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31 Dec 2023, 06:48
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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
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
31 Dec 2023, 06:48
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Official Solution:
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 less than \(-4*7 = -28\) and more 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
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 less than \(-4*7 = -28\) and more 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
31 Jan 2024, 02:47
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Bunuel
This is what i donot understand.
You say that mn must be more than −4∗7=−28, meaning mn >-28 or -28<mn
and that mn must be less than −9∗11=−99, meaning mn<-99 or -99>mn.
Then you go on and say: −99<mn<−28. How is this possible?
How can we go from mn>-28 to mn<-28 and mn <-99 to -99<mn?
What is it that i donot see?
Can you please elaborate more on the above?
Thanks in advance!
This is what i donot understand.
You say that mn must be more than −4∗7=−28, meaning mn >-28 or -28<mn
and that mn must be less than −9∗11=−99, meaning mn<-99 or -99>mn.
Then you go on and say: −99<mn<−28. How is this possible?
How can we go from mn>-28 to mn<-28 and mn <-99 to -99<mn?
What is it that i donot see?
Can you please elaborate more on the above?
Thanks in advance!
