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09 May 2022, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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48% (02:19) correct
52%
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wrong
based on 67
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If \(2^{3m} = n + 1\), where n is an integer. What is a value of m?
(1) \(3^{5n} = 5^{3k}\), where k is an integer.
(2) \(n − m ≤ 1\)
(1) \(3^{5n} = 5^{3k}\), where k is an integer.
(2) \(n − m ≤ 1\)
09 May 2022, 05:40
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Pre-thinking
n is an integer, but m does not need to be an integer.
If n=0, then m=0
If n=1, then 3m=1 => m=1/3
If n=3, then 3m=2 => m=2/3
It follows that if n=2, m is between 1/3 and 2/3. (Note: It is 0.52832...)
n can also be between -1 and 0.
(1) Only
Because both n and k are integers, the only way 3^(5n)=5^(3k) is that n=k=0
So m=0
Sufficient.
(2) Only
From (1), we already know that one possible answer is n=m=0. In this case n-m=0
We should be able to increase n a little bit (say, n=0.1), m should also be increased slightly. (Note: it is 0.04583...)
Still, n-m<=1
Not sufficient.
The answer is thus (A).
n is an integer, but m does not need to be an integer.
If n=0, then m=0
If n=1, then 3m=1 => m=1/3
If n=3, then 3m=2 => m=2/3
It follows that if n=2, m is between 1/3 and 2/3. (Note: It is 0.52832...)
n can also be between -1 and 0.
(1) Only
Because both n and k are integers, the only way 3^(5n)=5^(3k) is that n=k=0
So m=0
Sufficient.
(2) Only
From (1), we already know that one possible answer is n=m=0. In this case n-m=0
We should be able to increase n a little bit (say, n=0.1), m should also be increased slightly. (Note: it is 0.04583...)
Still, n-m<=1
Not sufficient.
The answer is thus (A).
Sushil117
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09 May 2022, 09:54
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If 2^3m=n+1, where n is an integer. What is a value of m?
n=m=0 in which case both sides will be equal
if m=1 then n =7..so on
(1) 3^5n=5^3k, where k is an integer.
only case where n=k=o
gives an answer
(2) n−m≤1
here n=m=0 or can be 2&,3&2 etc
not sufficient
IMO A
n=m=0 in which case both sides will be equal
if m=1 then n =7..so on
(1) 3^5n=5^3k, where k is an integer.
only case where n=k=o
gives an answer
(2) n−m≤1
here n=m=0 or can be 2&,3&2 etc
not sufficient
IMO A
