12 Days of Christmas GMAT Competition - Day 6: If -9

Question

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If  -9 < m < -4  and  7 < n < 11 , which of the following can be a value of  \sqrt {-mn} ?

I. 2
II. 3
III. 4

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Bunuel · Accepted Answer

GMAT Club Official Explanation:

If  -9 < m < -4  and  7 < n < 11 , which of the following can be a value of  \sqrt {-mn} ?

I. 2
II. 3
III. 4

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

mn must be more than -4*7 = -28 and less than -9*11 = -99:

-99 < mn < -28

Multiplying by -1 gives:

28 < -mn < 99

Taking the fourth root gives:

\sqrt {28} < \sqrt {-mn} < \sqrt {99}

Now, considering that  2^4 < 28 < 3^4 < 99 < 4^4 , it follows that  \sqrt {-mn}  can only be 3.

Answer: B.

VivekSri · Answer

Posted from my mobile device

sj296 · Answer

−9<m<−4 and 7<n<11

Range of mn = -99< mn< -28

Range of -mn = 28 < -mn < 99

only 81 which is 3^4 falls in this range.

OA should be B.

missionmba2025 · Answer

Lowest value = -9*11 = -99
Highest value = -7 * 4 = -28

-99 < mn < -28

28 < -mn < 99

2^4 = 16 ; not possible

3^4 = 81 ; possible

4^4 = 256; not possible

IMO B

Archit3110 · Answer

Hi  Bunuel 
Although i understood your explanation but my query is that in the question there is no restriction that value of square root has to be an integer.. so if rounded off we do get both 2 & 3 as values.. 
Shouldn't option D be correct in that case...

Posted from my mobile device

Bunuel · Answer

For  \sqrt {-mn}  to equal 2, mn would need to be -16, which isn't possible given that  -9 < m < -4  and  7 < n < 11 . Also, the question requires exact values, not approximations.

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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 <

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