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Which is greater x or 90
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17 Apr 2023, 10:19
17 Apr 2023, 10:19
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Question Stats:
45% (01:44) correct
54% (00:50) wrong based on 11 sessions
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GRE center of the circle.jpg [ 17.93 KiB | Viewed 1865 times ]
O is the center of the circle
Quantity A |
Quantity B |
x |
90 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: Which is greater x or 90
[#permalink]
22 Apr 2023, 04:00
22 Apr 2023, 04:00
Expert Reply
OE
Use Quantity B as a benchmark by trying to make x equal to 90. That is, try to prove (C). If it doesn’t work, you’ll have your answer. Mark the angle as 90 degrees and use the Pythagorean Theorem to find the hypotenuse, using the two legs of 2:
\(2^2+2^2=c^2\)
\(C=2 \sqrt{2}\)
However, you know that the “hypotenuse” (the long side) is actually 3, not 2.8. The bigger the long side is, the larger angle x is going to be (picture how the triangle opens as x increases). If angle x were 90 degrees, the hypotenuse would be about 2.8. However, long side that looks like a hypotenuse is actually 3, so angle x must be greater than 90 degrees. The answer is (A).
Use Quantity B as a benchmark by trying to make x equal to 90. That is, try to prove (C). If it doesn’t work, you’ll have your answer. Mark the angle as 90 degrees and use the Pythagorean Theorem to find the hypotenuse, using the two legs of 2:
\(2^2+2^2=c^2\)
\(C=2 \sqrt{2}\)
However, you know that the “hypotenuse” (the long side) is actually 3, not 2.8. The bigger the long side is, the larger angle x is going to be (picture how the triangle opens as x increases). If angle x were 90 degrees, the hypotenuse would be about 2.8. However, long side that looks like a hypotenuse is actually 3, so angle x must be greater than 90 degrees. The answer is (A).
gmatclubot
Re: Which is greater x or 90 [#permalink]
22 Apr 2023, 04:00
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