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08 Apr 2024, 01:30
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C
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Difficulty:
65%
(hard)
Question Stats:
59% (01:49) correct
41%
(02:04)
wrong
based on 334
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If \(p > 0\) and \(p^5 + k^5 = 250\), then the greatest possible value of \(k\) is between
A. 0 and 1.5
B. 1.5 and 3
C. 3 and 4.5
D. 3.5 and 6
E. 6 and 7.5
A. 0 and 1.5
B. 1.5 and 3
C. 3 and 4.5
D. 3.5 and 6
E. 6 and 7.5
08 Apr 2024, 08:00
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Let's just do some number crunching
\(2^5 = 32\)
\(3^5 = 243\)
\(4^5 = 1024\)
Now, if we assume that k is 3 then \(p^5 = 7\) which is positive
i.e. k can definitely go upto 3 and can marginally be greater than 3 as well if p is very small and close to zero
therefore, k should be between 3 and 4.5 as per the ranges given in options
Answer: Option C
\(2^5 = 32\)
\(3^5 = 243\)
\(4^5 = 1024\)
Now, if we assume that k is 3 then \(p^5 = 7\) which is positive
i.e. k can definitely go upto 3 and can marginally be greater than 3 as well if p is very small and close to zero
therefore, k should be between 3 and 4.5 as per the ranges given in options
Answer: Option C
Bunuel
08 Apr 2024, 09:10
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Given p>0
\(p^5 + k^5 = 250\)
Therefore \(k^5 = 250 - p^5\)
For k^5 to be maximum p^5 has to be minimum and since it is greater than 0 but not mentioned as an integer assume it to be a value very close to 0 like 0.01 which when raised to 5 will be approximately 0 so p^5 can be completely ignored.
We are now left with \(k^5 = 250\) and since it is known \(3^5 = 243\), k has to be slightly greater than 3
\(p^5 + k^5 = 250\)
Therefore \(k^5 = 250 - p^5\)
For k^5 to be maximum p^5 has to be minimum and since it is greater than 0 but not mentioned as an integer assume it to be a value very close to 0 like 0.01 which when raised to 5 will be approximately 0 so p^5 can be completely ignored.
We are now left with \(k^5 = 250\) and since it is known \(3^5 = 243\), k has to be slightly greater than 3
