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Integers

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Integers

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In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2
B. 3
C. 5
D. 6
E. 8

OA is B

Which option is correct, OA says B. But I got E. Pls an Expert should help out.

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GMAT/MBA Expert

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Quote:
In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2
B. 3
C. 5
D. 6
E. 8

OA is B

Which option is correct, OA says B. But I got E. Pls an Expert should help out.
Hi Roland2rule,
Let's take a look at your question.

N is a positive integer less than 200, and 14N/60 is an integer.
$$\frac{14N}{60}=\frac{7N}{30}$$

N must be a multiple of 30 for 7N/30 to be an integer.

Also N<200, therefore, we can only consider multiples of 300 less than 200, i.e.

$$30\times1,\ 30\times2,\ 30\times3,\ 30\times4,\ 30\times5,\ 30\times6$$
$$\text{Factors of 30}\ =\ 1,\ 2,\ 3,\ 5,\ 6,\ 10,\ 15,\ 30$$

Prime factors for all possibles multiples of 30 will be 2, 3, 5.
Hence, N has 3 possible prime factors.

Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

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GMAT/MBA Expert

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Roland2rule wrote:
In N is a positive integer less than 200, and 14N/60 is an integer, then N has how many different positive prime factors?

A. 2
B. 3
C. 5
D. 6
E. 8
Let's choose a nice value of N that satisfies the given information.

GIVEN: 14N/60 is an integer
Prime factorize the numerator and denominator to get: (7)(2)(N)/(2)(2)(3)(5) is an integer
Simplify: (7)(N)/(2)(3)(5) is an integer
Notice that, when N = 30 (aka the product of 2, 3, and 5), then (7)(N)/(2)(3)(5) = (7)(2)(3)(5)/(2)(3)(5) = 7, which IS an integer
So, N = 30 satisfies the given information.

N has how many different positive prime factors?
30 = (2)(3)(5)
So, N has 3 different positive prime factors (2, 3 and 5)

Answer: B

Cheers,
Brent

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Hi Roland2rule,

We're told that N is a positive integer that is less than 200 and 14N⁄60 is also an integer. We're asked for the the number of different positive prime factors that N has. This question can be solved by TESTing VALUES. As long as we pick a value for N that fits the given 'restrictions', we'll get the correct answer.

IF.... N=60.... (14)(60)/(60) = 14 so we have a value that fits everything that we were told.

60 = (2)(2)(3)(5) so N has 3 different prime factors

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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