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If n is positive integer, is 35 a factor of n?

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Math Revolution GMAT Instructor
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If n is positive integer, is 35 a factor of n?  [#permalink]

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New post 20 Jul 2018, 00:25
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[GMAT math practice question]

If \(n\) is positive integer, is \(35\) a factor of \(n\)?

1) \(35\) is a factor of \(n^2\)
2) \(35\) is a factor of \(5n\)

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Re: If n is positive integer, is 35 a factor of n?  [#permalink]

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New post 20 Jul 2018, 01:42
MathRevolution wrote:
[GMAT math practice question]

If \(n\) is positive integer, is \(35\) a factor of \(n\)?

1) \(35\) is a factor of \(n^2\)
2) \(35\) is a factor of \(5n\)



1. 35 is a factor of n^2

35=7*5
n^2=5*7*p
n=root5*7*p
since n is a positive integer the root must have atleast another set of 5 and 7 in it
therefore
n=35*p
sufficient

2. 35 is a factor of 5n

35=7*5
5n=7*5*q
n=7q
now q can be any value not necessarily 5
insufficient

A
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Re: If n is positive integer, is 35 a factor of n?  [#permalink]

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New post 20 Jul 2018, 08:36
If \(n\) is positive integer, is \(35\) a factor of \(n\)?

1) \(35\) is a factor of \(n^2\) - there is a rule to remember n and n^2 will always have the same prime factors
2) \(35\) is a factor of \(5n\) - clearly NS

Answer A.
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Re: If n is positive integer, is 35 a factor of n?  [#permalink]

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New post 22 Jul 2018, 17:15
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since 35=5*7 is a factor of \(n^2\), 5 and 7 are factors of \(n^2\).
Since 5 and 7 are prime integers and n2 is divisible by 5 and 7, n is divisible by both 5 and 7.
Thus, 35 is a factor of n.
Condition 1) is sufficient.

Condition 2)
If n = 35, then 35 is a factor of n.
If n = 7, then 35 is not a factor of n.
Since we don’t have a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: If n is positive integer, is 35 a factor of n? &nbs [#permalink] 22 Jul 2018, 17:15
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