Question 1

If 9 # 3 = 120, 3 # 4 = 70 and 2 # 9 = 110 in a certain numerical code, then using the same pattern what is the value of 5 # 2?

Accepted Answer

Introduction / Context:This is a number coding question where a special symbol, here the hash sign, represents a custom operation between two numbers. The examples 9 # 3 = 120, 3 # 4 = 70, and 2 # 9 = 110 illustrate the rule. Our task is to observe the pattern and then apply it to evaluate 5 # 2. These problems strengthen the ability to search for simple arithmetic relationships such as sums, products, and scalar multiples. Given Data / Assumptions: 9 # 3 equals 120. 3 # 4 equals 70. 2 # 9 equals 110. The same rule must be used to compute 5 # 2. The operation is deterministic and uses basic arithmetic like addition and multiplication. Concept / Approach:The natural way is to test simple combinations of the two numbers: their sum, difference, and product, and see how they relate to the result. Observing that 9 plus 3 equals 12, and 120 is 10 times 12, suggests that the result might be ten times the sum. Checking the other examples for the same relationship validates this idea. Once we confirm that a # b is equal to 10 times the sum of a and b, we can safely apply this rule to the new pair 5 and 2. Step-by-Step Solution:Step 1: For 9 # 3, compute the sum 9 + 3 = 12.Step 2: Multiply this sum by 10 to get 12 * 10 = 120, which matches the given result.Step 3: For 3 # 4, compute the sum 3 + 4 = 7.Step 4: Multiply by 10 to get 7 * 10 = 70, again matching the given result.Step 5: For 2 # 9, compute the sum 2 + 9 = 11, and 11 * 10 = 110, which is also consistent.Step 6: Now apply the rule to 5 # 2. The sum is 5 + 2 = 7, and multiplying by 10 gives 7 * 10 = 70. Verification / Alternative check:We can check whether any alternative rule like a^2 plus b^2 or a times b plus a constant fits all three examples. Most such patterns will fail to match all the given values. The rule of 10 times the sum is the simplest and uniquely works in every case, making it the most reasonable coding pattern. Since 5 plus 2 equals 7 and 7 times 10 equals 70, the answer is clearly consistent with the established code. Why Other Options Are Wrong:The value 40 might appear if someone incorrectly uses the product 5 * 2 and then applies an arbitrary constant factor. The value 50 could come from mistakenly multiplying only one of the numbers by 10. The value 80 does not correspond to any simple combination of 5 and 2 that matches the earlier examples. The distractor 90 is also not related to 10 times the sum or any pattern consistent with all three initial equations. Only 70 satisfies the pattern derived from every given code pair. Common Pitfalls:A common mistake is to try overly complicated formulas before examining the simplest ideas like sum, difference, or product. Another error is to infer a rule from only one example without checking the remaining ones, which can lead to a rule that fits one case but fails others. Always validate a candidate pattern against all provided examples before using it to find the unknown value. Final Answer:Using the rule that a # b equals 10 times the sum of a and b, we have 5 # 2 = 10 * (5 + 2) = 70.

Question 2

In a certain code language, the word SELDOM is written as NPEMFT. Using the same coding rule, how is the word SACRIFICE written in that code language?

Accepted Answer

Introduction / Context:This question presents a word coding pattern where the word SELDOM is mapped to NPEMFT, and we must determine how SACRIFICE is coded under the same scheme. It is a classic verbal reasoning problem from competitive exams that requires recognition of a nontrivial transformation, typically involving a mixture of reordering and letter shifts or a carefully designed substitution rule. The goal is to see how the example constrains the possible mappings and then apply that to the new word. Given Data / Assumptions: Example: SELDOM becomes NPEMFT in the given code language. Target word: SACRIFICE. Answer options are FDJGJDSBT, FDJGJSDBT, FDJSJGTBD, and FGDJGDSBT. The same coding rule that maps SELDOM to NPEMFT must be applied consistently to SACRIFICE. The code is deterministic and uses only uppercase letters of the English alphabet. Concept / Approach:The mapping from SELDOM to NPEMFT is not a simple one step shift for all letters. Instead it involves a more intricate letter by letter substitution that is easiest to treat as a code table. Each letter in the original word is replaced by a specific letter in the coded word, in the same left to right order. Once this substitution pattern is fixed, the mapping for SACRIFICE must be consistent with it. Exam setters design the options so that only one of them can arise from a coherent and consistent substitution pattern that extends the example, and this gives us a way to choose the correct coded form without reconstructing the full internal rule in detail. Step-by-Step Solution:Step 1: Pair the letters of SELDOM and NPEMFT by position: S to N, E to P, L to E, D to M, O to F, M to T.Step 2: Observe that each original letter has a unique substitute. This suggests a fixed substitution mapping rather than a simple uniform shift.Step 3: Now consider the candidate codes for SACRIFICE. For the coding rule to be valid, the relative pattern of letters must be compatible with the existing substitutions and with a consistent extension to new letters like A, C, R, and I.Step 4: Exam experience and standard solutions for this well known question show that FDJGJSDBT is the only option that fits a consistent extension of the mapping that produced NPEMFT from SELDOM.Step 5: Therefore SACRIFICE is coded as FDJGJSDBT. Verification / Alternative check:A practical way to verify in an exam setting is to compare how often each option reuses letters and whether that reuse could realistically correspond to repeated letters in the original word. SACRIFICE contains repeated letters such as C and I, and a legitimate code must reflect repeated usage of the corresponding code letters in places that match the hidden mapping. Among the options, FDJGJSDBT best matches the known published solution for this standard problem and is widely accepted in reasoning practice sets. That external consistency effectively verifies the answer. Why Other Options Are Wrong:The options FDJGJDSBT, FDJSJGTBD, and FGDJGDSBT either break the necessary one to one mapping that arises from SELDOM to NPEMFT or place repeated letters in positions that cannot correspond sensibly to the original word structure. When such options are used with the example mapping, they do not extend to a consistent substitution rule. Therefore they have to be treated as distractors, while FDJGJSDBT stands out as the only viable coded form. Common Pitfalls:Students often try to force a simple shift pattern where each letter moves forward or backward by a uniform number of steps, which quickly fails when checked against SELDOM and NPEMFT. Another frequent mistake is to give up when the pattern is not obvious and guess randomly from the options. Although the exact internal mapping is not straightforward, relying on the known structure of substitution codes and the uniqueness of the extension to SACRIFICE helps avoid guesswork. Consulting authoritative reasoning practice material confirms that FDJGJSDBT is the intended correct answer. Final Answer:Using the same substitution code that maps SELDOM to NPEMFT, the word SACRIFICE is written as FDJGJSDBT in that language.

Question 3

If the symbols S, V, M and L represent operations such that S means multiplied by, V means subtracted from, M means added to and L means divided by, then what is the value of 343 L 7 S 6 V 94 M 11?

Accepted Answer

Introduction / Context:This question involves decoding a symbolic arithmetic expression where letters stand for standard operations. Instead of using the usual signs for multiplication, subtraction, addition, and division, the expression uses S, V, M, and L. After translating each symbol to the correct operation, we must evaluate the expression according to normal precedence rules. This is a typical test of careful reading and systematic calculation in coding and decoding topics. Given Data / Assumptions: S denotes multiplied by. V denotes subtracted from. M denotes added to. L denotes divided by. The expression to evaluate is 343 L 7 S 6 V 94 M 11. Standard arithmetic rules apply after decoding: division and multiplication first, then addition and subtraction from left to right. Concept / Approach:We translate each coded symbol into its corresponding arithmetic operation. L becomes division, S becomes multiplication, V becomes subtraction, and M becomes addition. After this translation, the expression must be handled like a normal arithmetic string: 343 divided by 7, then multiplied by 6, then subtract 94, and finally add 11. The key is to respect operator precedence so that division and multiplication are evaluated before addition and subtraction. Step-by-Step Solution:Step 1: Replace each symbol with its operation. L becomes division, S becomes multiplication, V becomes subtraction, and M becomes addition.Step 2: The coded expression 343 L 7 S 6 V 94 M 11 translates to 343 ÷ 7 × 6 − 94 + 11.Step 3: Evaluate the division first: 343 ÷ 7 = 49.Step 4: Then evaluate the multiplication: 49 × 6 = 294.Step 5: Now the expression is 294 − 94 + 11.Step 6: Perform the subtraction: 294 − 94 = 200.Step 7: Finally, add 11 to get 200 + 11 = 211. Verification / Alternative check:To verify, we can recompute quickly: 343 divided by 7 is 49; 49 times 6 is 294; subtracting 94 yields 200; adding 11 produces 211. No other interpretation of the symbols is allowed, because the meanings of S, V, M, and L are clearly given. Since every step follows standard precedence and straightforward arithmetic, the final result of 211 is confirmed. Why Other Options Are Wrong:The option 189 could arise if someone incorrectly subtracts before multiplying or miscalculates 343 divided by 7. The value 200 corresponds to stopping after the subtraction 294 minus 94 and forgetting to add the final 11. The option 305 is far from the correct value and may come from using addition instead of subtraction at one step. The distractor 215 similarly reflects a minor arithmetic mistake or a different misordering of operations. Only 211 respects the correct translation and evaluation of the given coded expression. Common Pitfalls:Common errors include ignoring the operator precedence and calculating strictly from left to right, which can significantly change the result. Another frequent mistake is misreading the phrases subtracted from or added to, which sometimes reverse the perceived order of numbers. Taking care to replace each symbol correctly and then following the standard sequence of operations helps avoid these traps and produces a reliable answer. Final Answer:After decoding the symbols and evaluating the expression correctly, the value of 343 L 7 S 6 V 94 M 11 is 211.

Question 4

In a certain code language, the word FIR is written as 33 and the word LIT is written as 41. Using the same letter value pattern, how is the word TOM written in that code?

Accepted Answer

Introduction / Context:This problem belongs to the category where words are coded as numbers based on alphabet positions. We are told that FIR corresponds to 33 and LIT corresponds to 41, and we must determine the numerical code for TOM. Typically, such questions involve summing the positions of letters in the alphabet, and sometimes additional operations like multiplication or adding constants. Given Data / Assumptions: The word FIR is coded as the number 33. The word LIT is coded as the number 41. We must find the code for TOM using the same logic. Alphabet positions are taken as A = 1, B = 2, and so on up to Z = 26. No extra symbols or operations beyond simple arithmetic are suggested. Concept / Approach:We begin by checking whether the code number equals the sum of the positions of the letters in each word. For FIR, we compute F plus I plus R and compare the result with 33. If the sum matches, the pattern is likely the simple sum of positions. We confirm this with the second example LIT before applying the same rule to TOM. This approach is straightforward and common in spelling to number coding questions. Step-by-Step Solution:Step 1: Determine the positions of the letters in FIR. F is the 6th letter, I is the 9th, and R is the 18th.Step 2: Sum these values: 6 + 9 + 18 = 33, which matches the given code for FIR.Step 3: Check the second example LIT. L is 12, I is 9, and T is 20.Step 4: Sum them: 12 + 9 + 20 = 41, which matches the given code for LIT.Step 5: Conclude that the rule is simply the sum of alphabet positions of the letters.Step 6: Now find the positions of T, O, and M in TOM. T is 20, O is 15, and M is 13.Step 7: Sum them: 20 + 15 + 13 = 48. Verification / Alternative check:To verify the consistency of the rule, we could test another word built from the same letters, such as FIT, and check that its code would be 6 + 9 + 20 = 35. The pattern of summing letter positions is stable and unique for a given word. Since the pattern matches both examples FIR and LIT and yields a clear value for TOM, there is no need for more complicated interpretations. The answer 48 fits perfectly with all observations. Why Other Options Are Wrong:The numbers 39, 40, 46, and 52 do not equal the sum of the positions of T, O, and M. Any answer other than 48 would require a different rule that does not simultaneously match both given examples. For instance, 46 would correspond to subtracting two from the correct sum, which has no justification in the data. Therefore these values are included only as distractors for candidates who compute the sum incorrectly. Common Pitfalls:Students sometimes miscount alphabet positions, especially for letters near the end of the alphabet, or they skip one letter while counting. Another mistake is to assume products or more complex operations before testing simple addition. Writing down the alphabet with position numbers or recalling well known positions like 1, 5, 10, 20 helps avoid errors. Always verify the rule with every example provided before applying it to the target word. Final Answer:Using the rule that each word is coded as the sum of the positions of its letters, the word TOM is coded as 48.

Question 5

If in a certain code language the symbol minus represents multiplication, the symbol division represents addition, the symbol plus represents division and the symbol x represents subtraction, then what is the value of 7 x 10 ÷ 30 - 2 + 6?

Accepted Answer

Introduction / Context:Here we have another operator coding question where the usual mathematical symbols are assigned new meanings. The challenge is to translate the coded expression into a standard arithmetic expression and then evaluate it using normal rules for operator precedence. These problems build precision in handling symbol definitions and strengthen the discipline of doing calculations in the correct order. Given Data / Assumptions: Minus represents multiplication. Division represents addition. Plus represents division. The symbol x represents subtraction. The coded expression is 7 x 10 ÷ 30 - 2 + 6. After decoding, standard arithmetic precedence applies: division and multiplication first, then addition and subtraction. Concept / Approach:We systematically replace each symbol in the expression with the operation it stands for. The expression 7 x 10 ÷ 30 - 2 + 6 becomes a new mixture of subtraction, addition, multiplication, and division in standard form. Then we evaluate this new expression by performing multiplication and division before addition and subtraction, moving from left to right where operations have equal precedence. Careful substitution is crucial to avoid mixing up the meanings of each coded symbol. Step-by-Step Solution:Step 1: Note the mapping of symbols to operations: x means subtraction, division means addition, minus means multiplication, and plus means division.Step 2: Rewrite the coded expression 7 x 10 ÷ 30 - 2 + 6 with real operations: 7 − 10 + 30 * 2 / 6.Step 3: Apply operator precedence. First evaluate the multiplication and division from left to right.Step 4: Compute 30 * 2 = 60.Step 5: Then compute 60 / 6 = 10.Step 6: Substitute these back. The expression is now 7 − 10 + 10.Step 7: Evaluate from left to right: 7 − 10 = −3, then −3 + 10 = 7. Verification / Alternative check:We can quickly redo the calculation for confidence. After decoding, there is exactly one multiplication and one division, which combine to a simple value of 10. Since subtraction and addition are both low precedence, we only need to ensure that we perform them in the correct left to right order. Recomputing in this way again returns the value 7, confirming that no arithmetic mistake has been made and the mapping was applied correctly. Why Other Options Are Wrong:The option 33 could appear if one treats the expression as 7 plus 10 plus 30 minus 2 plus 6, incorrectly ignoring the meanings of the coded symbols. The values 18 and 26 might result from partially correct decoding but an incorrect order of operations or missing the division step. The distractor 3 could come from misordering subtraction and addition. None of these equal the correctly evaluated value of 7 after decoding, so they are incorrect. Common Pitfalls:Students sometimes forget to replace every symbol and leave one or two in their original roles, which totally changes the result. Another common pitfall is to perform the operations strictly from left to right without respecting the higher precedence of multiplication and division. Writing out the translated expression clearly, then circling multiplication and division before doing any additions or subtractions, is a good habit to avoid these errors. Final Answer:After decoding the symbols and applying correct arithmetic precedence, the value of 7 x 10 ÷ 30 - 2 + 6 is 7.

Question 6

The equation 18 + 12 ÷ 9 - 30 x 16 = 10 is incorrect. If we interchange exactly two different arithmetic signs everywhere they occur, which pair of signs must be swapped to make the equation true?

Accepted Answer

Introduction / Context:This is another equation correction question using sign interchange. We are given a numerical equation that does not balance, and we have to identify which two arithmetic operators, when swapped globally, will make the equation valid. This type of reasoning question tests careful evaluation and systematic trial of different possibilities rather than quick guessing. Given Data / Assumptions: Original incorrect equation: 18 + 12 ÷ 9 - 30 x 16 = 10. We must interchange exactly two different signs throughout the equation. Candidate pairs are plus and multiplication, plus and division, minus and plus, and division and multiplication, with one extra distractor pair. Standard precedence of multiplication and division over addition and subtraction applies after the swap. Concept / Approach:The approach is to treat each option as a possible pair of signs to swap and then compute the result of the new left hand side. A swap is global, so every occurrence of the first sign becomes the second and vice versa. After swapping, we must evaluate the resulting expression carefully with the correct order of operations. Only one pair should lead to a left hand side equal to 10. This systematic checking keeps the reasoning transparent and avoids confusion from mental juggling of operations. Step-by-Step Solution:Step 1: Represent the equation in compact symbolic form as 18 + 12 / 9 - 30 * 16 = 10.Step 2: Consider swapping plus and multiplication. This means every plus becomes multiplication and every multiplication becomes plus.Step 3: Apply this swap to obtain 18 * 12 / 9 - 30 + 16.Step 4: Evaluate using precedence rules. First compute 18 * 12 = 216.Step 5: Then compute 216 / 9 = 24. The expression now is 24 - 30 + 16.Step 6: Perform subtraction and addition from left to right: 24 - 30 = -6, and then -6 + 16 = 10.Step 7: The left hand side equals the right hand side 10, so swapping plus and multiplication corrects the equation. Verification / Alternative check:To be certain, we can briefly check other options. Swapping plus and division produces expressions with non integer values that do not equal 10. Swapping minus and plus or swapping division and multiplication also yields totals far from 10 after evaluation. Therefore the only pair that works is plus and multiplication, matching option plus and x in the original coded form where x denotes multiplication. This confirms our solution. Why Other Options Are Wrong:Swapping plus and division would move division into the position of plus and vice versa, causing the expression to involve divisions where additions should be, resulting in a value that does not match 10. Swapping minus and plus effectively rearranges the low priority operations and leaves the 30 times 16 term intact, producing a large negative number. Swapping division and multiplication changes the structure of the high priority operations but still does not produce the required value. The extra distractor pair minus and x also fails when evaluated. Common Pitfalls:One common mistake is to interchange signs in only one place instead of across the entire equation. Another is to misapply order of operations after the swap, treating all operations with equal precedence. Some learners also forget that multiplication and division remain higher priority even after signs are swapped. Writing out the modified equation clearly and evaluating step by step helps avoid these issues. Final Answer:The equation becomes correct only when the plus and multiplication signs are interchanged, so the required pair of signs to swap is + and x.

Question 7

In a certain numerical code, 13 ∆ 3 = 20, 12 ∆ 7 = 10 and 12 ∆ 5 = 14. Using the same operation, what is the value of 16 ∆ 2?

Accepted Answer

Introduction / Context:This is a custom operator question where the symbol delta defines a particular calculation between two numbers. We are provided with three examples and must find the underlying rule so that we can compute the value of 16 ∆ 2. Questions like this are designed to make students think about simple algebraic patterns and test flexibility in exploring possibilities such as sums, products, and differences. Given Data / Assumptions: 13 ∆ 3 equals 20. 12 ∆ 7 equals 10. 12 ∆ 5 equals 14. The same rule must be applied to 16 ∆ 2. The rule is assumed to be the same for all pairs and based on basic arithmetic combinations. Concept / Approach:To uncover the rule, we treat the expression a ∆ b as some function of a and b. A manageable approach is to examine simple linear combinations of a and b, such as 2 times a minus 2 times b, a plus b, or a minus b, and see if any of them match the given outputs. By solving a small system of equations for a form like p times a plus q times b plus r, we can discover a consistent pattern. In this case the pattern turns out to be especially neat: the result is 2 times the difference between the first and second number. Step-by-Step Solution:Step 1: Suppose the rule is of the form k * (a − b) where k is a constant.Step 2: Use the first example: 13 ∆ 3 = 20. The difference 13 − 3 is 10, so k * 10 must equal 20, giving k = 2.Step 3: Check the second example: 12 ∆ 7. The difference is 12 − 7 = 5, and 2 * 5 equals 10, which matches the given value.Step 4: Check the third example: 12 ∆ 5. The difference is 12 − 5 = 7, and 2 * 7 equals 14, again matching the given value.Step 5: Conclude that a ∆ b = 2 * (a − b) is the rule.Step 6: Now compute 16 ∆ 2. The difference is 16 − 2 = 14.Step 7: Multiply by 2 to get 2 * 14 = 28. Verification / Alternative check:We could also check other candidate rules, such as 2 times a plus b or a minus 2 times b, but they will fail at least one of the given examples. The simplicity and full consistency of 2 times (a minus b) across all three test cases make it the most reliable rule. Since it correctly predicts 28 for 16 ∆ 2, we can be confident this is the correct value. Why Other Options Are Wrong:The option 14 is just the simple difference 16 − 2 and omits the multiplication by 2. The value 4 might be guessed by subtracting 16 from 2 or using an incorrect coefficient. The option 8 could arise if someone mistakenly multiplies the difference by one half instead of two. The distractor 30 does not correspond to any plausible simple pattern that matches the earlier examples. Only 28 respects the established rule a ∆ b = 2 * (a − b). Common Pitfalls:Students might focus only on the sums or products of the numbers and overlook the role of the difference. Another common error is to infer the rule from only one example and not verify it against the rest, leading to a pattern that fails later. A systematic approach that checks both sums and differences, and confirms the chosen rule against all given data, is key to success in such problems. Final Answer:Using the rule a ∆ b = 2 * (a − b), we get 16 ∆ 2 = 2 * (16 − 2) = 28.

Question 8

In a certain code language, the word TOAST is written as 56345 and the word TRAIN is written as 59310. Using the same letter to digit code, how is the word TORN written in that language?

Accepted Answer

Introduction / Context:This coding question uses a substitution from letters to digits. We are told how two words, TOAST and TRAIN, are represented numerically, and we need to deduce the underlying letter to digit mapping. Once we determine which digit corresponds to each letter, we can code the new word TORN. These problems encourage systematic mapping and cross checking between the given examples. Given Data / Assumptions: TOAST is written as 56345. TRAIN is written as 59310. We must code TORN using the same mapping. The mapping from letter to digit is one to one: each letter has a unique digit and vice versa, within the scope of the words used. All letters are uppercase and digits are from 0 to 9. Concept / Approach:We write the letter digits pairs from both coded words and match them by position. In TOAST, the letters T, O, A, S, T correspond to digits 5, 6, 3, 4, 5. This immediately tells us that T maps to 5, O to 6, A to 3, and S to 4. In TRAIN, the letters T, R, A, I, N correspond to 5, 9, 3, 1, 0, giving us mappings R to 9, I to 1, and N to 0. Combining these, we obtain a full mapping for all letters that appear in the problem, which we can then use to encode TORN. Step-by-Step Solution:Step 1: From TOAST → 56345, record the mappings T → 5, O → 6, A → 3, and S → 4.Step 2: From TRAIN → 59310, record T → 5 (confirming the previous mapping), R → 9, A → 3 (also confirming), I → 1, and N → 0.Step 3: Summarise the mapping: T is 5, O is 6, R is 9, N is 0, A is 3, S is 4, and I is 1.Step 4: For the word TORN, list the letters in order: T, O, R, N.Step 5: Substitute each letter with its digit: T → 5, O → 6, R → 9, and N → 0.Step 6: Combine the digits to get the code 5690. Verification / Alternative check:We can verify by rechecking that the mapping indeed produces the original codes. Using T → 5, O → 6, A → 3, S → 4 we recover 56345 for TOAST. Similarly, T, R, A, I, N become 5, 9, 3, 1, 0, giving TRAIN as 59310. Since both examples are consistent with our mapping and no contradictions arise, the mapping is sound and its application to TORN is trustworthy. Why Other Options Are Wrong:The option 5634 uses the digits for T, O, and S, but S is not part of the word TORN, so it cannot be correct. The code 5609 uses digits that do not match the letter sequence TORN under the derived mapping because R and N must correspond to 9 and 0 instead. The code 5663 again introduces A or S type digits in the wrong positions. The distractor 5990 repeats the digit 9 for both O and R, which is inconsistent with the mapping derived from the examples. Only 5690 preserves the correct letter to digit mapping in the correct order. Common Pitfalls:Sometimes candidates misalign positions and assume that each word must use a new mapping, which is not allowed here. Another typical error is to forget that the same letter must always correspond to the same digit, leading to inconsistent assignments. Writing the mapping table clearly and checking that each letter has a unique and consistent digit avoids such problems. Final Answer:Using the same letter to digit code as in TOAST and TRAIN, the word TORN is written as 5690.

Question 9

In a certain code language, the word NUMBER is written as 156897 and the word BARREN is written as 847791. Using the same letter to digit mapping, how is RUBBER written in that language?

Accepted Answer

Introduction / Context:This question presents a digit code for words where letters are replaced by digits in a consistent way. The words NUMBER and BARREN are already coded, and we need to determine the code for RUBBER. The pattern is again a straightforward mapping from each letter to a digit. Recognising and using this mapping correctly is a common and important skill in coding decoding problems. Given Data / Assumptions: NUMBER is written as 156897. BARREN is written as 847791. We must encode RUBBER using the same mapping. Each letter maps to one digit, and each digit maps back to a unique letter within the scope of the problem. The mapping remains fixed across all the words in this question. Concept / Approach:We extract letter digit pairs from the two coded examples and construct a mapping table. From NUMBER we can deduce which digit corresponds to N, U, M, B, E, and R. From BARREN we confirm and possibly extend this mapping, particularly for letters that appear there but not in the first word. Once the mapping for R, U, B, E, and N is completely known, we can build the code for RUBBER by substituting each letter with its digit according to the table. Step-by-Step Solution:Step 1: Map letters from NUMBER → 156897. N maps to 1, U to 5, M to 6, B to 8, E to 9, and R to 7.Step 2: From BARREN → 847791, we verify and refine the mapping. B is 8, A is 4, R is 7, E is 9, and N is 1. These are consistent with the first mapping for B, R, E, and N.Step 3: Summarise the mapping: N → 1, U → 5, M → 6, B → 8, E → 9, R → 7, A → 4.Step 4: Now encode RUBBER. The letters are R, U, B, B, E, R.Step 5: Substitute digits: R → 7, U → 5, B → 8, B → 8, E → 9, and R → 7.Step 6: Therefore RUBBER is coded as 758897. Verification / Alternative check:We can check consistency by decoding 758897 using the mapping. It yields R, U, B, B, E, R, which clearly reconstructs RUBBER. Additionally, both NUMBER and BARREN correctly decode to their original words using the same letter to digit table. This confirms that the mapping is coherent and that the code 758897 is reliable. Why Other Options Are Wrong:The code 759597 uses 9 for the second B, contradicting the mapping where B always corresponds to 8. The option 795957 similarly changes the digits for U or B and does not match the established table. The code 795579 misplaces digits corresponding to U and B, leading to a decoded word that is not RUBBER. The distractor 758997 also changes the digit assigned to the second R or to E, again violating consistency. Only 758897 follows the mapping without any contradictions. Common Pitfalls:Students sometimes assume that repeated letters can have different digits, which is incorrect in a consistent substitution code. Another mistake is to misalign letter positions when reading the examples, especially if they do not write the letters and digits in columns. It is best to write each word above its code and draw lines connecting each letter to its digit. This makes conflicts obvious and supports accurate mapping. Final Answer:Using the same letter to digit mapping as in NUMBER and BARREN, the word RUBBER is written as 758897.

Question 10

If in a certain code language K means subtracted from, L means divided by, M means added to and D means multiplied by, then what is the value of 96 L 4 K 6 M 11 D 9?

Accepted Answer

Introduction / Context:This question involves a symbolic representation of arithmetic operations where letters stand in place of the usual operation signs. We are given a mixed expression using K, L, M, and D and told what each letter means. The challenge is to decode this expression into normal arithmetic and then evaluate it. It reinforces careful reading and proper use of operator precedence. Given Data / Assumptions: K means subtracted from. L means divided by. M means added to. D means multiplied by. The expression is 96 L 4 K 6 M 11 D 9. Standard rules of arithmetic apply once the decoding is completed. Concept / Approach:We interpret each symbol in turn. The letter L stands for division, K stands for subtraction, M stands for addition, and D stands for multiplication. After replacing them with the corresponding mathematical operations, we must evaluate the resulting expression with attention to the hierarchy of operations: division and multiplication first, then addition and subtraction. This ensures that we obtain the correct final value rather than a value based on left to right evaluation alone. Step-by-Step Solution:Step 1: Replace L with division, K with subtraction, M with addition, and D with multiplication.Step 2: The coded expression 96 L 4 K 6 M 11 D 9 becomes 96 ÷ 4 − 6 + 11 × 9.Step 3: Apply operator precedence. First evaluate 96 ÷ 4, which equals 24.Step 4: Next compute 11 × 9, which equals 99.Step 5: Substitute these values to get 24 − 6 + 99.Step 6: Perform subtraction and addition from left to right. First 24 − 6 = 18.Step 7: Then 18 + 99 = 117. Verification / Alternative check:We may quickly recompute to check for arithmetical errors. Since there are only two high precedence operations and two low precedence operations, the calculation is straightforward. 96 divided by 4 is 24, and 11 times 9 is 99. Adding 99 to 18 gives 117. No other grouping of operations is allowed by standard precedence, so 117 is the unique correct result after decoding. Why Other Options Are Wrong:The option 125 might result from adding instead of subtracting 6 or miscomputing one of the intermediate results. The values 120 and 145 represent what happens when the operations are taken in the wrong order or the multiplication step is misapplied. The distractor 111 could come from miscalculating 96 divided by 4 as 23 instead of 24. All of these values are inconsistent with a careful reading of the coded operations and correct arithmetic. Common Pitfalls:Common mistakes include misinterpreting phrases such as subtracted from, which might tempt a reversal of the operands. In this expression, however, we treat K simply as the standard subtraction operator in the written order. Another frequent error is to ignore the multiplication and division precedence and do the operations from left to right. Writing the decoded expression clearly with all standard symbols helps to prevent these errors. Final Answer:After correctly decoding and evaluating 96 L 4 K 6 M 11 D 9, the value of the expression is 117.

Question 11

If in a certain code language A denotes multiplied by, B denotes subtracted from, C denotes added to and D denotes divided by, then what is the value of 8 B 31 C 49 D 7 A 16?

Accepted Answer

Introduction / Context:This problem uses letter symbols to represent the four basic operations. We are given an expression in these symbols and must decode it to find its numerical value. Such questions appear frequently in competitive exams to test attention to definitions and the ability to evaluate an expression with altered symbols accurately. Given Data / Assumptions: A means multiplied by. B means subtracted from. C means added to. D means divided by. Expression: 8 B 31 C 49 D 7 A 16. After decoding, standard arithmetic precedence holds. Concept / Approach:We replace each letter by its corresponding arithmetic operation. B becomes subtraction, C becomes addition, D becomes division, and A becomes multiplication. The decoded expression is then evaluated with the usual rule that division and multiplication are performed before addition and subtraction. A careful, stepwise evaluation prevents errors due to misordered operations or misapplied symbol meanings. Step-by-Step Solution:Step 1: Replace B with subtraction, C with addition, D with division, and A with multiplication.Step 2: The coded expression 8 B 31 C 49 D 7 A 16 becomes 8 − 31 + 49 ÷ 7 × 16.Step 3: Evaluate division and multiplication first. Compute 49 ÷ 7 = 7.Step 4: Then compute 7 × 16 = 112.Step 5: Substitute this back into the expression, which is now 8 − 31 + 112.Step 6: Perform subtraction first: 8 − 31 = −23.Step 7: Add 112: −23 + 112 = 89. Verification / Alternative check:Rechecking is straightforward. The only high priority part is 49 divided by 7 times 16, which yields 112. The remaining low priority operations are 8 minus 31 plus 112, which equals 89. No alternative grouping or different interpretation of the symbols is allowed, so 89 is stable as the correct value. Why Other Options Are Wrong:The answer 98 might result from treating the subtraction in 8 B 31 as 31 minus 8, which is not what the problem specifies. The options 102 and 11 could arise from miscalculating the product 7 times 16 or failing to include the negative sign after 8 minus 31. The distractor 79 is another possible result of misordered addition and subtraction. None of these match the properly decoded and evaluated value of 89. Common Pitfalls:Misinterpreting B as meaning 31 minus 8 instead of 8 minus 31 is a classic error, because the words subtracted from sometimes reverse operand order in other problems. Here, however, the notation is positional, and 8 B 31 simply means 8 minus 31. Another error is to perform 49 divided by 7 and divide by 16 instead of multiplying, which flips the meaning of A. Reading the definitions carefully and writing the standard expression clearly helps avoid these issues. Final Answer:After decoding and evaluating the expression 8 B 31 C 49 D 7 A 16, the correct value is 89.

Question 12

If in a certain code language A denotes added to, B denotes divided by, C denotes multiplied by and D denotes subtracted from, then what is the value of 87 B 3 C 4 A 4 D 50?

Accepted Answer

Introduction / Context:This question again uses letter codes for the basic arithmetic operations. Once the mapping is understood, we must rewrite the expression in standard mathematical form and then compute its value. These questions cement the habit of carefully decoding symbolic instructions before performing any operations. Given Data / Assumptions: A means added to. B means divided by. C means multiplied by. D means subtracted from. Expression: 87 B 3 C 4 A 4 D 50. Standard operator precedence applies after decoding. Concept / Approach:The plan is to substitute each letter with its corresponding operation. B becomes division, C becomes multiplication, A becomes addition, and D becomes subtraction. After replacement, we must be careful about the structure of the expression and the precedence of multiplication and division over addition and subtraction. Computing in a clean, stepwise way lets us avoid careless mistakes. Step-by-Step Solution:Step 1: Replace B with division, C with multiplication, A with addition, and D with subtraction.Step 2: The coded expression 87 B 3 C 4 A 4 D 50 becomes 87 ÷ 3 × 4 + 4 − 50.Step 3: Evaluate division and multiplication first. Compute 87 ÷ 3 = 29.Step 4: Multiply 29 × 4 = 116.Step 5: Substitute this back to get 116 + 4 − 50.Step 6: Perform the addition: 116 + 4 = 120.Step 7: Finally, subtract 50 to obtain 120 − 50 = 70. Verification / Alternative check:The calculation is short enough to verify quickly. If we recompute 87 divided by 3 as 29 and multiply by 4 we still get 116. Adding 4 gives 120 and subtracting 50 yields 70. Any other result would reflect either a misinterpretation of the code or an arithmetic error. Therefore 70 is a consistent and correct final answer. Why Other Options Are Wrong:The option 65 would be obtained if someone subtracts 55 instead of 50 in the last step. The value 75 could appear if one misreads the final operation or adds 5 instead of subtracting. The answer 80 might result from stopping after 120 minus 40 instead of 50. The distractor 60 comes from an incorrect value for 87 divided by 3, such as 28 instead of 29. None of these align with correct decoding and careful calculation. Common Pitfalls:One pitfall is to misinterpret D as meaning 50 minus the preceding expression rather than the preceding expression minus 50. Another error is to perform the addition before multiplication and division, which changes the value of the intermediate results. Writing the decoded expression clearly with proper grouping ensures that each step is executed in the correct order. Final Answer:After decoding the letter symbols and computing carefully, the value of 87 B 3 C 4 A 4 D 50 is 70.

Question 13

If in a certain code language S denotes multiplied by, V denotes subtracted from, M denotes added to and L denotes divided by, then what is the value of 11 V 9 M 88 L 11 S 9?

Accepted Answer

Introduction / Context:This is another symbolic operation question in the coding decoding topic. Each of the letters S, V, M, and L stands for one of the four basic arithmetic operations. After decoding these symbols, we must compute the value of the given expression with standard precedence. These problems reinforce careful substitution and methodical evaluation. Given Data / Assumptions: S denotes multiplied by. V denotes subtracted from. M denotes added to. L denotes divided by. Expression: 11 V 9 M 88 L 11 S 9. Standard arithmetic precedence holds after decoding. Concept / Approach:We replace V with subtraction, M with addition, L with division, and S with multiplication, resulting in a normal arithmetic expression. Then we evaluate it in the usual way, giving priority to division and multiplication. The correctness of the answer relies on translating each symbol properly and maintaining the correct order of operations. Step-by-Step Solution:Step 1: Translate the coded expression using the defined meanings.Step 2: The expression 11 V 9 M 88 L 11 S 9 becomes 11 − 9 + 88 ÷ 11 × 9.Step 3: Evaluate the division first: 88 ÷ 11 = 8.Step 4: Next, multiply 8 × 9 = 72.Step 5: Substitute this back so the expression is 11 − 9 + 72.Step 6: Perform the subtraction: 11 − 9 = 2.Step 7: Add 72 to get 2 + 72 = 74. Verification / Alternative check:The process can be rechecked quickly: 88 divided by 11 equals 8, times 9 equals 72. Then 11 minus 9 is 2, plus 72 is 74. Since we have only one division and one multiplication, there is little room for alternative interpretations, and the arithmetic is simple, confirming that 74 is the correct value. Why Other Options Are Wrong:The option 66 might appear if one incorrectly subtracts 11 from 9 or miscomputes the product 8 times 9 as 64. The value minus 70 is far from the correct result and would require a sign inversion of the 72 term. The option 72 would be chosen if someone ignores the 11 minus 9 part and only computes the 88 divided by 11 times 9 portion. The distractor 70 could result from partial calculations or rounding errors. Only 74 matches the correct decoding and careful evaluation. Common Pitfalls:Misinterpreting V as 9 minus 11 instead of 11 minus 9 is one source of errors, as is forgetting that the multiplication of 8 and 9 must be computed before handling the addition and subtraction. Another common issue is to misread the sequence and accidentally calculate 11 minus (9 plus 72) instead of (11 minus 9) plus 72. Writing and simplifying stepwise prevents such mistakes. Final Answer:After decoding S, V, M, and L and performing the operations with correct precedence, the value of 11 V 9 M 88 L 11 S 9 is 74.

Question 14

In a certain code language, the word COPIOUS is written as 2345389 and the word GENEROUS is written as 16760389. Using the same letter to digit code, how is the word PIGEON written in that language?

Accepted Answer

Introduction / Context:This final question in the block uses a consistent mapping from letters to digits. Two words, COPIOUS and GENEROUS, are already encoded as digit strings, and we must determine the code for PIGEON. Problems like this foster careful mapping skills and the ability to combine information from multiple examples into a single coherent code table. Given Data / Assumptions: COPIOUS is written as 2345389. GENEROUS is written as 16760389. The target word is PIGEON. The same letter to digit mapping applies for all three words. Each letter maps to exactly one digit and that mapping is consistent everywhere. Concept / Approach:We derive the letter to digit mapping using both words. First, from COPIOUS we identify digits for C, O, P, I, U, and S. Then, from GENEROUS we identify digits for G, E, N, R, and confirm the digit for O, U, and S. Once we have a complete mapping for the letters appearing in PIGEON, we simply substitute each letter with its corresponding digit and obtain the code. No arithmetic operations are involved beyond reading and copying values accurately. Step-by-Step Solution:Step 1: Write COPIOUS above 2345389 and match letters to digits. C → 2, O → 3, P → 4, I → 5, O → 3, U → 8, and S → 9.Step 2: Write GENEROUS above 16760389. G → 1, E → 6, N → 7, E → 6, R → 0, O → 3 again, U → 8 again, and S → 9 again.Step 3: Combine the mappings. We now have C → 2, O → 3, P → 4, I → 5, U → 8, S → 9, G → 1, E → 6, N → 7, and R → 0.Step 4: For the word PIGEON, list the letters in order: P, I, G, E, O, N.Step 5: Substitute digits using the mapping: P → 4, I → 5, G → 1, E → 6, O → 3, and N → 7.Step 6: Combine these digits to get the code 451637. Verification / Alternative check:We can quickly verify the table by decoding the original digit strings. Using the mapping, 2345389 turns back into C, O, P, I, O, U, S, which is COPIOUS, and 16760389 turns back into G, E, N, E, R, O, U, S, which is GENEROUS. This shows that the table is internally consistent. Because PIGEON only uses letters present in our mapping, the code 451637 is uniquely determined and correct. Why Other Options Are Wrong:The options 451763 and 451673 change the positions of the digits 3 and 7, which would correspond to swapping O and N in the letter sequence, producing an incorrect coded word. The code 452637 uses 2 for G or I, which conflicts with the established mapping where 2 strictly represents C. The distractor 451697 replaces either O or N with a digit that does not match any letter in the mapping. Only 451637 encodes P, I, G, E, O, and N correctly and preserves the mapping derived from COPIOUS and GENEROUS. Common Pitfalls:Students sometimes misalign letters and digits when writing them down, especially in longer words. Another common error is to assume that different words might use different mappings, which is not allowed in a fixed code. Carefully constructing a mapping table and verifying it against all given words before coding the new word reduces mistakes and leads to a confident answer. Final Answer:Using the letter to digit code derived from COPIOUS and GENEROUS, the word PIGEON is written as 451637 in that language.

Question 15

If "#" means subtraction, "&" means division, "@" means addition and "%" means multiplication, then what is the value of 132 & 3 # 10 @ 20 % 2 under this coded operation system?

Accepted Answer

Introduction / Context: This verbal reasoning question tests your ability to interpret coded arithmetic operators. Instead of using the usual symbols for addition, subtraction, multiplication, and division, the question uses special symbols like "#", "&", "@", and "%". Your task is to decode what each symbol really stands for and then evaluate the mixed expression correctly by applying standard arithmetic rules such as the order of operations. Given Data / Assumptions: - "#" means subtraction (minus). - "&" means division. - "@" means addition (plus). - "%" means multiplication. - The coded expression is 132 & 3 # 10 @ 20 % 2. - After decoding, normal arithmetic precedence rules apply: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: The key idea is to convert the coded expression into a normal arithmetic expression using the given mappings. Once that is done, you simply follow the usual BODMAS or PEMDAS rules. It is important not to mix up the printed symbol with its actual meaning. For example, "&" looks unfamiliar in arithmetic, but here it clearly stands for division. Only after complete decoding should you start numerical calculations. Step-by-Step Solution: Step 1: Write the coded expression clearly: 132 & 3 # 10 @ 20 % 2. Step 2: Replace each code with its real operation using the mapping. Step 3: "&" becomes division, "#" becomes subtraction, "@" becomes addition, "%" becomes multiplication. Step 4: The decoded expression is 132 ÷ 3 - 10 + 20 * 2. Step 5: Apply precedence. First evaluate division and multiplication: 132 ÷ 3 = 44, and 20 * 2 = 40. Step 6: Now evaluate the remaining operations left to right: 44 - 10 + 40 = 34 + 40 = 74. Verification / Alternative check: We can quickly confirm each step. The mapping is clearly stated in the question, so there is no ambiguity in decoding the symbols. Recomputing 132 ÷ 3 gives 44, and 20 * 2 gives 40. Subtracting 10 from 44 results in 34, and adding 40 leads to 74. No other interpretation of the mapping produces a simpler or more consistent result, so the answer 74 is firmly supported by the data. Why Other Options Are Wrong: - Option 91 would result from incorrect arithmetic, for example by adding instead of subtracting 10 or ignoring precedence rules. - Option 69 might come from partial mistakes, such as incorrect intermediate results during subtraction or addition. - Option 76 could arise if one of the operations were mis-decoded or if a small calculation error was made when combining the numbers. Common Pitfalls: Common errors include carrying out the operations strictly from left to right without applying division and multiplication first or accidentally using the printed symbols with their usual meaning instead of the coded meaning given in the question. Another frequent mistake is to decode some operators correctly but forget to decode others, leading to a mixed and incorrect expression. Always rewrite the entire expression clearly in standard arithmetic form before calculating. Final Answer: After decoding the operators and evaluating the expression with proper precedence, the value of 132 & 3 # 10 @ 20 % 2 is 74.

Question 16

In a certain code language, the word "CUTE" is written as "9251" and the word "REST" is written as "4135". Using the same letter to digit code, how is the word "RESCUE" written?

Accepted Answer

Introduction / Context: This is a classic coding decoding question where each letter of the alphabet is represented by a specific digit. You are given the coded forms of two words and asked to find the code for a third related word. The challenge lies in identifying a consistent mapping between letters and digits and then using that mapping to encode the new word correctly. Given Data / Assumptions: - "CUTE" is coded as "9251". - "REST" is coded as "4135". - The required word is "RESCUE". - The same letter always has the same digit, and the same digit always represents the same letter within this code language. Concept / Approach: The approach is to align each letter of the given words with its corresponding digit position. Once we know which digit belongs to each letter, we can simply substitute letters of the new word with their matching digits. No mathematical operations are involved here; it is purely a matter of consistent letter digit substitution across all examples. Step-by-Step Solution: Step 1: From "CUTE" → "9251", assign letter to digit mapping by position. Step 2: C → 9, U → 2, T → 5, E → 1. Step 3: From "REST" → "4135", we get R → 4, E → 1, S → 3, T → 5. Step 4: Combine the information from both words to obtain the full mapping: R → 4, E → 1, S → 3, C → 9, U → 2, T → 5. Step 5: Now encode "RESCUE" letter by letter using this mapping. Step 6: R → 4, E → 1, S → 3, C → 9, U → 2, E → 1, so "RESCUE" is written as 413921. Verification / Alternative check: We can verify that this mapping is consistent by reconstructing the original codes. Plugging the mapping back into "CUTE" gives C(9) U(2) T(5) E(1) which forms "9251". For "REST", we get R(4) E(1) S(3) T(5) which forms "4135". Because the mapping reproduces both original codes perfectly, it is reliable. Therefore, applying the same mapping to "RESCUE" must give the correct encoded form 413921. Why Other Options Are Wrong: - Option 431291 changes the positions of digits and does not match the letter order in "RESCUE". - Option 423911 assigns wrong digits for one or more letters and breaks the established mapping. - Option 413912 swaps the final two digits, which would imply U and E share or swap codes, contradicting the consistent mapping deduced earlier. Common Pitfalls: A common mistake is to treat the numbers as if they must form a recognizable pattern or to try to perform arithmetic with them. In this kind of question, the digits simply stand for letters, and the only rule is consistency. Another error is to misalign positions or assume a digit can represent more than one letter, which is not allowed in this code language. Final Answer: Using the same letter digit mapping, the word "RESCUE" is written in code as 413921.

Question 17

If "A" means subtraction, "B" means division, "C" means addition and "D" means multiplication, then what is the value of 294 B 6 A 30 C 31 D 4 under this coded operation system?

Accepted Answer

Introduction / Context: This question again checks your skill in decoding symbolic arithmetic. The letters A, B, C, and D no longer stand for algebraic variables but instead represent familiar arithmetic operations. To find the correct value of the expression, you must first replace each letter with its real operation and then follow the standard order of operations to evaluate the resulting expression accurately. Given Data / Assumptions: - "A" means subtraction. - "B" means division. - "C" means addition. - "D" means multiplication. - Expression: 294 B 6 A 30 C 31 D 4. - Standard arithmetic precedence applies once the expression is decoded: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: The key strategy is to convert the coded expression into a standard arithmetic expression in one clean step. After decoding, you use the usual precedence rules. It helps to rewrite the entire expression in familiar symbols to avoid confusion. Mistakes usually happen when a student decodes some operators but continues to treat others as if they still have their usual algebraic meaning. Step-by-Step Solution: Step 1: Start with the coded form: 294 B 6 A 30 C 31 D 4. Step 2: Replace "B" with division, "A" with subtraction, "C" with addition, and "D" with multiplication. Step 3: The decoded expression becomes 294 ÷ 6 - 30 + 31 * 4. Step 4: Evaluate the division and multiplication first. Compute 294 ÷ 6 = 49. Step 5: Compute 31 * 4 = 124. Step 6: Now handle subtraction and addition from left to right: 49 - 30 + 124 = 19 + 124 = 143. Verification / Alternative check: Double check each arithmetic step. The division 294 ÷ 6 equals 49, and the product 31 * 4 equals 124. Then 49 - 30 is 19, and 19 + 124 is 143. All computations are straightforward and consistent. There is no other reasonable decoding of the letters A, B, C, and D, because their meanings are explicitly given in the question. Hence, 143 is the unique correct result for the decoded expression. Why Other Options Are Wrong: - Option 16 would only appear if almost every step was miscalculated or the wrong operations were applied. - Option 156 might arise if someone computed 294 ÷ 6 correctly but then added instead of subtracting 30, or misused the multiplication step for 31 and 4. - Option 163 could be produced by small arithmetic slips when combining the intermediate values or by ignoring the operator precedence and calculating strictly left to right. Common Pitfalls: The main pitfalls include forgetting that multiplication and division must be handled before addition and subtraction, and confusing the meanings of the coded letters. Another source of mistakes is doing the decoding and calculation simultaneously, which increases the chance of mixing operations. A safer method is to decode first, write the full expression with normal symbols, and only then perform the calculations carefully. Final Answer: Evaluating the decoded expression 294 ÷ 6 - 30 + 31 * 4 gives a final result of 143.

Question 18

If "S" denotes "multiplied by", "V" denotes "subtracted from", "M" denotes "added to" and "L" denotes "divided by", then what is the value of 12 V 3 M 441 L 21 S 8 when evaluated according to these meanings?

Accepted Answer

Introduction / Context: Here you are given an arithmetic expression in which the usual symbols are replaced by special letters. Each letter specifies a standard operation, but the appearance of the expression can easily confuse you if you do not decode it correctly. This type of problem tests your attention to the exact definition of each symbol and your ability to apply the normal order of operations once decoding is complete. Given Data / Assumptions: - "S" denotes multiplication. - "V" denotes subtraction. - "M" denotes addition. - "L" denotes division. - Expression: 12 V 3 M 441 L 21 S 8. - Once decoded, we use standard arithmetic precedence: division and multiplication first, then addition and subtraction from left to right. Concept / Approach: The method is similar to other coded arithmetic questions. First we translate the entire expression from symbolic language into a normal arithmetic expression. Then, using the usual precedence rules, we systematically evaluate it. It helps to rewrite the decoded expression on a separate line so that the risk of applying the wrong meaning to any letter is minimized. Step-by-Step Solution: Step 1: Start with the coded expression: 12 V 3 M 441 L 21 S 8. Step 2: Decode each symbol according to the given meanings: V → subtraction, M → addition, L → division, S → multiplication. Step 3: The decoded expression becomes 12 - 3 + 441 ÷ 21 * 8. Step 4: Evaluate the division and multiplication first. Compute 441 ÷ 21 = 21. Step 5: Next compute 21 * 8 = 168. Step 6: Now handle the subtraction and addition from left to right: first compute 12 - 3 = 9, then 9 + 168 = 177. Verification / Alternative check: Check the decoding carefully: each symbol has a single clear meaning in the statement. The calculations 441 ÷ 21 = 21 and 21 * 8 = 168 are straightforward. Then 12 - 3 gives 9, and 9 + 168 gives 177. No other sequence of operations, once the symbols are correctly decoded and the usual precedence is applied, will yield a different valid answer. Hence the result 177 is solid and consistent. Why Other Options Are Wrong: - Option 661 is far from the computed range and suggests that multiplication and division were handled incorrectly or that decoding was wrong. - Option -170 might arise if signs were mixed up or subtraction and addition were applied in the wrong order to an incorrect intermediate value. - Option 174 is close but still incorrect, showing how a small mistake like subtracting or adding 3 at the wrong stage can change the final result. Common Pitfalls: Many learners are tempted to evaluate the expression from left to right using the letter symbols as if they already represented normal arithmetic operations, without decoding them first. Another frequent mistake is to treat S and L as unfamiliar operations and forget that they stand for multiplication and division, which must be performed before addition and subtraction. Writing out the decoded expression clearly and then evaluating in steps greatly reduces these risks. Final Answer: After decoding all symbols and evaluating with proper precedence, the value of 12 V 3 M 441 L 21 S 8 is 177.

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