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Data Sufficiency - Minimum value of sum of squares

CAT 2007 Slot 1 · Quantitative Ability · Easy · Data Sufficiency

This is an easy Quantitative Ability question from the CAT 2007 Slot 1 paper. It tests Data Sufficiency. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Consider integers x,y,zx, y, z. What is the minimum possible value of x2+y2+z2x^2 + y^2 + z^2?

A: x+y+z=89x + y + z = 89. B: Among x,y,zx, y, z two are equal.

  1. A.

    Question can be answered using A alone but not using B alone

  2. B.

    Question can be answered using B alone but not using A alone

  3. C.

    Question can be answered using A and B together, but not using either A or B alone

  4. D.

    Question cannot be answered even using A and B together

Answer

A

Explanation

For a fixed sum x+y+z=89x + y + z = 89, x2+y2+z2x^2 + y^2 + z^2 is minimized when x,y,zx, y, z are as close to each other as possible, i.e., 30, 30, 29. Statement A alone is sufficient. Statement B alone gives no constraint on the sum.

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