Problem Solving

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

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

BTGmoderatorRO 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

OA is B

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

We are given that N is a positive integer less than 200, and 14N/60 is an integer, and we need to determine the number of different positive prime factors of N. Let's begin by simplifying 14N/60.

14N/60 = 7N/30

In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30. The multiples of 30 less than 200 are: 30, 60, 90, 120, 150 and 180. First let's investigate 30, the smallest positive number that is a multiple of 30.

Since 30 = 2 x 3 x 5, N has 3 different positive prime factors.

However, even if we break 60, 90, 120, 150, or 180 into prime factors, we will see that each of those numbers also has 3 different prime factors (2, 3, and 5).

Thus, we can conclude that N has 3 different positive prime factors

Answer: B