Data Sufficiency - Top academic performers in school

CAT 2007 Slot 1 · DILR · Easy · Data Sufficiency

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In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?

A. Sixty per cent of the top academic performers were not athletes. B. All the top academic performers were not necessarily athletes.

  1. A.

    Statement A alone is sufficient but statement B alone is not sufficient

  2. B.

    Statement B alone is sufficient but statement A alone is not sufficient

  3. C.

    Either statement alone is sufficient

  4. D.

    Both statements together are sufficient but neither alone is sufficient

  5. E.

    Statements A and B together are not sufficient

Answer

A

Explanation

Let TT be total top academic performers. 1010 are athletes, so T−10T - 10 are not athletes. Statement A says 60%60\% of TT were not athletes   ⟹  0.60T=T−10  ⟹  0.40T=10  ⟹  T=25\implies 0.60 T = T - 10 \implies 0.40 T = 10 \implies T = 25. Sufficient. Statement B gives no numeric information. A alone is sufficient.

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