Problem Solving

aleph777 wrote:If n is a positive integer less than 200 and 14n�60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8

14n/60 = 7n/30 is an integer.
Hence, n must be a multiple of 30 = 2*3*5

Thus, we know for sure that n has at least 3 different prime factors, i.e. 2, 3, and 5.

Now if n has one more different prime factor, let's say the minimum one, i.e. 7, minimum value of n will be 210 > 200. Hence n doesn't have any other prime factor.

The correct answer is B.

aleph777 wrote:If n is a positive integer less than 200 and 14n�60 is also an integer, then n has how many different positive prime factors
a. 2
b. 3
c. 5
d. 6
e. 8

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 has 3 different prime factors (2, 3, and 5).

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

Answer: B

Hi All,

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