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Re: Is 12 a factor of the positive integer n? [#permalink]
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08 Nov 2017, 22:10
Bunuel wrote:
Is 12 a factor of the positive integer n?
(1) n is a factor of 36.
(2) 3 is a factor of n.
Is 12 a factor of n--> does n have 2^2 *3 ?
1.n is a factor of 36 36= 2^2 * 3^2 Not sufficient since n can be 1 , multiple of 2 or 3 or can be 12 or a multiple of 12
2. 3 is a factor of n Not sufficient as if n might have 2^2 also
Combining 1 and 2 , we get Not sufficient If n = 12 or its multiple , then Yes If n = 3 , then No
Answer E
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Target question:Is 12 a factor of the positive integer n?
Statement 1: n is a factor of 36 This statement doesn't FEEL sufficient, so I'll TEST some values. There are several values of n that satisfy statement 1. Here are two: Case a: n = 12, in which case 12 IS a factor of n Case b: n = 6, in which case 12 is NOT a factor of n Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 3 is a factor of n Once again, there are several values of n that satisfy statement 2. Here are two: Case a: n = 12, in which case 12 IS a factor of n Case b: n = 6, in which case 12 is NOT a factor of n Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED. In other words, Case a: n = 12, in which case 12 IS a factor of n Case b: n = 6, in which case 12 is NOT a factor of n Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
We do not have enough information to answer the question. If n is 1, then n/12 is not an integer; however, if n is 36, then n/12 is an integer. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
3 is a factor or n.
We do not have enough information to answer the question. If n is 3, then n/12 is not an integer; however, if n is 36, then n/12 is an integer. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
We still do not have enough information to answer the question. If n is 3, then n/12 is not an integer; however, if n is 36, then n/12 is an integer.
Answer: E
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