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01 Feb 2020, 19:29
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D
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42% (02:41) correct
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based on 92
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GMATBusters’ Quant Quiz Question -5
For questions from previous quizzes click here
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
Attachment:
Q.JPG [ 29.54 KiB | Viewed 7227 times ]
01 Feb 2020, 19:32
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The Official Solution is as follows:
WhatsApp Image 2020-02-03 at 6.49.55 PM (4).jpeg [ 75.87 KiB | Viewed 7065 times ]
Attachment:
WhatsApp Image 2020-02-03 at 6.49.55 PM (4).jpeg [ 75.87 KiB | Viewed 7065 times ]
01 Feb 2020, 20:54
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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
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
