find the value of OP

Geometry Level 1

one of the toughest questions from CAT 2012


The answer is 4.

Anand Shah by Anand Shah , 22, India

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2 solutions

Satvik Golechha
Mar 7, 2014

Can be solved by similarity in triangles MPR and NQR, and then adding 1 to both sides of equation 3/7 = PR/OP.

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Krishna Garg
Mar 11, 2014

Since OQ is bisecting rectangle, angle MOP=45 degree,,OR given is 40/7 = 5.7 angle OMP will be also 45 degree and angle OMR will be 75 degree(line MP is parallel toQN. ( angle PMR =30 degree Thus PR will be 1/3 rd of OR that is 5.7 divided by 1/3 or 1.9 Therefore length of OP is 5.7-1.9 approx 4 ( integer) Ans

K.K.GARG.India

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