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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42 GPA: 3.82
What is the number of factors of a positive integer n?  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 65% (00:39) correct 35% (00:42) wrong based on 102 sessions

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[GMAT math practice question]

What is the number of factors of a positive integer $$n$$?

1) $$n$$ is a multiple of $$7$$
2) $$n$$ is a prime number

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Joined: 07 Jan 2016
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GMAT 1: 710 Q49 V36 Re: What is the number of factors of a positive integer n?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the number of factors of a positive integer $$n$$?

1) $$n$$ is a multiple of $$7$$
2) $$n$$ is a prime number

1) n is a multiple of 7 n can be 7 14 21 and each number has different factors
insufficient

2) n is prime

we know prime number has 2 factors i.e 1 and itself
sufficient

(B) imo
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MathRevolution wrote:
[GMAT math practice question]

What is the number of factors of a positive integer $$n$$?

1) $$n$$ is a multiple of $$7$$
2) $$n$$ is a prime number

Target question: What is the number of factors of a positive integer n?

Statement 1: n is a multiple of 7
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 7. In this case, n has TWO factors (1 and 7)
Case b: n = 14. In this case, n has FOUR factors (1, 2, 7 and 14)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a prime number
ALL prime numbers have exactly TWO factors.
So, if n is a prime number, then the TWO factors are 1 and n
In other words, n has exactly TWO factors
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: What is the number of factors of a positive integer n?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

What is the number of factors of a positive integer $$n$$?

1) $$n$$ is a multiple of $$7$$
2) $$n$$ is a prime number

solution IMO B
statement 1 n is a multiple of 7
then n can be 7 or 14 or 70 so this answer is insufficient
statement 2 tell us its a prime number then it must have 2 factors from its definition 1 and its self so B is sufficient
because question just ask about no. of factors not what is n.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8007
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: What is the number of factors of a positive integer n?  [#permalink]

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=>

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)
$$n = 7$$ : The number of factors of n is $$2$$.
$$n = 14$$ : The number of factors of n is $$4$$.
Since the answer is not unique, condition 1) is not sufficient.

Condition 2)
$$n = p^1$$, where p is a prime number.
The number of factors on n is $$1 + 1 = 2.$$
Thus, condition 2) is sufficient.

Therefore, the answer is B.

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.
_________________ Re: What is the number of factors of a positive integer n?   [#permalink] 01 Mar 2018, 03:43
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