In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?
(1) y = x+ 3
(2) x = 2
OA: A
Hi, Experts! Please share the solution to this problem. Thank you.
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OG2015 DS In triangle PQR, if
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lionsshare
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Jay@ManhattanReview
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An important property of a triangle:lionsshare wrote:In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?
(1) y = x+ 3
(2) x = 2
OA: A
Hi, Experts! Please share the solution to this problem. Thank you.
The shortest side is opposite the smallest angle and the longest side is opposite the largest angle.
Statement 1: y = x+ 3
=> PR = x + 3 is the longest side, hence the angle PQR opposite of side PR is greatest. Sufficient.
Statement 2: x = 2
=> PQ = x = 2 and QR = x + 2 = 4
The value of PR = y is indeterminable. So, we cannot determine which side is the longest QR or PR, thus the determination of the greatest angle is not possible. Not sufficient.
The correct answer: A
Hope this helps!
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ceilidh.erickson
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We know that the 3 side lengths are x, x + 2, and y. We also know that in any triangle, the greatest angle will be across from the longest side. Therefore, we can rephrase our question this way:lionsshare wrote:In triangle PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of triangle PQR has the greatest degree measure?
(1) y = x+ 3
(2) x = 2
OA: A
Hi, Experts! Please share the solution to this problem. Thank you.
Which is longest: x, x + 2, or y?
Since x + 2 is obviously longer than x, we can ignore that side. Rephrase again: which is longer, x + 2 or y? We can turn this into a yes/no question to write it as an inequality:
Target question: x + 2 > y ?
(1) y = x+ 3
If y = x + 3, we have a definitive answer to our target question: x + 2 is NOT greater than y. Therefore, y must be the longest side.
Sufficient.
(2) x = 2
This only gives information about x, not y. It cannot answer the target question.
Insufficient.
The answer is A.
NB: this question is one that we would classify as a C-trap - if we put the 2 statements together, we very obviously get all the values we need, but we didn't do any conceptual work. If you recognize that happening, the answer is probably not C. More here:
https://www.beatthegmat.com/og-13-156-t ... tml#766502
https://www.manhattanprep.com/gmat/blog ... fficiency/
https://www.manhattanprep.com/gmat/blog ... ncy-traps/
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
