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In the figure above, what is the length of PQ times the leng

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by BTGmoderatorDC » Fri Sep 13, 2019 5:18 pm

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Answers

A

B

C

D

E

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Difficulty—

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In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.

OA B

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by GMATGuruNY » Sat Sep 14, 2019 2:57 am
Image

Any side of a triangle may be considered the base.
Each base has a corresponding height.
To draw the height that corresponds to a given base, start at the vertex opposite the base and draw a line segment that forms a right angle with the base.

In the triangle above:
RS is the height that corresponds to base PQ.
QR is the height that corresponds to base PR.

For any triangle, area = (bh)/2.
The area must remain constant no matter which base and corresponding height are used.
Thus, in the figure above:
(PQ*RS)/2 = (PR*QR)/2
PQ*RS = PR*QR
In the figure above, what is the length of PQ times the length of RS?

(1) The length of PQ is 5.
(2) The length of QR times the length of PR is equal to 12.
Statement 1:
Since the length of RS can be any nonnegative value, INSUFFICIENT.

Statement 2:
Thus, PQ*RS = QR*PR = 12.
SUFFICIENT.

The correct answer is B.
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