Triangles - GMATPrep Test 1

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Triangles - GMATPrep Test 1

by kwah » Wed Feb 22, 2012 6:01 pm
I have attached a question from GMATPrep Test.

Answer: C

I got the right answer however, would appreciate if someone can explain steps to figure out the answer.

I understand that 1) and 2) are telling us the triangles are equilateral. However, how does this give us 'x' degrees?

Help is appreciated,
K
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by Anurag@Gurome » Wed Feb 22, 2012 7:14 pm
kwah wrote:I have attached a question from GMATPrep Test.

Answer: C

I got the right answer however, would appreciate if someone can explain steps to figure out the answer.

I understand that 1) and 2) are telling us the triangles are equilateral. However, how does this give us 'x' degrees?

Help is appreciated,
K

Note that the measure of angle x depends upon the position of points Q, S and U only. Unless we don't know the fixed positions of these three points, we cannot uniquely determine the measure of angle x.

Statement 1: QR = RS
Thus position of Q and S is fixed. But U can be any point on PT and accordingly value of x will be different; NOT sufficient.

Statement 2: ST = TU
Thus position of S and U is fixed. But Q can be any point on PR and accordingly value of x will be different; NOT sufficient.

Combining (1) and (2), the three points are fixed. Let's see whether we can find x. Refer to the image below.

Image

On point S, the sum of the three angles must be equal to 180°.
Thus, (x + y + z) = 180° ...Equation 1

angle PQS = (180° - angle RQS) = (180° - z)
angle PUS = (180° - angle TUS) = (180° - y)

Now in quadrilateral PQSU,

Sum of all the internal angles = 360°
=> [x + 90° + (180° - y) + (180° - z)] = 360°
=> (x - y - z + 90°) = 0 ...Equation 2

Adding equations 1 and 2, we get (2x + 90°) = 180° => x = 45°; SUFFICIENT.

The correct answer is C.
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by [email protected] » Sun Mar 18, 2012 7:20 am
I did it in a different way but got the same answer as x = 45 degrees...

I proved the two triangles RQS and SQT similar... wait let me give you a detailed explanation...

From the given diagram it can be proved that the two triangles are similar. (By AA test of similarity)

Therefore it is a 45-45-90 triangle. from that i get the same value of z and y as 67.5

that is 2z = 180 - 45 = 67.5 and same for y i.e 67.5

also x = 45 i.e 180 - 135 = 45...


Hope this explanation really helped...
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by mcdesty » Thu Jul 10, 2014 9:48 am
See Image for alternative approach with two variables.
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