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C
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Difficulty:
55%
(hard)
Question Stats:
60% (02:05) correct
40%
(02:06)
wrong
based on 227
sessions
History
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If \(a^m = b^n\), and if \(a \neq b \neq m \neq n\), what is the value of a + b + m + n?
(1) a, b, m and n are all non negative integers less than 10.
(2) \(b^n = 81\).
(1) a, b, m and n are all non negative integers less than 10.
(2) \(b^n = 81\).
01 Feb 2010, 16:03
Kudos
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I'm sure you mean the question to read as follows (if the '!' symbols represent factorials, the question doesn't make sense):
If \(a^m = b ^n\) and if \(a \neq b \neq m \neq n\), what is the value of a + b + m + n?
(1) a, b, m and n are all non negative integers less than 10.
(2) \(b^n = 81\)
Now, from S1, we have a lot of possibilities. For example, if a =1, and n = 0, then m and b can be anything; we get the equation 1^m = b^0, and the left side and right side will both be equal to 1 if m and b are positive integers. So S1 is not sufficient.
From S2, we know that b^n = 81. The question doesn't even mention that b and n are integers, so there are far too many ways this can be true: b could be 81 and n could be 1, or b could be 81^2 and n could be 0.5, for example. So S2 is not sufficient.
From S1+S2 combined, we know that b^n = 81, and that b and n are integers between 0 and 9 inclusive. The only possibilities for b^n are then 9^2 or 3^4. Now a^m = b^n, so a^m is also equal to 81, and must also be either 3^4 or 9^2. Since a and b are different, one of the two is 3, the other 9, and since n and m are different, one of the two is 2 and the other is 4. So a+b+m+n = 9+3+2+4 = 18, and the answer is C.
If \(a^m = b ^n\) and if \(a \neq b \neq m \neq n\), what is the value of a + b + m + n?
(1) a, b, m and n are all non negative integers less than 10.
(2) \(b^n = 81\)
Now, from S1, we have a lot of possibilities. For example, if a =1, and n = 0, then m and b can be anything; we get the equation 1^m = b^0, and the left side and right side will both be equal to 1 if m and b are positive integers. So S1 is not sufficient.
From S2, we know that b^n = 81. The question doesn't even mention that b and n are integers, so there are far too many ways this can be true: b could be 81 and n could be 1, or b could be 81^2 and n could be 0.5, for example. So S2 is not sufficient.
From S1+S2 combined, we know that b^n = 81, and that b and n are integers between 0 and 9 inclusive. The only possibilities for b^n are then 9^2 or 3^4. Now a^m = b^n, so a^m is also equal to 81, and must also be either 3^4 or 9^2. Since a and b are different, one of the two is 3, the other 9, and since n and m are different, one of the two is 2 and the other is 4. So a+b+m+n = 9+3+2+4 = 18, and the answer is C.
02 Feb 2010, 04:58
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The answer cannot be A.
a=4, m=0, b=1, n=7
a=3, m=0, b=1, n=2
and many many other posibilities.
C should be the answer. The two facts, when combined, narrow down to 4 individual numbers.
a=4, m=0, b=1, n=7
a=3, m=0, b=1, n=2
and many many other posibilities.
C should be the answer. The two facts, when combined, narrow down to 4 individual numbers.
