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705-805 (Hard)|   Inequalities|   Number Properties|   Roots|         
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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 18 Dec 2023, 07:00
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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


 


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for the 12 Days of Christmas Competition

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B
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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 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.
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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 18 Dec 2023, 07:24
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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


 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 18 Dec 2023, 07:59
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−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.
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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 18 Dec 2023, 13:45
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Bunuel
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


 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 

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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
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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 19 Dec 2023, 13:07
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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...

Bunuel

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.
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Bunuel
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12 Days of Christmas GMAT Competition - Day 6: If -9 < m < -4 and 7 < 19 Dec 2023, 13:53
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Archit3110
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...

Bunuel

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.

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For \(\sqrt[4]{-mn}\) 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 < 04 Jan 2026, 01:07
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