If arc PQR above is a semicircle, what is the length of diameter PR?
(1) a = 4
(2) b = 1
Please refer to page 288 for the diagram. I would like to know why in the explanation they say that PQ + QR is basically the same length as a + b. The substitution used in the explanation is confusing.
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OG 12 Data Sufficiency 173 (Hard as Hell)
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bynddrvn
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Some of the Official Guide solutions are not very clear. Question #173 for the 12th edition was question #152 in the 11th edition. I found this video on youtube, and I think it is a much clearer explanation for this problem.
https://www.youtube.com/watch?v=dmN_s286dHc
https://www.youtube.com/watch?v=dmN_s286dHc
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edvhou812
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Ha. I got this one right. 
By looking at both options, I was able to see that there is enough information to determine the size of the inscribed triangles. Although I have neglected the study of chords and segments for circles, I deducted that if we know the size of all of sides of any of the triangles, we must know the size of PQ and QR which means we must have enough information to find the size of PR/diameter.
1) a=4. Gives enough information to determine the size of the larger triangle that includes points P and Q (Sufficient)
2) b=1. Gives enough information to determine the size of the smaller triangle that includes points Q and R. (Sufficient)
Answer: D
By looking at both options, I was able to see that there is enough information to determine the size of the inscribed triangles. Although I have neglected the study of chords and segments for circles, I deducted that if we know the size of all of sides of any of the triangles, we must know the size of PQ and QR which means we must have enough information to find the size of PR/diameter. 1) a=4. Gives enough information to determine the size of the larger triangle that includes points P and Q (Sufficient)
2) b=1. Gives enough information to determine the size of the smaller triangle that includes points Q and R. (Sufficient)
Answer: D
I don't know what to say, really. Three minutes to the biggest battle of our professional lives. You find out life's this game of inches, so is football. Because in either game - life or football - the margin for error is so small. I mean, one half a step too late or too early and you don't quite make it. One half second too slow, too fast and you don't quite catch it. I'll tell you this, in any fight it's the guy whose willing to die whose gonna win that inch. That's football guys, that's all it is. Now, what are you gonna do?
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GMATGuruNY
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I posted solutions to similar problems here:
https://www.beatthegmat.com/inscribed-tr ... 74152.html
https://www.beatthegmat.com/length-of-th ... 71979.html
https://www.beatthegmat.com/geo-question ... nta-14-649
https://www.beatthegmat.com/inscribed-tr ... 74152.html
https://www.beatthegmat.com/length-of-th ... 71979.html
https://www.beatthegmat.com/geo-question ... nta-14-649
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
