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18 Dec 2023, 07:00
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B
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Difficulty:
95%
(hard)
Question Stats:
55% (02:20) correct
45%
(02:27)
wrong
based on 428
sessions
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Not Attempted Yet
12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
If \(-9 < m < -4\) and \(7 < n < 11\), which of the following can be a value of \(\sqrt[4]{-mn}\)?
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
If \(-9 < m < -4\) and \(7 < n < 11\), which of the following can be a value of \(\sqrt[4]{-mn}\)?
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
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19 Dec 2023, 09:12
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GMAT Club Official Explanation:
If \(-9 < m < -4\) and \(7 < n < 11\), which of the following can be a value of \(\sqrt[4]{-mn}\)?
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:
- \(\sqrt[4]{28} < \sqrt[4]{-mn} < \sqrt[4]{99}\)
Now, considering that \(2^4 < 28 < 3^4 < 99 < 4^4\), it follows that \(\sqrt[4]{-mn}\) can only be 3.
Answer: B.
General Discussion
18 Dec 2023, 07:24
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Bunuel
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