Data sufficiency (Problems on Ages): What is Teja's present age? Statements: A) Four years ago, Raju was as old as Teja is at present. B) Sita's present age is 2 times Raju's present age. C) The average of Teja's and Sita's present ages is 19 years. Choose the correct option about which statements are necessary and sufficient to determine Teja's age uniquely.
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AOnly statement C is sufficient
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BOnly statements A and C are sufficient
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CAll three statements A, B, and C are necessary to determine the answer
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DOnly statements A and B are sufficient
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EEven using all three statements, the answer cannot be determined
Answer
Correct Answer: All three statements A, B, and C are necessary to determine the answer
Explanation
Introduction:This is a data sufficiency question in ages. The goal is not to compute Teja's age directly from one equation, but to decide which statements provide enough independent information to solve for Teja uniquely. The safest strategy is to define variables for present ages and test each statement (or combination) to see whether it produces a unique value for Teja.
Given Data / Assumptions:
- Let Teja's present age = T
- Let Raju's present age = R
- Let Sita's present age = S
- A: Four years ago, Raju was as old as Teja is now
- B: S = 2R
- C: (T + S) / 2 = 19
Concept / Approach:Translate each statement into equations and check if T can be uniquely determined. If not, add more statements until T becomes uniquely solvable.
Step-by-Step Solution:From A: R - 4 = T, so R = T + 4From B: S = 2RFrom C: (T + S) / 2 = 19 => T + S = 38Use A and B and C together:R = T + 4 => S = 2(T + 4) = 2T + 8T + S = 38 => T + (2T + 8) = 383T = 30 => T = 10 (unique)
Verification / Alternative check:Now test sufficiency of smaller sets: A + C gives R = T + 4 and T + S = 38, but no link between R and S, so infinite solutions. B + C gives S = 2R and T + S = 38, but no link between T and R, so infinite solutions. A + B gives R = T + 4 and S = 2R, but no numeric total, so not unique. Hence all three are required.
Why Other Options Are Wrong:“Only C”: gives T + S = 38 but cannot separate T.“A and C only”: still leaves S unknown.“A and B only”: gives relations but no fixed number.“Cannot be determined”: false because A+B+C gives T = 10 uniquely.
Common Pitfalls:Assuming an average equation alone can give Teja's age.Forgetting that data sufficiency asks about necessity, not just calculation.Not testing smaller combinations before concluding.
Final Answer:All three statements A, B, and C are necessary to determine the answer