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For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
 12 Dec 2012, 03:59
Question Stats:
69% (01:56) correct
30% (01:31) wrong based on 9 sessions
For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to (A) 2 (B) 3 (C) 4 (D) 8 (E) 18
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Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
12 Dec 2012, 04:02
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Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
14 Dec 2012, 03:20
Ans: 72= 2^3x3^2, since 2^3 is a divisor of 72 k can be 3. Also 2^4=(2^(k+1)) is not a divisor of 72 , therefore the answer is (B).
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Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
14 Dec 2012, 23:44
Initially looking to the problem one may try to plugin the numbers one by one. Here, 2^2=4 is a divisor of 72 and 2^3=8 is also a divisor of 72. But, we have to choose only one answer.
72=2x2x2x3x3=2^3 *3^2 and it is given that 72/2^k = integer. Here, we can equate 2^3=2^k and hence k=3. But, in fact 2^2 is also a divisor of 72 hence 2 could also be the answer. But, since it is additionally given that k+1 is not a divisor i.e. 2 in this case does not satisfy the condition because 2+1=3 and 2^3 is a divisior of 72. where as 3 satisfies the condition i.e. 3+1= 4 turning into 2^4 which is not a divisor of 72. This is how only one answer choice is left which is equal to 3 = answer choice B.
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Re: For the positive integers a, b, and k, a^k||b means that a^k [#permalink]
19 Dec 2012, 07:15
2^k has to be a factor of 72.
Factors of 72: 3^2 x 2^3
Hence, k = 3.
Answer B.
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Re: For the positive integers a, b, and k, a^k||b means that a^k
[#permalink]
19 Dec 2012, 07:15
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