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12 Jul 2017, 01:37
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E
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78% (02:14) correct
22%
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In the figure above, segment PT has length 36, Q is the midpoint of PR, R is the midpoint of QS, and S is the midpoint of QT. What is the length of segment QS?
(A) 7.2
(B) 12.2
(C) 12.4
(D) 14.2
(E) 14.4
Attachment:
2017-07-12_1235.png [ 3.49 KiB | Viewed 2878 times ]
Bunuel
In the figure above, segment PT has length 36, Q is the midpoint of PR, R is the midpoint of QS, and S is the midpoint of QT. What is the length of segment QS?
(A) 7.2
(B) 12.2
(C) 12.4
(D) 14.2
(E) 14.4
Attachment:
2017-07-12_1235.png
PQ = QR
QR = RS, and therefore
PQ = RS
Those are three segments of equal length. Call their length x. Distance between P to Q, from Q to R, and from R to S is x. Or PQ = QR = RS = x
Also by definition of midpoint, QS = ST
QS = (QR + RS) = (x + x) = 2x and
QS = ST, so
ST = QR + RS = 2x
To the left of point S, we have x + x + x (P -> Q -> R) = 3x
To the right of point S = ST, which from above is 2x.
3x + 2x = 5x
5x = 36
x = 7.2
From above, QS = 2x = 14.4
Answer E
12 Jul 2017, 05:22
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Bunuel
In the figure above, segment PT has length 36, Q is the midpoint of PR, R is the midpoint of QS, and S is the midpoint of QT. What is the length of segment QS?
(A) 7.2
(B) 12.2
(C) 12.4
(D) 14.2
(E) 14.4
Attachment:
2017-07-12_1235.png
It should be E.
If we can mark PQ = x, QR is also x, similarly, RS is also S, but ST becomes 2x. This may not be easy to comprehend initially but just drawing on paper and working your way through it should help you understand it fairly quickly.
5x = 36
x = 7.2
Since QS is 2 times x, it should be 14.4.
