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If -8＜x＜-6 and 2＜y＜3, which of the following could b

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by Max@Math Revolution » Fri Jan 19, 2018 12:14 am
[GMAT math practice question]

If -8＜x＜-6 and 2＜y＜3, which of the following could be the value of $$\sqrt{\left(-xy\right)}$$ ?

A. 3
B. 4
C. 5
D. 6
E. 7
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by DrMaths » Fri Jan 19, 2018 12:23 am
Upper bound (biggest possibility) < SQRT(8 * 3) = SQRT(24) < 5
Lower bound (smallest possibility) > SQRT(6*2) = SQRT(12) > 3

Hence the answer is B. 4
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by GMATGuruNY » Fri Jan 19, 2018 4:38 am
Max@Math Revolution wrote:[GMAT math practice question]

If -8＜x＜-6 and 2＜y＜3, which of the following could be the value of $$\sqrt{\left(-xy\right)}$$ ?

A. 3
B. 4
C. 5
D. 6
E. 7
The question stem indicates that √(-xy) could be equal to one of the five answer choices:
3, 4, 5, 6, 7.
Implication:
-xy could be equal to the SQUARE of one of the five answer choices:
9, 16, 25, 36, 49.

Multiplying -8 < x < 6 by -1 and flipping the inequality symbols, we get:
6 < -x < 8.

Resulting ranges:
6 < -x < 8
2 < y < 3.

Since -x > 6 and y > 2, -xy > 12.
Since -x < 8 and y < 3, -xy < 24.
Thus:
12 < -xy < 24.
Of the blue options above, only 16 -- option B -- is between 12 and 24.

The correct answer is B.
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EDIT

by Max@Math Revolution » Sun Jan 21, 2018 5:33 pm
=>

Multiplying -8 < x < -6 by -1 yields 6 < -x < 8. Since 2 < y < 3, it follows (by multiplication) that 12 < (-x)y < 24. Taking square roots (since all numbers are positive) yields √12 < √(-xy) < √24.
Since 3 < √12 and 5 > √24, 4 is one possible value of √(-xy).

Therefore, the answer is B.
Answer : B
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