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Data Sufficient Geometry Question - advice to tackle

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by Orla M » Sat Feb 16, 2013 5:45 am
Am seeking your help with the following, thanks!

I am given two parallel lines as in the image I have attached. PS being parallel to QR. The question asks whether the line segment PQ is smaller in length than the line segment SR. Two angles are given and I see that y is also at angle PSR by deduction. The given statements are:

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

Answer is A. Just not sure how to get there.

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Source: — Data Sufficiency |
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by pemdas » Sat Feb 16, 2013 7:28 am
Orla M wrote:Am seeking your help with the following, thanks!

I am given two parallel lines as in the image I have attached. PS being parallel to QR. The question asks whether the line segment PQ is smaller in length than the line segment SR. Two angles are given and I see that y is also at angle PSR by deduction. The given statements are:

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

Answer is A. Just not sure how to get there.

Image
what's the source of this q.. The answer isn't A here. The angle x may be greater than angle y and we may end with different lengths of PQ.
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by Orla M » Sat Feb 16, 2013 8:18 am
It's one of the GMAC practice tests. Here is camera shot showing that Answer A is the correct answer - solution 1 being sufficient.


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by pemdas » Sat Feb 16, 2013 8:26 am
nice, you have a constraint here that x<90. Then answer is A. You missed some info interpreting q.
Orla M wrote:It's one of the GMAC practice tests. Here is camera shot showing that Answer A is the correct answer - solution 1 being sufficient.


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by Orla M » Sat Feb 16, 2013 8:41 am
OK,

So the logic would be that if both angles are less than 90 and we are given info that x>y, then we can determine that the line segment PQ is shorter than SR. However, if we only have info in answer B that basically tells us what both add up to but not which angle is greater among the two, it's impossible to tell if one is smaller than the other?

Would appreciate your explanation on this.

Thanks.
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by pemdas » Sat Feb 16, 2013 9:28 am
yes your logic is sound. One angle, x, is greater than another angle y to tell us that PQ has less inclination and less length than the other line segment. To help your thinking, imagine PQ as geometrically posed line segment in right triangle being a hypotenuse or placed on the space and starting from one point to reach another point, the line segment with an angle (inclination) set at the horizontal base.
Orla M wrote:OK,

So the logic would be that if both angles are less than 90 and we are given info that x>y, then we can determine that the line segment PQ is shorter than SR. However, if we only have info in answer B that basically tells us what both add up to but not which angle is greater among the two, it's impossible to tell if one is smaller than the other?

Would appreciate your explanation on this.

Thanks.
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by GMATGuruNY » Sat Feb 16, 2013 11:54 am
Image

Statement 1: x>y
EXAGGERATE the difference between x and y:
Image
The figure above shows that PQ<SR.
SUFFICIENT.

Statement 2: x+y>90
If x>y, then PQ<SR, as shown in the figure above.
If x<y, then PQ>SR:
Image
INSUFFICIENT.

The correct answer is A.
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