Ages (sum shift comparison): The sum of A and B is 12 more than the sum of B and C. How many years younger is C than A?
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A10
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B12
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C24
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DData inadequate
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E8
Answer
Correct Answer: 12
Explanation
Introduction / Context:Comparing two sums that share one common term is a quick route to a direct difference between the other two terms. No time-shift is involved; it is a pure algebraic rearrangement task.
Given Data / Assumptions:A + B = (B + C) + 12.
Concept / Approach:Cancel the common B from both sides to isolate A and C. The resulting equation immediately reveals how much older A is than C.
Step-by-Step Solution:
A + B = B + C + 12 ⇒ A = C + 12. Therefore, C is 12 years younger than A.Verification / Alternative check:Pick any C and add 12 to obtain A; then sums differ by 12 for all values of B, confirming generality.
Why Other Options Are Wrong:10 and 24 contradict the derived identity; “Data inadequate” is incorrect because the relation uniquely fixes the difference A − C.
Common Pitfalls:Forgetting to cancel B or overcomplicating with unnecessary assumptions about actual ages.
Final Answer:12