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Data Sufficiency - Drawing a square with a point on a side

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

This is a medium 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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Rahim plans to draw a square JKLM with point O on the side JK but is not successful. Why is Rahim unable to draw the square?

A: The length of OM is twice that of OL. B: The length of OM is 4 cm.

  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 point O on side JK of square JKLM, maximum possible ratio of OMOL\frac{OM}{OL} occurs when O is at K, giving OKOL=2<2\frac{OK}{OL} = \sqrt{2} < 2. Thus OMOM can never be twice OLOL. Statement A alone explains why it's impossible.

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