In the figure above, if x and y are each less than 90 and PS

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In the figure above, if \(x\) and \(y\) are less than \(90^0\) and \(PS \parallel QR\), is the length of the segment \(PQ\) less than the length of segment \(SR\)?

1) \(x > y\)
2) \(x+y > 90\)

OA A

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by Jay@ManhattanReview » Mon Mar 18, 2019 12:01 am

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In the figure above, if \(x\) and \(y\) are less than \(90^0\) and \(PS \parallel QR\), is the length of the segment \(PQ\) less than the length of segment \(SR\)?

1) \(x > y\)
2) \(x+y > 90\)

OA A
This can be solved with little imagination.

Let's take each statement one by one.

1) \(x > y\)

=> \(90 > x > y\)

Imagine x = 75 and y = 30; you would observe that PQ << SR. Even if x and y are close to each other, ensuring that x > y, we have PQ < SR. The answer is yes. Sufficient.

2) \(x+y > 90\)

Clearly insufficient. So, we have all the possible three cases: (1) x = y = 45. (2) x > y and (3) x < y. no unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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