Problem Solving

[Math Revolution GMAT math practice question]

If 0 < x < 2 and 0 < y < 2 on the xy-plane, what is the probability that x+y < 1?

A. 1/2
B. 1/4
C. 1/6
D. 1/8
E. 1/10

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If a point (x,y) is randomly chosen in the region 0 < x < 2 and 0 < y < 2 of the xy-plane, what is the probability that x+y < 1?

A. 1/2
B. 1/4
C. 1/6
D. 1/8
E. 1/10

$$? = {{{S_{\Delta OAB}}} \over {{S_{{\rm{square}}}}}}\,\,\,\,\,\,\,\left( {{\rm{geometric}}\,\,{\rm{probability}}} \right)$$
$$A = \left( {0,1} \right)\,\,,\,\,B = \left( {1,0} \right)$$
$$? = {{\,\,{{1 \cdot 1} \over 2}\,\,} \over {2 \cdot 2}} = {1 \over 8}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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The outside square contains all points satisfying 0 < x < 2 and 0 < y < 2.
The shaded region consists of all points satisfying 0 < x < 2 and 0 < y < 2 such that x + y < 1. Its area is 1/2, and the area of the outside square is 4.
Thus, the required probability is (1/2) / 4 = 1/8.

Therefore, the answer is D.
Answer: D