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If the positive integer n has 4 different factors, n=?

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Math Revolution GMAT Instructor
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If the positive integer n has 4 different factors, n=?  [#permalink]

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New post 02 Jul 2018, 01:15
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:08) correct 44% (01:06) wrong based on 59 sessions

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[GMAT math practice question]

If the positive integer \(n\) has \(4\) different factors, \(n=?\)

1) \(n\) has \(1\) prime factor
2) \(n<10\)

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Re: If the positive integer n has 4 different factors, n=?  [#permalink]

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New post 02 Jul 2018, 03:48
MathRevolution wrote:
[GMAT math practice question]

If the positive integer \(n\) has \(4\) different factors, \(n=?\)

1) \(n\) has \(1\) prime factor
2) \(n<10\)


n can be any cube(since it has 4 different factors) greater than 1
or numbers formed when two prime numbers are multiplied

1. n can take values 8,27,or 64 (Insufficient)

2. n can be 6(factors - 1,2,3,6) or 8(factors - 1,2,4,8) (Insufficient)

On combining the information in both the statements,
the only possibility for the value of n is 8 (Sufficient - Option C)

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Re: If the positive integer n has 4 different factors, n=?  [#permalink]

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New post 04 Jul 2018, 01:50
=>

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)
\(2^3\) and \(3^3\) are positive integers with \(4\) different factors.
Since the solution is not unique, condition 1) is not sufficient.

Condition 2)
\(6 = 2*3\) and \(8 = 2^3\) are positive integers with \(4\) different factors.
Since the solution is not unique, condition 2) is not sufficient.

Condition 1) & 2)
\(8 = 2^3\) is the unique positive integer less than \(10\) with \(4\) different factors and one prime factor.
Since the solution is unique, both conditions 1) & 2) are sufficient, when considered together.

Therefore, the answer is C.
Answer: C

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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The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Re: If the positive integer n has 4 different factors, n=? &nbs [#permalink] 04 Jul 2018, 01:50
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