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The answer is D. please see the explanation in attached document.
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File comment: Geometry problem solution- quiz 2nd Feb 20
Solution-Geometry problem.jpg
Solution-Geometry problem.jpg [ 583.74 KiB | Viewed 7100 times ]

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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.
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#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
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Hello from the GMAT Club BumpBot!

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