, U = 21, N = 14. Sum = 19 + 21 + 14 = 54. The pattern is consistent. Step 3: Check CAKE = 20. Positions: C = 3, A = 1, K = 11, E = 5. Sum = 3 + 1 + 11 + 5 = 20. Again the pattern holds. Step 4: Apply the same to MISTAKE. Write down positions: M = 13, I = 9, S = 19, T = 20, A = 1, K = 11, E = 5. Step 5: Add these values: 13 + 9 = 22, 22 + 19 = 41, 41 + 20 = 61, 61 + 1 = 62, 62 + 11 = 73, 73 + 5 = 78. Step 6: The total value obtained for MISTAKE is 78. Verification / Alternative check: As a quick verification, compare the size of the word and the magnitude of the final value. MISTAKE has seven letters and the average position value is around 10 to 11, so a total near 70 to 80 is reasonable. This rough check supports the calculated result of 78. Also, none of the other options represent the correct sum of the letter values, so the answer is uniquely determined. Why Other Options Are Wrong: Option 68 is too small and would correspond to a lower overall sum of letter positions than actually present in MISTAKE. Option 59 is much smaller and clearly does not match the detailed addition. Option 48 is even further away from the computed total and does not fit the established pattern. Option 88 is larger than the correct sum and cannot be obtained from the given letter values. Common Pitfalls: Common mistakes include miscounting letter positions, especially confusing letters around the middle of the alphabet such as M, N, O, P, and mixing up the order of additions. Some learners rush and try to guess based on approximate length, which can easily lead to an incorrect option. It is safer to write the positions clearly and add them systematically. Final Answer: Using alphabet positions and summing them, the code for MISTAKE is 78.

Question 19

In a certain coded arithmetic system, the usual operators are replaced by new meanings as follows: the symbol + stands for multiplication, the symbol - stands for addition, and the symbol x stands for division. Under this coding scheme, what is the …

Accepted Answer

Introduction / Context: This question belongs to the category of coded arithmetic operations, where familiar mathematical symbols are reassigned different meanings. The challenge is not simply to evaluate the expression mechanically, but to correctly interpret each symbol according to the new code and then apply normal rules of arithmetic, including the usual precedence of multiplication and division before addition and subtraction. This tests both attention to detail and conceptual understanding of operator precedence. Given Data / Assumptions: • The code specifies: + means multiplication. • The code specifies: - means addition. • The code specifies: x means division. • The written expression is 128 + 9 - 16 x 4. • After replacing operators by their coded meanings, we then use standard arithmetic rules. Concept / Approach: The method has two main stages. First, translate the coded expression into its real mathematical form by replacing each symbol with its coded meaning. Second, evaluate the resulting expression using the usual operator precedence rules: multiplication and division first (from left to right), followed by addition and subtraction. Carefully following both stages ensures that the final value is correct. Step-by-Step Solution: Step 1: Rewrite each operator with its real meaning based on the code. Step 2: In the expression 128 + 9 - 16 x 4, replace + with multiplication to get 128 * 9. Step 3: Replace - with addition to get + 16. Step 4: Replace x with division to get ÷ 4. Step 5: The coded expression now becomes 128 * 9 + 16 ÷ 4. Step 6: Apply operator precedence. First compute 128 * 9 = 1152. Step 7: Compute 16 ÷ 4 = 4. Step 8: Now perform the remaining addition: 1152 + 4 = 1156. Verification / Alternative check: A quick verification is to check whether any alternate interpretation could give a different result. However, once the mapping of each symbol is fixed, there is only one consistent way to write the real expression. Evaluating it again with the same precedence rules will always give 1156. This confirms that the answer is stable and not dependent on any arbitrary choice of grouping. Why Other Options Are Wrong: Option 73 is much smaller and would correspond to treating some operations incorrectly or ignoring precedence. Option 256 might arise if someone performs 128 * 2, misreading part of the expression and not interpreting the code properly. Option 1352 could come from incorrect multiplication such as 128 * 10 or a mistaken additional step. Option 1024 resembles 32 * 32 or 2^10 and is unrelated to the coded calculation here. Common Pitfalls: Common errors include assuming that after decoding the symbols, all operations are done strictly from left to right, ignoring precedence. Another frequent mistake is to replace the numbers instead of only the operators, or to forget which symbol stands for which operation. Writing down the real expression clearly after decoding is a very helpful way to avoid such confusion. Final Answer: After decoding the operators and evaluating the expression with correct precedence, the value of the expression is 1156.

Question 20

In a certain code language, the five letter word PRIME is written as VNRIK. Observing how the positions of the letters change from PRIME to VNRIK, the first and fifth letters are shifted forward by six positions in the alphabet, the second and fourt…

Accepted Answer

Introduction / Context: This question involves a letter shifting code applied position wise to a five letter word. The example given shows how PRIME is coded as VNRIK. We are expected to identify the numerical shift applied to each letter position, and then apply the same pattern to the new word MICRO. Such problems test how well you can analyze alphabet positions and detect non uniform, position based transformations rather than a simple uniform shift for all letters. Given Data / Assumptions: • Original word: PRIME. • Coded form: VNRIK. • Target word to code: MICRO. • Alphabet positions: A = 1, B = 2, …, Z = 26. • The same pattern of shifts must be applied position by position. Concept / Approach: We first convert letters of both PRIME and VNRIK into their alphabet positions. Then we calculate the difference between the coded letter and the original letter at each position. This produces a pattern of offsets for positions 1 to 5. Once the offset pattern is known, we apply it to the letters of MICRO, again using alphabet positions and wrapping forward within A to Z if needed. The resulting letters give the coded form of MICRO. Step-by-Step Solution: Step 1: Write the positions for PRIME: P = 16, R = 18, I = 9, M = 13, E = 5. Step 2: Write the positions for VNRIK: V = 22, N = 14, R = 18, I = 9, K = 11. Step 3: Find differences for each position: position 1, 16 to 22 is +6; position 2, 18 to 14 is -4; position 3, 9 to 18 is +9; position 4, 13 to 9 is -4; position 5, 5 to 11 is +6. Step 4: So the pattern of shifts is: +6, -4, +9, -4, +6 for positions 1 to 5. Step 5: Now apply this to MICRO. Positions: M = 13, I = 9, C = 3, R = 18, O = 15. Step 6: Position 1: 13 + 6 = 19, which is S. Step 7: Position 2: 9 - 4 = 5, which is E. Step 8: Position 3: 3 + 9 = 12, which is L. Step 9: Position 4: 18 - 4 = 14, which is N. Step 10: Position 5: 15 + 6 = 21, which is U. Step 11: Combining these letters gives SELNU as the code for MICRO. Verification / Alternative check: You can verify your method by re applying the pattern to PRIME. Using +6, -4, +9, -4, +6 on P, R, I, M, and E again reproduces V, N, R, I, and K respectively. Since the same transformation that works on PRIME also works consistently for MICRO, the pattern is reliable and the result SELNU is valid. Checking that no other option fits this exact systematic transformation confirms the uniqueness of the answer. Why Other Options Are Wrong: Option SENLU changes the order of E and L and does not respect the precise numerical shifts. Option SLEUN rearranges internal letters in a way that does not match the derived offset pattern. Option SLNEU puts N and L at incorrect positions relative to the shift sequence. Option SUNEL is more of a random rearrangement and does not come from the consistent +6, -4, +9, -4, +6 rule. Common Pitfalls: Learners sometimes guess the code for MICRO by visual similarity or by applying a single uniform shift to all letters, which fails here because the shift is position dependent. Another common mistake is to omit the negative shifts or miscalculate large forward shifts like +9. Writing out positions clearly and computing each shift separately prevents such errors. Final Answer: Using the same pattern of letter shifts that changes PRIME into VNRIK, the word MICRO is coded as SELNU.

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