Question 1

In a certain code language, the word "ARMS" is written as "5467" and the word "LIAR" is written as "1254". Using the same letter to digit substitutions, how is the word "SMALL" written in that code language?

Accepted Answer

Introduction: This question tests your ability to decode and apply a simple substitution cipher in which each letter is replaced by a specific digit. We are given coded forms for two words, "ARMS" and "LIAR", and must determine the code for a third word, "SMALL". The core skill here is to extract consistent letter to digit mappings and then reuse them in the required word without contradiction. Given Data / Assumptions: The word "ARMS" is coded as "5467" and the word "LIAR" is coded as "1254". Each letter is assumed to map to exactly one digit, and the same letter always has the same code wherever it appears. We also assume that there is no position based trick and that the code is a straightforward one to one substitution from letters to digits. Concept / Approach: To solve this, we must first determine the digit corresponding to each letter by aligning letters with their positions in the code. Once we know the mappings for the letters S, M, A, and L, we can write the complete code for "SMALL". The idea is to build a mapping table such as A to a specific digit, R to another, and so on, and then read off the encoded version of the new word. Step-by-Step Solution: Step 1: Consider "ARMS" coded as "5467". Match letters and digits position wise: A corresponds to 5, R to 4, M to 6, and S to 7.Step 2: Now consider "LIAR" coded as "1254". Matching the letters: L corresponds to 1, I to 2, A to 5, and R to 4.Step 3: From these two words we have the following consistent mappings: A = 5, R = 4, M = 6, S = 7, L = 1, I = 2. All mappings agree where letters repeat.Step 4: We now need the code for the word "SMALL". The letters in order are S, M, A, L, L.Step 5: Using the mappings: S = 7, M = 6, A = 5, and L = 1.Step 6: Therefore, "SMALL" becomes the string of digits 7 6 5 1 1, that is, 76511. Verification / Alternative check: We can double check by inserting each individual mapping back into the earlier examples. Substituting A = 5, R = 4, M = 6, S = 7 in "ARMS" regenerates "5467" and substituting L = 1, I = 2, A = 5, R = 4 in "LIAR" regenerates "1254". Since there is no contradiction, the mapping is valid, and our encoding of "SMALL" is reliable. Why Other Options Are Wrong: The option 76521 assigns the last two letters L and L to 2 and 1, which conflicts with the mapping L = 1 established from "LIAR". The option 76512 also breaks the requirement that both L letters have code 1. The option 76544 would require L to map to 4, but that digit is already fixed for R. The option 76514 similarly introduces inconsistent digit assignments for L. Common Pitfalls: A common mistake is to attempt to guess the final code without carefully listing the mappings, which can lead to mixing up digits for letters that look similar or appear multiple times. Another pitfall is forgetting that the same letter must always have the same code, which immediately invalidates many tempting but incorrect options. Final Answer: The word "SMALL" is written in the code language as 76511.

Question 2

In a certain code, the word "FRIEND" is written as "HTKGPF". Using the same rule, how will the word "REVEAL" be coded in that code language?

Accepted Answer

Introduction: This is a letter shifting coding question where each letter of a word is transformed according to a consistent alphabetic rule. We are told how the word "FRIEND" becomes "HTKGPF" and asked to apply the same pattern to the word "REVEAL". Such questions measure your ability to detect systematic shifts in the alphabet and then apply them accurately to new inputs. Given Data / Assumptions: The given coding is FRIEND → HTKGPF. We assume that each letter in the original word is shifted by a fixed number of positions in the alphabet to obtain the corresponding coded letter and that the same rule applies to every letter. We also assume that the transformation is forward along the alphabet and that there is no mixing of positions or rearrangement of letters. Concept / Approach: The approach is to compare corresponding letters from the original word and the coded word and determine how many positions the alphabet is shifted in each case. Once we know this shift, we can apply the same shift to each letter of "REVEAL". Because the pattern must be consistent, every letter in "FRIEND" should exhibit the same shift when compared to its coded counterpart. Step-by-Step Solution: Step 1: Write down alphabetical positions. For example, F is 6, R is 18, I is 9, E is 5, N is 14, and D is 4.Step 2: Now identify the positions of the coded letters H, T, K, G, P, and F which are 8, 20, 11, 7, 16, and 6 respectively.Step 3: Compute the differences: F to H is 6 to 8, a shift of +2; R to T is 18 to 20, again +2; I to K is 9 to 11, +2; E to G is 5 to 7, +2; N to P is 14 to 16, +2; D to F is 4 to 6, +2.Step 4: Since all letters are shifted forward by exactly 2 positions in the alphabet, the coding rule is: replace each letter with the letter that comes two positions after it.Step 5: Now apply this rule to the word "REVEAL".Step 6: R (18) becomes T (20), E (5) becomes G (7), V (22) becomes X (24), E (5) becomes G (7), A (1) becomes C (3), and L (12) becomes N (14).Step 7: Therefore, "REVEAL" is coded as T G X G C N, that is, TGXGCN. Verification / Alternative check: A quick verification can be done by reversing the process: shift the coded letters of "REVEAL" backwards by two positions. T back to R, G back to E, X back to V, G back to E, C back to A, and N back to L. We indeed recover "REVEAL", so the rule works perfectly in both directions. Why Other Options Are Wrong: The option TGXFCN incorrectly changes the fifth letter to F instead of C, which would require an inconsistent shift. The option TGXNGC rearranges letters and breaks the consistent positional shift. The option TXGNCG shuffles positions and letters. The option TGXGNC has the last two letters interchanged, which is again not supported by the systematic shift rule. Common Pitfalls: Students sometimes miscount alphabet positions or apply different shifts to different letters, especially near the end of the alphabet. Another frequent mistake is to accidentally rearrange letters instead of only shifting them. Careful letter by letter checking avoids these errors. Final Answer: The correct coded form of "REVEAL" is TGXGCN.

Question 3

Select the correct combination of mathematical signs to replace the asterisks so that the following equation becomes true when evaluated with normal precedence rules: 48 * 4 * 6 * 3 * 30

Accepted Answer

Introduction: This is a coded operator placement question. We are given a numerical expression with asterisks in place of arithmetic operators. A set of possible operator combinations is provided, and we must select the one that makes the equation valid when standard rules of arithmetic are followed. The equation must ultimately have an equality sign that correctly balances the left and right sides. Given Data / Assumptions: The expression is 48 * 4 * 6 * 3 * 30, and there are four asterisks to be replaced by operators in a fixed left to right order. Each option provides a sequence of four symbols which correspond to the first, second, third, and fourth asterisk respectively. The operators involved are addition, subtraction, multiplication, division, and equality. We assume ordinary operator precedence, where multiplication and division are performed before addition and subtraction. Concept / Approach: The strategy is to test each option by substituting its operators into the expression and then checking whether the resulting statement is a true numerical equation. Because there are only four options given in the original list, and the structure is not too long, we can systematically evaluate each candidate without much difficulty. Step-by-Step Solution: Step 1: Consider option a: -, +, =, x. Substituting gives 48 - 4 + 6 = 3 x 30. The left side is 48 - 4 + 6 = 50. The right side is 3 * 30 = 90. Since 50 is not equal to 90, option a is invalid.Step 2: Consider option b: ÷, =, x, +. Substituting gives 48 ÷ 4 = 6 x 3 + 30. The left side is 48 ÷ 4 = 12. The right side is 6 * 3 + 30 = 18 + 30 = 48. Since 12 is not equal to 48, option b is also invalid.Step 3: Consider option c: ÷, +, x, =. Substituting gives 48 ÷ 4 + 6 x 3 = 30. First compute the left side using precedence: 48 ÷ 4 = 12 and 6 x 3 = 18, so the left side becomes 12 + 18 = 30.Step 4: With option c, the equation is 30 = 30, which is a true statement. Therefore option c balances the equation correctly.Step 5: For completeness, option d gives 48 - 4 = 6 x 3 + 30 which becomes 44 = 48, clearly false, and option e also fails to balance the equation when evaluated. Verification / Alternative check: We can directly see that 48 ÷ 4 = 12 and 6 x 3 = 18, and these two quantities sum to 30, matching the right side. There is no other straightforward combination among the options that yields such a neat equality. Why Other Options Are Wrong: Each incorrect option generates a left side and right side that do not match. They either make the left side smaller or larger than the right side, or produce an equation that is obviously unbalanced. None of them produce the required 30 on both sides at the same time. Common Pitfalls: One common mistake is to ignore operator precedence and evaluate strictly left to right, which would produce different values and potentially mislead you into thinking an incorrect option is correct. Another error is to misread the mapping of operators to asterisks and put them in the wrong positions. Final Answer: The correct sequence of operators is ÷, +, x, =, corresponding to option c.

Question 4

In a certain code language, the word "FAILURE" is written as "FRULIAG". Using the same coding rule, how is the word "SUCCESS" written in that code language?

Accepted Answer

Introduction: This verbal reasoning question involves a non obvious code applied to words rather than a simple letter shift. We are told that the word "FAILURE" becomes "FRULIAG" under a certain transformation and are asked to determine the code for "SUCCESS" using the same rule. The question tests pattern recognition, the ability to analyze letter rearrangements, and the capacity to combine reversal and substitution ideas. Given Data / Assumptions: The given mapping is FAILURE → FRULIAG. We assume that the same algorithm is applied to any word to generate its coded form. The code seems to involve both rearranging letters and changing some of them, because the first and last letters in the coded word are not exactly the same as in the original. We look for a structured pattern that could be applied to "SUCCESS" mechanically. Concept / Approach: A helpful observation is to compare the coded word with the reversed original. If we reverse "FAILURE", we get "ERULIAF". The coded form "FRULIAG" appears to be closely related to this reversed version. Specifically, most middle letters seem to remain the same, while the first and last letters of the reversed word have been shifted to the next letter in the alphabet. Discovering and verifying this transformation allows us to apply the same steps to "SUCCESS". Step-by-Step Solution: Step 1: Reverse the original word "FAILURE". The reversed word is "ERULIAF".Step 2: Compare "ERULIAF" with the code "FRULIAG". We see: E becomes F, R stays R, U stays U, L stays L, I stays I, A stays A, and F becomes G.Step 3: From this, infer the rule: take the reversed word, shift the first letter of the reversed word one step forward in the alphabet, keep the middle letters unchanged, and shift the last letter of the reversed word one step forward in the alphabet as well.Step 4: Now apply this rule to the new word "SUCCESS". First reverse "SUCCESS" to get "SSECCUS".Step 5: In "SSECCUS", the first letter is S and the last letter is S. Shift both of these S letters forward by one position in the alphabet, giving T for each end position. The middle letters remain unchanged.Step 6: This produces the code "TSECCUT".Step 7: Therefore, according to the discovered pattern, "SUCCESS" is written as "TSECCUT". Verification / Alternative check: We can verify the logic by reapplying the same steps to "FAILURE". Reversing gives "ERULIAF". Shifting the first and last letters one step forward transforms E to F and F to G while leaving R, U, L, I, and A unchanged, giving "FRULIAG". Since this matches the given coded form exactly, the rule is confirmed. Why Other Options Are Wrong: The option "SSECCUS" merely reverses or preserves the original without applying the end letter shifts. "TSECCUS" shifts only the first letter and not the last one. "TSECCUU" introduces an extra U at the end which does not correspond to the systematic transformation. "SSECCUT" shifts only the last letter but not the first, again violating the discovered pattern. Common Pitfalls: Many learners initially search for a simple letter by letter substitution without noticing that the word is reversed first. Others may reverse the word but forget to apply the alphabetic shift to both ends or may apply the shift to all letters, which does not match the example. Looking carefully at both the order of letters and which specific letters change is crucial. Final Answer: The word "SUCCESS" is written as TSECCUT in the given code language.

Question 5

If "A" denotes "added to", "B" denotes "divided by", "C" denotes "multiplied by" and "D" denotes "subtracted" (used as the ordinary minus sign), then what is the value of 154 B 11 C 6 A 6 D 27 when evaluated with normal precedence rules?

Accepted Answer

Introduction: This question is another example of coded arithmetic operations where letters represent standard mathematical operators. Our task is to decode the expression 154 B 11 C 6 A 6 D 27, convert it into a usual arithmetic expression, and then evaluate it while respecting operation precedence. These types of questions check understanding of operator mapping and consistent application of arithmetic rules. Given Data / Assumptions: We are told that A means "added to", B means "divided by", C means "multiplied by", and D means "subtracted". The coded expression given is 154 B 11 C 6 A 6 D 27. We assume that division and multiplication are evaluated before addition and subtraction according to standard precedence, and that D functions as the ordinary minus sign between numbers in the sequence. Concept / Approach: The basic idea is to first translate every coded symbol into its corresponding arithmetic operator. Once this is done, we apply the standard BODMAS or PEMDAS rules to compute the result. The key is not to treat the letters as variables but as placeholders for operations, and then to be meticulous with the order of evaluation. Step-by-Step Solution: Step 1: Replace each coded letter: B is division, C is multiplication, A is addition, and D is subtraction.Step 2: The expression 154 B 11 C 6 A 6 D 27 becomes 154 / 11 * 6 + 6 - 27.Step 3: Apply precedence rules. First handle division and multiplication from left to right. Compute 154 / 11. Since 11 * 14 = 154, we get 154 / 11 = 14.Step 4: Next, multiply 14 by 6 to get 14 * 6 = 84.Step 5: The expression now simplifies to 84 + 6 - 27.Step 6: Perform the addition and subtraction from left to right. First, 84 + 6 = 90.Step 7: Then subtract 27 from 90, giving 90 - 27 = 63.Step 8: Therefore, the final value of the expression is 63. Verification / Alternative check: We can quickly recompute to verify: 154 divided by 11 is 14, 14 times 6 is 84, 84 plus 6 is 90, and 90 minus 27 is 63. There are no ambiguous brackets or alternative interpretations when D is treated as a straightforward minus sign, so the calculation is stable. Why Other Options Are Wrong: The value 60 might result from an incorrect subtraction such as 90 minus 30 instead of 27. The value 33 could come from misplacing the operations or subtracting both 6 and 27 from 84 before adding. The value 64 would occur if someone mistakenly added 27 instead of subtracting it. The option 69 does not correspond to any consistent misapplication of precedence in this setting. Common Pitfalls: A common error is to evaluate strictly from left to right and perform 154 / 11, then immediately add 6 without doing the multiplication first. Another pitfall is misreading the mapping and swapping the roles of A, B, C, and D. Writing out the fully translated expression before computing helps avoid these mistakes. Final Answer: The value of the coded expression is 63.

Question 6

In a certain code language, the word "TRUMPET" is written as "7591427" and the word "SORROW" is written as "385586". Using the same letter to digit code, how is the word "EMPRESS" written in that code language?

Accepted Answer

Introduction: This coding and decoding question deals with a substitution cipher in which each letter of the alphabet is replaced by a specific digit. We are given two coded words, "TRUMPET" and "SORROW", along with their digit sequences. Our task is to determine the digit string corresponding to the word "EMPRESS" by extracting and using a consistent set of letter to digit mappings. Given Data / Assumptions: The mappings are provided through two examples: TRUMPET is coded as 7591427 and SORROW is coded as 385586. We assume that the code is consistent across all words. That means each letter always maps to the same digit, and no two different letters share the same digit within this question. The word to be encoded is "EMPRESS", which contains letters E, M, P, R, and S, all of which appear in the given examples. Concept / Approach: The approach is to align letters and digits position wise in the given coded words and then build a mapping table. Once we know the digit for each relevant letter, the encoding of "EMPRESS" is a straightforward lookup operation. Consistency is crucial: every appearance of a letter must be associated with the same digit in all examples. Step-by-Step Solution: Step 1: Consider "TRUMPET" coded as "7591427". Match letters to digits: T corresponds to 7, R to 5, U to 9, M to 1, P to 4, E to 2, and again T to 7 which confirms T = 7.Step 2: Now consider "SORROW" coded as "385586". Match letters: S corresponds to 3, O to 8, R to 5, R again to 5 confirming R = 5, O again to 8 confirming O = 8, and W to 6.Step 3: From these examples, we have the following mappings: T = 7, R = 5, U = 9, M = 1, P = 4, E = 2, S = 3, O = 8, W = 6.Step 4: The word "EMPRESS" has letters E, M, P, R, E, S, S in that order.Step 5: Using the mapping, we get E = 2, M = 1, P = 4, R = 5, E again = 2, S = 3, and S again = 3.Step 6: Therefore, the code for "EMPRESS" is 2 1 4 5 2 3 3, which is 2145233. Verification / Alternative check: We can verify our mapping by substituting the digits back into the original coded examples. For "TRUMPET", T = 7, R = 5, U = 9, M = 1, P = 4, E = 2, T = 7 gives 7591427, matching the given code. For "SORROW", S = 3, O = 8, R = 5, R = 5, O = 8, W = 6 gives 385586, again matching perfectly. Why Other Options Are Wrong: Option 2145237 incorrectly changes the final digit to 7, which would correspond to T rather than S. Option 2154323 reorders digits in a way that would require inconsistent letter mappings. Option 3154233 assigns the first digit 3 to E, which contradicts E = 2. Option 2154233 misaligns the middle digits and again conflicts with the established mapping for M and P. Common Pitfalls: Candidates sometimes mix up digits when transferring them from the mapping table to the target word or fail to distinguish between similar looking letters. Another mistake is to forget to check for consistency across both given coded words, which can lead to incorrect interpretations of the mapping. Final Answer: The word "EMPRESS" is written as 2145233 in the given code language.

Question 7

If "P" denotes "multiplied by", "R" denotes "subtracted", "S" denotes "added to" and "Q" denotes "divided by", then what is the value of 6 P 7 S 169 Q 13 R 5 under normal arithmetic precedence?

Accepted Answer

Introduction: This question is based on coded arithmetic operations similar to earlier ones, where letters stand in place of conventional operators. We are required to decode the expression 6 P 7 S 169 Q 13 R 5 into standard arithmetic form and then compute its numerical value. Understanding how to map each symbol and then correctly apply precedence is essential. Given Data / Assumptions: We are given that P means multiplication, R means subtraction, S means addition, and Q means division. The expression to evaluate is 6 P 7 S 169 Q 13 R 5. We assume that multiplication and division are done before addition and subtraction, and we treat R as the simple minus operator between numbers in sequence. Concept / Approach: The approach is straight: substitute each coded symbol with its corresponding arithmetic operator to obtain a conventional expression. After that, apply BODMAS or PEMDAS rules. The most common places to make mistakes are in misreading the mapping or in ignoring operator precedence because of the unfamiliar notation. Step-by-Step Solution: Step 1: Substitute the operators. P is multiplication, S is addition, Q is division, and R is subtraction.Step 2: The coded expression 6 P 7 S 169 Q 13 R 5 becomes 6 * 7 + 169 / 13 - 5.Step 3: Apply precedence rules. First resolve multiplication and division from left to right.Step 4: Compute 6 * 7 = 42.Step 5: Compute 169 / 13. Since 13 * 13 = 169, we get 169 / 13 = 13.Step 6: Substitute these values into the expression: it becomes 42 + 13 - 5.Step 7: Now perform the addition and subtraction from left to right. First, 42 + 13 = 55.Step 8: Then subtract 5: 55 - 5 = 50.Step 9: Therefore, the value of the expression is 50. Verification / Alternative check: Recomputing quickly, 6 times 7 is 42, adding 13 gives 55, and subtracting 5 yields 50. There are no conflicting interpretations if the mappings are applied as given, so the result is stable. Why Other Options Are Wrong: The value 55 would occur if someone ignored the final subtraction and stopped after 42 + 13. The value 45 might result from incorrectly subtracting 10 rather than 5. The value 43 and 41 do not follow from any consistent misapplication of precedence independent of gross errors in the arithmetic or mapping, so they are implausible. Common Pitfalls: Students sometimes reverse the roles of addition and subtraction or confuse which letter maps to which operation. Another error is to evaluate the expression strictly from left to right without respecting that multiplication and division must be resolved before addition and subtraction. Translating the expression clearly before computing helps avoid these problems. Final Answer: The numerical value of the expression is 50.

Question 8

In a certain code language, the word "DONKEY" is written as "YEKNOD". Using the same code rule, how is the word "RAINBOW" written in that language?

Accepted Answer

Introduction: This is a straightforward coding and decoding question based on reversing the order of letters in a word. The code for "DONKEY" is given as "YEKNOD", and we must apply the same transformation to the word "RAINBOW". Problems like this test your ability to spot simple structural patterns rather than complicated substitutions. Given Data / Assumptions: We are told that DONKEY becomes YEKNOD. There is no indication of any letter substitutions or shifts, only an apparent rearrangement. We assume that every word is encoded by reversing its sequence of letters, with no extra changes to individual characters. Concept / Approach: The first step is to observe how DONKEY and YEKNOD relate. If we write DONKEY forwards and YEKNOD underneath, we can immediately see that YEKNOD is simply DONKEY written backwards. Once this is clear, we adopt the rule "reverse the letters of the word" and apply it to the new word RAINBOW. Step-by-Step Solution: Step 1: Write the word DONKEY and compare it to YEKNOD. The letters are D O N K E Y and Y E K N O D, which are in exactly opposite order.Step 2: Conclude that the coding rule is to reverse the word, placing the last letter first, the second last letter second, and so on.Step 3: Now apply this rule to the word RAINBOW. The letters of RAINBOW in order are R, A, I, N, B, O, W.Step 4: Reverse this order. Starting from the end, we get W, O, B, N, I, A, R.Step 5: The reversed sequence gives the coded form WOBNIAR. Verification / Alternative check: If we again reverse WOBNIAR, we should return to the original word RAINBOW. Reading WOBNIAR from right to left yields R, A, I, N, B, O, W, which confirms that our transformation is simply a reversal and that it has been applied correctly. Why Other Options Are Wrong: The option WOBNAIR misplaces the letters A and I, which means it is not a pure reversal of RAINBOW. The option WONBAIR rearranges letters in a different pattern and does not match the simple reverse rule observed with DONKEY. The option WOBNRAI incorrectly orders the last three letters. The option WOBINAR also fails to keep the correct reversed sequence of the middle letters. Common Pitfalls: Students sometimes reverse only part of the word or accidentally swap the positions of letters in the middle. It can help to write the word in a column and then write the reversed sequence directly underneath to avoid mistakes. Final Answer: The word "RAINBOW" is written as WOBNIAR in the given code language.

Question 9

In a certain code language, the word "BORROW" is written as "769965" and the word "BOMB" is written as "7647". Using the same code, how is the word "WOMB" written in that language?

Accepted Answer

Introduction: This coding and decoding question involves mapping letters of words to digits. We are told how "BORROW" and "BOMB" are written in a numeric code and asked to determine the code for "WOMB". Such questions require building a consistent letter to digit mapping by carefully aligning letters with their corresponding digits in the examples. Given Data / Assumptions: The word BORROW is written as 769965. The word BOMB is written as 7647. We assume each letter corresponds to exactly one digit and that the code is consistent between both examples. The target word WOMB includes only letters that appear in the given examples, namely W, O, M, and B. Concept / Approach: The approach is to determine the digit associated with each letter by comparing positions in the coded words. Once we know the codes for B, O, M, and W, we can directly encode the word WOMB by substituting digits for each letter in order. Step-by-Step Solution: Step 1: Consider BORROW coded as 769965. The letters in order are B, O, R, R, O, W, and the digits are 7, 6, 9, 9, 6, 5.Step 2: From this, we can deduce: B = 7, O = 6, R = 9, and W = 5.Step 3: Now look at BOMB coded as 7647. The letters are B, O, M, B, and the digits are 7, 6, 4, 7.Step 4: This confirms B = 7 and O = 6 again, and gives M = 4.Step 5: We now have the mappings: B = 7, O = 6, M = 4, W = 5.Step 6: The word WOMB has letters W, O, M, B in that order.Step 7: Substitute the digits: W = 5, O = 6, M = 4, B = 7 which gives 5 6 4 7.Step 8: Therefore, "WOMB" is written as 5647 in the code language. Verification / Alternative check: By reapplying the mappings to the original words, BORROW becomes 7 6 9 9 6 5, and BOMB becomes 7 6 4 7, which match the given codes exactly. This double check confirms that our mapping table is correct and that the encoding of WOMB is consistent. Why Other Options Are Wrong: The option 5467 would assign 4 to O instead of M, contradicting O = 6. The option 5677 cannot be formed from the consistent mappings because W and B cannot both map to 7. The option 5776 assigns 7 to W and 6 to B, both of which contradict the established mapping. The option 5967 introduces 9, which belongs to R, a letter not present in WOMB. Common Pitfalls: A frequent mistake is to copy the digits in the wrong order or to assume that the numeric positions in the code directly follow alphabetical order, which is not the case. Another error is forgetting to verify the mapping with both given coded words, which can allow an inconsistent assignment to slip through unnoticed. Final Answer: The word "WOMB" is written as 5647 in the given code language.

Question 10

If "A" denotes "multiplied by", "B" denotes "subtracted", "C" denotes "added to" and "D" denotes "divided by", then what is the value of 7 B 17 C 88 D 11 A 6 according to the usual rules of arithmetic?

Accepted Answer

Introduction: This question uses letter symbols to represent standard arithmetic operators, similar to earlier operator coding problems. The expression 7 B 17 C 88 D 11 A 6 needs to be decoded and evaluated. Mastering this type of question requires careful mapping from letters to operations and precise application of precedence rules for multiplication, division, addition, and subtraction. Given Data / Assumptions: We are told that A means multiplication, B means subtraction, C means addition, and D means division. The coded expression is 7 B 17 C 88 D 11 A 6. We assume that the operations follow normal precedence, with division and multiplication executed before addition and subtraction, and that B is simply used as the minus sign. Concept / Approach: The steps are straightforward: first, replace each letter with its associated operator to form a standard arithmetic expression. Second, perform the calculations, starting with division and multiplication, then moving on to addition and subtraction from left to right. Care must be taken not to change the order of the numbers. Step-by-Step Solution: Step 1: Replace A with multiplication, B with subtraction, C with addition, and D with division.Step 2: The coded expression 7 B 17 C 88 D 11 A 6 becomes 7 - 17 + 88 / 11 * 6.Step 3: Apply precedence rules. Start with the division 88 / 11. Since 11 * 8 = 88, we get 88 / 11 = 8.Step 4: Next, perform the multiplication: 8 * 6 = 48.Step 5: Now the expression reduces to 7 - 17 + 48.Step 6: Evaluate the expression from left to right: 7 - 17 = -10.Step 7: Then -10 + 48 = 38.Step 8: Therefore, the value of the original coded expression is 38. Verification / Alternative check: We can quickly verify by recomputing the key steps: 88 divided by 11 is 8, 8 times 6 is 48, and then combining with 7 and 17 as 7 minus 17 plus 48 yields -10 plus 48 which is 38. No alternative bracketing is suggested in the statement, so this result is definitive under the given interpretation. Why Other Options Are Wrong: The value 27 or 28 might appear if someone incorrectly adds or subtracts the numbers, perhaps by treating 7 and 17 differently or by mishandling the intermediate negative result. The value 26 may result from subtracting 22 instead of 17 or miscomputing the multiplication. The value 58 would require misinterpreting an operation or effectively adding 20 more than justified, which is inconsistent with the defined mappings. Common Pitfalls: A frequent mistake is to neglect the fact that 7 - 17 is negative and proceed as if the result were 10, leading to an incorrect final answer. Also, some may reverse the order of operands or misread the mapped operations, especially if they process letters quickly without writing the full expression in symbols first. Final Answer: The value of the expression is 38.

Question 11

In a certain code language, the word "RIVER" is written as "12351" and the word "RED" is written as "156". Using the same letter to digit assignments, how is the word "DRIVER" written in that code language?

Accepted Answer

Introduction: This is a straightforward letter to digit coding problem. We are given numeric codes for the words "RIVER" and "RED" and are asked to determine the code for "DRIVER". The core of the problem is to deduce a consistent mapping from letters to digits and then apply it to the new word. Given Data / Assumptions: The word RIVER is written as 12351 and the word RED is written as 156. We assume each letter corresponds to exactly one digit and that these correspondences are the same in both words. The target word DRIVER contains letters D, R, I, V, E, and R, all of which appear in the given examples. Concept / Approach: The technique is to align each letter in the known words with the digit in the same position in the code. This gives a mapping from letters to digits. Once the mapping is clear, we write the code for DRIVER by substituting the mapped digit for each letter sequentially. Step-by-Step Solution: Step 1: Consider "RIVER" coded as "12351". The letters are R, I, V, E, R and the digits are 1, 2, 3, 5, 1.Step 2: From this, we deduce R = 1, I = 2, V = 3, and E = 5. The second R confirms R = 1.Step 3: Now consider "RED" coded as "156". The letters are R, E, D and the digits are 1, 5, 6.Step 4: From this, we confirm R = 1 and E = 5 again, and we learn that D = 6.Step 5: We now have the mapping: R = 1, I = 2, V = 3, E = 5, D = 6.Step 6: The word "DRIVER" has letters D, R, I, V, E, R in that order.Step 7: Substitute each letter with its digit: D = 6, R = 1, I = 2, V = 3, E = 5, R = 1, giving 6 1 2 3 5 1.Step 8: Therefore, "DRIVER" is written as 612351. Verification / Alternative check: We can verify the mapping by rechecking both original words. RIVER becomes 1 2 3 5 1 and RED becomes 1 5 6, exactly matching the given codes. Since there is no conflict, our mapping is correct. Why Other Options Are Wrong: The option 612311 changes the last two digits and would require E to map to 1 rather than 5, which contradicts the code for RED and RIVER. The option 612531 swaps the roles of V and E in the digit sequence. The option 621351 misplaces the digits for R and I at the beginning. The option 621531 introduces inconsistent mapping for several letters. Common Pitfalls: Students may rush and misalign letters, especially when the same letter repeats. Another mistake is to forget to check both given words when building the mapping, which can lead to incorrect assignments for shared letters like R and E. Final Answer: The word "DRIVER" is written as 612351 in the given code language.

Question 12

If "+" means "minus", "x" means "divided by", "÷" means "plus" and "-" means "multiplied by", then what is the value of 126 x 14 + 7 - 3 ÷ 2 when interpreted with these coded operations?

Accepted Answer

Introduction: This question presents an expression in which the usual arithmetic symbols have been reassigned new meanings. We must carefully decode the expression 126 x 14 + 7 - 3 ÷ 2 according to the given mappings and then compute the result. It is a test of attention to detail and correct application of operator precedence after decoding. Given Data / Assumptions: The mappings are as follows: the symbol "+" actually means minus, the symbol "x" actually means divided by, the symbol "÷" actually means plus, and the symbol "-" actually means multiplied by. The expression to evaluate is 126 x 14 + 7 - 3 ÷ 2. We assume standard precedence rules after decoding the operators. Concept / Approach: The key is to first translate the coded operators into their real arithmetic counterparts, turning the expression into one with standard symbols. Then we apply ordinary precedence: division and multiplication first, followed by addition and subtraction, proceeding from left to right within the same precedence level. Step-by-Step Solution: Step 1: Replace each operator with its true meaning. "x" becomes "/", "+" becomes "-", "-" becomes "*", and "÷" becomes "+".Step 2: The coded expression 126 x 14 + 7 - 3 ÷ 2 becomes 126 / 14 - 7 * 3 + 2.Step 3: Apply precedence. First handle division and multiplication from left to right.Step 4: Compute 126 / 14. Since 14 * 9 = 126, we get 126 / 14 = 9.Step 5: Compute 7 * 3 = 21.Step 6: Now the expression reduces to 9 - 21 + 2.Step 7: Perform the addition and subtraction from left to right. First, 9 - 21 = -12.Step 8: Then -12 + 2 = -10.Step 9: Therefore, the value of the decoded expression is -10. Verification / Alternative check: We can double check by re reading the mappings and confirming each replacement: x as division, + as minus, - as multiplication, and ÷ as plus. Re applying these mappings confirms that we correctly transformed the expression to 126 / 14 - 7 * 3 + 2. Recomputing yields the same result of -10. Why Other Options Are Wrong: The value -12 would occur if someone stopped after 9 - 21 and forgot to add 2. The value -17 might result from miscomputing either 126 / 14 or 7 * 3. The value -41 is far off and would require a serious misinterpretation of operators or order of operations. The value -14 does not match any consistent variation of the correct decoding. Common Pitfalls: One common mistake is to apply the original meanings of the symbols instead of their reassigned meanings. Another is to ignore order of operations and simply calculate from left to right. Writing out the fully translated expression before calculating helps prevent these errors. Final Answer: The correct value of the expression is -10.

Question 13

In a certain code language, the word "DELETE" is written as "#@^@%@" and the word "GRAM" is written as "!?*&". Using the same symbol code, how is the word "TELEGRAM" written in that code language?

Accepted Answer

Introduction: This question involves a symbolic coding system where letters are replaced by special characters such as #, @, ^, %, !, ?, *, and &. We are given the coded forms of two words, "DELETE" and "GRAM", and asked to determine the code for "TELEGRAM". The objective is to deduce a consistent mapping from letters to symbols and then apply that mapping to the new word. Given Data / Assumptions: The word DELETE is written as #@^@%@. The word GRAM is written as !?*&. We assume that each letter corresponds to exactly one symbol and that the mapping is consistent across both words. The target word TELEGRAM is composed of letters T, E, L, E, G, R, A, M, all of which appear in DELETE or GRAM. Concept / Approach: We align the letters in each given word with their corresponding symbols in the same positions. This gives the mapping for D, E, L, T and G, R, A, M. Once we have the symbol for each letter, we construct the code for TELEGRAM by substituting letters with symbols in order. Step-by-Step Solution: Step 1: Analyze DELETE → #@^@%@. The letters D, E, L, E, T, E correspond to symbols #, @, ^, @, %, @.Step 2: From this, we deduce D = #, E = @, L = ^, and T = %.Step 3: Now analyze GRAM → !?*&. The letters G, R, A, M correspond to symbols !, ?, *, & respectively.Step 4: From this, we deduce G = !, R = ?, A = *, and M = &.Step 5: Collecting all mappings, we have D = #, E = @, L = ^, T = %, G = !, R = ?, A = *, and M = &.Step 6: The word TELEGRAM has letters T, E, L, E, G, R, A, M in that sequence.Step 7: Substitute each letter: T = %, E = @, L = ^, E = @, G = !, R = ?, A = *, M = &.Step 8: Concatenating these symbols, we get %@^@!?*&.Step 9: Therefore, TELEGRAM is written as %@^@!?*& in the given code language. Verification / Alternative check: We can verify our mappings by reapplying them to DELETE and GRAM. For DELETE, D = #, E = @, L = ^, T = %, so the sequence #@^@%@ matches exactly. For GRAM, G = !, R = ?, A = *, M = &, giving !?*& as required. This confirms that our mapping is correct. Why Other Options Are Wrong: Options that change any symbol position, such as replacing ! with ^ or moving @ into different positions, would contradict the fixed letter to symbol relationships already established. For instance, option a uses ^ where ! should appear, and option c introduces * in place of ^, both inconsistent with the mapping. Option b and option e similarly misplace symbols in a way that does not correspond to TELEGRAM letter by letter. Common Pitfalls: One typical mistake is to overlook that letters repeat, like E in DELETE, and thus to assign different symbols to the same letter. Another is to misalign positions when copying symbols from the mapping table to the target word. Careful, systematic substitution avoids these issues. Final Answer: The word "TELEGRAM" is written as %@^@!?*& in the given code language.

Question 14

In a certain code language, the word "NIGERIA" is written as "@#^$?#*". Using the same code, how is the word "GINGER" written in that code language?

Accepted Answer

Introduction: This symbolic coding question provides a code for the word "NIGERIA" and asks us to encode the word "GINGER" using the same scheme. Each letter appears to map to a specific special character. The question evaluates your ability to extract consistent letter to symbol relationships and apply them correctly to form a new coded word. Given Data / Assumptions: The code for NIGERIA is given as @#^$?#*. The letters of NIGERIA are N, I, G, E, R, I, A. We assume that each letter is mapped to one unique symbol, and that the mapping is used consistently for all occurrences of that letter. The word GINGER, which we must encode, is composed of letters G, I, N, G, E, R, all of which are present in NIGERIA. Concept / Approach: The method is to align each letter of NIGERIA with its corresponding symbol in position order. This yields a mapping table from letters to symbols. Then we take the word GINGER and replace each letter with its symbol using that table. Because all required letters appear in NIGERIA, no new mapping is needed. Step-by-Step Solution: Step 1: Write NIGERIA and its code together: N I G E R I A corresponds to @ # ^ $ ? # *.Step 2: From this, assign mappings: N = @, I = #, G = ^, E = $, R = ?, and A = *.Step 3: The word GINGER has letters G, I, N, G, E, R in that order.Step 4: Substitute using the mapping: G = ^, I = #, N = @, G again = ^, E = $, R = ?.Step 5: Writing these in sequence gives ^ # @ ^ $ ?.Step 6: Therefore, "GINGER" is coded as ^#@^$? in the given code language. Verification / Alternative check: We can re verify by checking that each symbol we used for GINGER appears correctly in NIGERIA. G is always ^, I is always #, N is always @, E is $, and R is ?. There are no inconsistencies, so the mapping is correct. Also, if we decode ^#@^$? back using our table, we retrieve GINGER which confirms that our answer is reversible. Why Other Options Are Wrong: Option a ^#$@^? places the @ and $ symbols in the wrong positions compared to the required letter order. Option c ^#@$^? misorders the symbols again and does not match the letter by letter mapping. Option d #$@$^? assigns wrong symbols to several letters, including putting # at the start instead of ^ for G. Option e ^#@^$* incorrectly uses * at the end, which corresponds to A not R. Common Pitfalls: Students sometimes forget that letters appearing more than once must always have the same code, leading to inconsistent symbol use. Another pitfall is to misread the sequence of special characters, especially when they are visually similar or crowded together. Carefully aligning positions avoids these errors. Final Answer: The word "GINGER" is written as ^#@^$? in the given code language.

Question 15

If "-" means "plus", "x" means "divide", "÷" means "multiply" and "+" means "minus", then how should the expression 26 + 400 x 20 - 21 ÷ 12 be evaluated and what is its final value?

Accepted Answer

Introduction: This problem provides an arithmetic expression in which each arithmetic symbol has been assigned a new meaning. The goal is to decode the expression 26 + 400 x 20 - 21 ÷ 12 according to the specified symbol mappings and then compute its value. This tests understanding of operator substitution and the correct application of precedence once decoding is done. Given Data / Assumptions: The mappings are: "-" means plus, "x" means divide, "÷" means multiply, and "+" means minus. The expression is 26 + 400 x 20 - 21 ÷ 12. We assume normal precedence rules after decoding, with division and multiplication evaluated before addition and subtraction. We also treat the minus symbol in the expression as the one whose meaning has been reassigned to plus. Concept / Approach: The correct approach is to rewrite the entire expression using the true operations that each symbol stands for. Once the expression has standard operators, we evaluate it using the standard order of operations. Care must be taken not to confuse the original meanings of the symbols with their reassigned roles in this question. Step-by-Step Solution: Step 1: Replace each symbol with its true meaning based on the mappings.Step 2: The symbol "+" stands for minus, so 26 + 400 becomes 26 - 400.Step 3: The symbol "x" stands for divide, so 400 x 20 becomes 400 / 20.Step 4: The symbol "-" stands for plus, so the segment - 21 becomes + 21.Step 5: The symbol "÷" stands for multiply, so 21 ÷ 12 becomes 21 * 12.Step 6: Putting it all together, the expression becomes 26 - 400 / 20 + 21 * 12.Step 7: Apply precedence rules: first evaluate division and multiplication from left to right.Step 8: Compute 400 / 20 = 20.Step 9: Compute 21 * 12 = 252.Step 10: The expression now simplifies to 26 - 20 + 252.Step 11: Perform addition and subtraction from left to right. First, 26 - 20 = 6.Step 12: Then 6 + 252 = 258.Step 13: Therefore, the value of the decoded expression is 258. Verification / Alternative check: We can verify by carefully reconfirming each mapping and the transformed expression. Using "-" as plus and "+" as minus, and substituting "x" and "÷" with divide and multiply respectively, we arrive at the same decoded form. Recomputing the numerical operations confirms the final result of 258. Why Other Options Are Wrong: The value 219 would require miscomputing one of the products or sums. The value 216 might be obtained by erroneously performing 26 - 400 first and then combining without respecting precedence. The value 230 or 240 could result from mixing up plus and minus or handling the division incorrectly. None of these alternate values emerge from a consistent application of the correct mappings and precedence rules. Common Pitfalls: Students may mistakenly apply the original meanings of the symbols, turning the expression into a completely different calculation. Another common error is performing arithmetic strictly left to right without handling multiplication and division first. Writing the fully decoded expression and then following standard rules step by step avoids such mistakes. Final Answer: The correctly evaluated value of the expression is 258.

Question 16

In a certain code language, the word "PEPPER" is written as "@#@@#!" and the word "AIM" is written as "^?*". Using the same symbol code, how is the word "PAMPER" written in that code language?

Accepted Answer

Introduction: This coding question uses special characters to represent letters. We are told that "PEPPER" is written as "@#@@#!" and "AIM" is written as "^?*". We must determine the code for "PAMPER" using the same consistent mapping from letters to symbols. The task checks how well you can maintain a coherent mapping when letters appear in multiple positions and combinations. Given Data / Assumptions: The code for PEPPER is @#@@#!, which corresponds to the letters P, E, P, P, E, R. The code for AIM is ^?*, corresponding to A, I, M. We assume that each letter corresponds to exactly one symbol and that this mapping is consistent across all words. The target word PAMPER is composed of letters P, A, M, P, E, R, which are all present in the mapping derived from PEPPER and AIM. Concept / Approach: The approach is to establish a letter to symbol mapping from the given examples by pairing letters with symbols in their respective positions. Once the mapping is complete, we apply it to PAMPER by substituting each letter with its symbol in order. Because all letters of PAMPER appear in the given examples, no guesswork is needed. Step-by-Step Solution: Step 1: Analyze PEPPER → @#@@#!. The letters P, E, P, P, E, R align with the symbols @, #, @, @, #, !.Step 2: From this, we deduce that P = @, E = #, and R = !.Step 3: Analyze AIM → ^?*. The letters A, I, M align with the symbols ^, ?, *.Step 4: From this, we deduce A = ^, I = ?, and M = *.Step 5: Combine the mappings: P = @, E = #, R = !, A = ^, M = *.Step 6: The word PAMPER consists of letters P, A, M, P, E, R in that sequence.Step 7: Substitute each letter using the mapping: P = @, A = ^, M = *, P again = @, E = #, R = !.Step 8: Putting these symbols together gives @^*@#!.Step 9: Therefore, "PAMPER" is written as @^*@#! in the code language. Verification / Alternative check: To verify, we can re check PEPPER and AIM with our map. PEPPER becomes @#@@#! and AIM becomes ^?*, exactly as given. There are no contradictions, and every letter in PAMPER is mapped from established relationships, so the encoding is consistent. Why Other Options Are Wrong: Option b @*^@#! would assign * to A and ^ to M, which contradicts the mapping from AIM. Option c @^*#@! misplaces the # symbol and breaks the consistent positions of P and E. Option d @^*@!# swaps the positions of # and !, effectively mis encoding E and R. Option e @*^#!@ introduces an incorrect ordering of symbols that does not follow the letter sequence P, A, M, P, E, R. Common Pitfalls: Some learners may incorrectly assume that positions in the word influence the mapping beyond the strict one to one letter symbol relationship, leading to inconsistent symbol use for repeated letters. Others may misread the sequence of special characters, particularly when several similar symbols appear together. Final Answer: The word "PAMPER" is written as @^*@#! in the given code language.

Question 17

If "#" means "subtraction", "&" means "division", "@" means "addition" and "%" means "multiplication", then what is the value of 217 & 7 # 3 @ 2 % 7 when it is evaluated using these coded operators?

Accepted Answer

Introduction: This coded arithmetic problem assigns new meanings to four different symbols and asks us to evaluate a compound expression. The symbols #, &, @, and % are interpreted as subtraction, division, addition, and multiplication respectively. Our task is to decode the expression 217 & 7 # 3 @ 2 % 7 and compute its result, carefully respecting operator precedence. Given Data / Assumptions: The mappings are: # stands for subtraction, & stands for division, @ stands for addition, and % stands for multiplication. The expression is 217 & 7 # 3 @ 2 % 7. We assume that after decoding, we follow standard arithmetic precedence, performing division and multiplication before addition and subtraction, and evaluating left to right within each level. Concept / Approach: The first step is to translate the coded expression into standard arithmetic symbols by replacing each symbol with its true operation. After we obtain a normal looking expression, we apply the usual BODMAS or PEMDAS order of operations. Being systematic in substitution and evaluation reduces the chance of error. Step-by-Step Solution: Step 1: Apply the mappings: & is division, # is subtraction, @ is addition, and % is multiplication.Step 2: Rewrite the expression 217 & 7 # 3 @ 2 % 7 as 217 / 7 - 3 + 2 * 7.Step 3: According to precedence rules, handle division and multiplication first from left to right.Step 4: Compute 217 / 7. Since 7 * 31 = 217, we get 217 / 7 = 31.Step 5: Compute 2 * 7 = 14.Step 6: Substitute these values back into the expression, which becomes 31 - 3 + 14.Step 7: Now evaluate the addition and subtraction from left to right. First, 31 - 3 = 28.Step 8: Then compute 28 + 14 = 42.Step 9: Therefore, the value of the coded expression is 42. Verification / Alternative check: We can recheck the transformation by confirming each mapping: & as division gives 217 / 7, # as subtraction gives - 3, @ as addition gives + 2, and % as multiplication gives * 7. Recomputing 217 / 7 = 31 and 2 * 7 = 14 and then 31 - 3 + 14 indeed results in 42, confirming the correctness of the calculation. Why Other Options Are Wrong: The value 21 would arise if someone mistakenly divided 217 by 7 and then divided again by 3 or halved the final answer. The value 19 could result from subtracting 14 instead of adding it. The value 22 or 28 might appear if the multiplication was omitted or the addition and subtraction were done before resolving all products. None of these alternative results respect both the correct mappings and proper precedence. Common Pitfalls: Students may forget that multiplication and division must be completed before addition and subtraction or may accidentally replace symbols with their original meanings instead of the reassigned ones. Another error is to miscalculate 217 / 7 or 2 * 7, which can propagate into a wrong final answer even if the decoding is correct. Final Answer: The computed value of the expression is 42.

Question 18

If the word FRISKED is coded as HTKUMGF (i.e., each letter is shifted forward by 2 positions in the English alphabet), then how will the word SUN be coded using the same letter-shift rule?

Accepted Answer

Introduction / Context: This question tests a basic coding-decoding pattern where each letter of a word is transformed using a consistent alphabet shift. The example FRISKED → HTKUMGF indicates a fixed forward movement in the alphabet for every character. Given Data / Assumptions: FRISKED is coded as HTKUMGF. The same rule must be applied to the word SUN. Alphabet is cyclic: after Z comes A. Concept / Approach: Compare each original letter with its coded letter in the example to detect the shift. If every letter moves by the same number of positions, apply that shift to each letter of the new word. Step-by-Step Solution: F → H means shift forward by 2 (F,G,H). R → T is also forward by 2. I → K forward by 2. S → U forward by 2. So, the rule is: shift every letter +2. Now apply to SUN: S → U (+2). U → W (+2). N → P (+2). Therefore, SUN → UWP. Verification / Alternative check: If the same +2 shift works consistently across all letters of FRISKED, it is valid to apply it directly to SUN. The transformation remains uniform for each character, confirming UWP. Why Other Options Are Wrong: SXO: implies 0 or negative shift from S. VZQ: inconsistent large jumps. TWQ: mixed shifts (S→T is +1, U→W is +2). RVM: shifts backward for S→R. Common Pitfalls: Assuming different shifts for different letters, forgetting alphabet wrap-around, or using reverse order instead of shifting are typical mistakes. Final Answer: UWP

Question 19

In a certain code language, the operator symbols are redefined as follows: '+' means multiplication (*), '-' means addition (+), 'x' means division (/), and '÷' means subtraction (-). Using this decoding, what is the correct value of: 80 + 2 ÷ 25 + …

Accepted Answer

Introduction / Context: This problem checks your ability to decode symbol substitutions and then evaluate an expression using standard arithmetic precedence. The key skill is to first replace each symbol with its actual meaning, and only then calculate. Given Data / Assumptions: '+' represents multiplication (*). '-' represents addition (+). 'x' represents division (/). '÷' represents subtraction (-). Use BODMAS/precedence: multiplication and division before addition and subtraction. Concept / Approach: Rewrite the entire expression by replacing each operator with its true operation. Then evaluate the rewritten expression normally. Do not mix coded precedence with real precedence. Step-by-Step Solution: Original: 80 + 2 ÷ 25 + 5 - 10 Replace '+' with *: 80 * 2 ÷ 25 * 5 - 10 (not correct yet because ÷ and - also change) Now apply all mappings correctly: 80 + 2 becomes 80 * 2 2 ÷ 25 becomes 2 - 25 25 + 5 becomes 25 * 5 5 - 10 becomes 5 + 10 So decoded expression is: 80 * 2 - 25 * 5 + 10 Compute: 80 * 2 = 160 Compute: 25 * 5 = 125 Now: 160 - 125 + 10 = 45 Verification / Alternative check: Quick check: since 25 * 5 = 125 cancels most of 160, the result should be near 35, and adding 10 gives 45. This matches the computed value. Why Other Options Are Wrong: 36: would come from incorrect operator replacement or order. 35: often from stopping at 160 - 125. 98: usually from treating + as + instead of *. 40: from partial precedence mistakes. Common Pitfalls: Replacing only some operators, evaluating before decoding, or applying wrong precedence to the coded symbols are common errors. Final Answer: 45

Question 20

A special symbol operation is defined using the following examples: 45 % 11 = 7 and 59 % 34 = 7. Based on the same pattern (using digit sums), what is the value of 55 % 4 = ?

Accepted Answer

Introduction / Context: This question tests pattern recognition in a custom operator. The symbol % here does not mean the usual remainder. Instead, it follows a rule that can be inferred from the given examples, typically involving digit sums or simple number properties. Given Data / Assumptions: 45 % 11 = 7 59 % 34 = 7 Find 55 % 4 using the same rule. Assume the rule is consistent across examples. Concept / Approach: A common coding-decoding approach is to compare the inputs with the output and test simple operations like digit-sum difference. We verify the rule on both examples before applying it to the new case. Step-by-Step Solution: Check 45 % 11 = 7. Digit sum of 45 = 4 + 5 = 9. Digit sum of 11 = 1 + 1 = 2. Difference = 9 - 2 = 7. Matches the result. Now verify with 59 % 34 = 7. Digit sum of 59 = 5 + 9 = 14. Digit sum of 34 = 3 + 4 = 7. Difference = 14 - 7 = 7. Matches again. So the rule is: a % b = (sum of digits of a) - (sum of digits of b). Now compute 55 % 4: Digit sum of 55 = 5 + 5 = 10. Digit sum of 4 = 4. Result = 10 - 4 = 6. Verification / Alternative check: The rule is validated by both examples, so applying it to 55 and 4 is logically consistent. The computed result 6 fits the same operation pattern. Why Other Options Are Wrong: 7: would imply no subtraction of digit sum for 4. 5: could come from taking 10 - 5 by mistake. 10: ignoring the second number completely. 4: using digit sum of only the first number incorrectly. Common Pitfalls: Using the normal modulo meaning, subtracting the numbers directly (55 - 4), or taking digit product instead of digit sum are frequent errors. Final Answer: 6

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