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

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GMATBusters’ Quant Quiz Question -5

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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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Official Answer

D

GMATBusters · Answer

The Official Solution is as follows: https://gmatclub.com/forum/download/file.php?id=52761 WhatsApp Image 2020-02-03 at 6.49.55 PM (4).jpeg

AndreV · Answer

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.
Answer: D

ITGMAT · Answer

The answer is D. please see the explanation in attached document.

bM22 · Answer

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 .

Answer is A.

Archit3110 · Answer

#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

bumpbot · Answer

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