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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42
GPA: 3.82
If 0<x<2 and 0<y<2 on the xy-plane, what is the probability that x+y<1  [#permalink]

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24 Dec 2018, 01:03
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Difficulty:

85% (hard)

Question Stats:

23% (01:26) correct 77% (01:33) wrong based on 50 sessions

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[Math Revolution GMAT math practice question]

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

$$A. \frac{1}{2}$$
$$B. \frac{1}{4}$$
$$C. \frac{1}{6}$$
$$D. \frac{1}{8}$$
$$E. \frac{1}{10}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 937 Re: If 0<x<2 and 0<y<2 on the xy-plane, what is the probability that x+y<1 [#permalink] ### Show Tags 24 Dec 2018, 02:39 1 MathRevolution wrote: [Math Revolution GMAT math practice question] If a point (x,y) is ramdomly chosen in the region $$0<x<2$$ and $$0<y<2$$ of the $$xy$$-plane, what is the probability that $$x+y<1$$? $$A. \frac{1}{2}$$ $$B. \frac{1}{4}$$ $$C. \frac{1}{6}$$ $$D. \frac{1}{8}$$ $$E. \frac{1}{10}$$ $$? = {{{S_{\Delta OAB}}} \over {{S_{{\rm{square}}}}}}\,\,\,\,\,\,\,\left( {{\rm{geometric}}\,\,{\rm{probability}}} \right)$$ $$A = \left( {0,1} \right)\,\,,\,\,B = \left( {1,0} \right)$$ $$? = {{\,\,{{1 \cdot 1} \over 2}\,\,} \over {2 \cdot 2}} = {1 \over 8}$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Manager Joined: 15 Aug 2018 Posts: 51 GMAT 1: 740 Q47 V45 GPA: 3.5 Re: If 0<x<2 and 0<y<2 on the xy-plane, what is the probability that x+y<1 [#permalink] ### Show Tags 24 Dec 2018, 03:32 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$0<x<2$$ and $$0<y<2$$ on the $$xy$$-plane, what is the probability that $$x+y<1$$? $$A. \frac{1}{2}$$ $$B. \frac{1}{4}$$ $$C. \frac{1}{6}$$ $$D. \frac{1}{8}$$ $$E. \frac{1}{10}$$ Hey MathRevolution guys i LOVE your out of the box questions and approaches! I am more than curious about why this must be 1/8 and not 1/4... please enlighten me! Best, gota900 _________________ A kudo a day... Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 0<x<2 and 0<y<2 on the xy-plane, what is the probability that x+y<1 [#permalink] ### Show Tags 26 Dec 2018, 01:45 => Attachment: 12.26.png [ 5.03 KiB | Viewed 298 times ] 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 $$\frac{1}{2}$$, and the area of the outside square is $$4$$. Thus, the required probability is $$(\frac{1}{2}) / 4 = \frac{1}{8}.$$ Therefore, the answer is D. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If 0<x<2 and 0<y<2 on the xy-plane, what is the probability that x+y<1   [#permalink] 26 Dec 2018, 01:45
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