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16 Jun 2022, 19:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
39% (01:23) correct
61%
(02:10)
wrong
based on 31
sessions
History
Date
Time
Result
Not Attempted Yet
What is the perimeter of the triangle OPQ?
(1) The area of triangle OPQ is 50.
(2) OQ = 20
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
18 Jun 2022, 12:27
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Bunuel
Breaking Down the Info:
Note point P is "adjustable"; there are many triangles we can draw that have two right angles and a height of 5.
Statement 1 Alone:
This tells us the base OQ is 20. Recall we need angle P to be a right angle. Intuitively, if you put the height (5) right in the middle of OQ, we will have an obtuse angle for P instead of a right angle, so you might see by moving the height around, there are only two symmetric cases where we have a right angle for P. Hence there is only one dimension where we have everything set up correctly. Sufficient.
To go more in-depth, set PH = 5 as the height. and set OH = x. We may write \(OP = \sqrt{x^2+25}\) from Pythagorean theorem on triangle OHP. Then from similar triangles, we have \(\frac{OH}{OP} = \frac{OP}{OQ}\), which is \(20x = x^2 + 25\).
The -20 on the b constant tells us solving this gives two solutions that add up to 20, hence the solutions are x and 20-x, so we'll get two solutions that give effectively the same triangle.
Statement 2 Alone:
This is the same as above. Sufficient.
Answer: D
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