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Sub 505 (Easy)|   Geometry|      
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Bunuel
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Segment PR is divided into two segments with lengths as shown above. 12 Jul 2017, 01:43
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94% (00:47) correct 6% (01:34) wrong based on 68 sessions

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Segment PR is divided into two segments with lengths as shown above. If Q is the midpoint of PR, which of the following statements must be true?

(A) 0
(B) x = y/2
(C) x = 2y/3
(D) x = y
(E) x = 2y

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2017-07-12_1242.png
2017-07-12_1242.png [ 4.15 KiB | Viewed 2607 times ]
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E
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Segment PR is divided into two segments with lengths as shown above. 12 Jul 2017, 01:51
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Bunuel

Segment PR is divided into two segments with lengths as shown above. If Q is the midpoint of PR, which of the following statements must be true?

(A) 0
(B) x = y/2
(C) x = 2y/3
(D) x = y
(E) x = 2y

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2017-07-12_1242.png
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x+y = 2x-y
=> 2y=x

Answer E
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Segment PR is divided into two segments with lengths as shown above. 15 Jul 2017, 22:49
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I assigned values for x and y. let x =2 and y=3 also since Q is the midpoint PQ+QR=PR therefore 3x=PR
PR=3*2=6 Only for option E the values hold good . So the correct answer is E
Hope this method helps
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Segment PR is divided into two segments with lengths as shown above. 15 Jul 2017, 23:36
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longhaul123
I assigned values for x and y. let x =2 and y=3 also since Q is the midpoint PQ+QR=PR therefore 3x=PR
PR=3*2=6 Only for option E the values hold good . So the correct answer is E
Hope this method helps
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Hi,

Will not be correct to give values to x and y when you are finding relation between x and y..
If you are taking x=2 n y=3.... PQ=x+y=2+3=5 and QR=2x-y=2*2-3=1..
Thus Q does not turn out to be the midpoint of PR..

Simple Q should be dealt straight and in a simple manner ONLY.
If Q is midpoint, \(x+y=2x-y.....2x-x=y+y.....X=2y\)

Or

Substitute the values given in choices to see if two segments are same in TERMS of one variable.

But straight is better..

E
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Segment PR is divided into two segments with lengths as shown above. 17 Jul 2017, 10:22
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Bunuel

Segment PR is divided into two segments with lengths as shown above. If Q is the midpoint of PR, which of the following statements must be true?

(A) 0
(B) x = y/2
(C) x = 2y/3
(D) x = y
(E) x = 2y

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2017-07-12_1242.png
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ANSWER:
=====

Since Q is the midpoint of PR.
It is clear that PQ=QR.
Hence, x+y=2x-y
2x-x=y+y
x=2y.

Which is option number E.

Hence, the answer is E
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Segment PR is divided into two segments with lengths as shown above. 20 Nov 2018, 08:36
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