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# In the figure above, QX = 10 and PQ = 6, what is the length of QY?

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Joined: 27 Oct 2017
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In the figure above, QX = 10 and PQ = 6, what is the length of QY?  [#permalink]

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01 Feb 2020, 18:29
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Question Stats:

52% (02:55) correct 48% (02:33) wrong based on 25 sessions

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GMATBusters’ Quant Quiz Question -5

In the figure above, QX = 10 and PQ = 6, what is the length of QY?
1) Angle QPY = 90 deg
2) Length of XZ = 100/6

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Q.JPG [ 29.54 KiB | Viewed 410 times ]

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WE: General Management (Education)
Re: In the figure above, QX = 10 and PQ = 6, what is the length of QY?  [#permalink]

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01 Feb 2020, 18:32
The Official Solution is as follows:

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WhatsApp Image 2020-02-03 at 6.49.55 PM (4).jpeg [ 75.87 KiB | Viewed 238 times ]

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Re: In the figure above, QX = 10 and PQ = 6, what is the length of QY?  [#permalink]

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01 Feb 2020, 19:54
1) Since Angle QPY = 90 deg, by the Pythagorean theorem, PX=sqr(10^2-6^2)=8. We also know that the altitude of the right triangle XYQ, PQ, can be calculated with the following formula: PQ^2=PY*PX. From here we can calculate PY since we already know the values of PQ and PX. Likewise, QY can also be determined by using the Pythagorean theorem in the right triangle PQY as the values of PQ and PY are known.
Clearly, this statement is sufficient.
2) Using the Pythagorean theorem, we can determine the value of QZ in the right triangle XQZ. Then, based on the same logic as explained in the case above, the altitude of right triangle XYZ, XQ, follows the formula: XQ^2=QZ*YQ. From here YQ can be also calculated.
Clearly, this statement is sufficient.
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Re: In the figure above, QX = 10 and PQ = 6, what is the length of QY?  [#permalink]

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01 Feb 2020, 21:09
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Re: In the figure above, QX = 10 and PQ = 6, what is the length of QY?  [#permalink]

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01 Feb 2020, 23:26
Statement 1: angle QPY = 90

let PY=k, QY=x; Since: angle QPY = 90,

XP = 8 (pythagoras theorem)
Since PQY is also a right angles triangle: 6^2 + PY^2 = OY^2 => 36+k^2 = x^2
Since XQY is also a right angled triangle: XQ^2 + QY^2 = XY^2 => 100+ x^2 = (8+k)^2

So 2 equations, 2 variables, implying statement 1 is sufficient.

Statement 2: Length of XZ = 100/6
Nothing can be deduced about QY so statement is Insufficient.

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Re: In the figure above, QX = 10 and PQ = 6, what is the length of QY?  [#permalink]

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02 Feb 2020, 00:59
#1
Angle QPY = 90 deg
so for ∆ XPQ ; XP = 8 ; 3:4:5
but PY not know ; insufficient
#2
Length of XZ = 100/6
∆ XQZ value can be determined ; sides QZ ; ∆ XYQ is similar so area / side ^2 ; we can determine the side YQ
sufficient
IMO B

In the figure above, QX = 10 and PQ = 6, what is the length of QY?
1) Angle QPY = 90 deg
2) Length of XZ = 100/6
Re: In the figure above, QX = 10 and PQ = 6, what is the length of QY?   [#permalink] 02 Feb 2020, 00:59