grandh01 wrote:If N is a positive integer, is the units digit of N equal to zero?

1) 14 and 35 are factors of N.
2) N=(2^5)(3^2)(5^7)(7^6)

I don't understand how #1 is sufficient, if anyone could explain this it would be much appreciated.
Thanks in advance.

OA is D

OA as D is correct.
For the first statement. 14 and 35 are factors.
If you break them into primes, 14 = 2*7 and 35 = 5*7 are factors.
Hence 2, 5, and 7 are factors.
Therefore 2*5 is a factor as well. Since 10 is a factor of a positive integer, the number must end in a 0. (If you multiply any integer by 10, the last digit is 0). Hence we know for certain that unit digit is 0. Sufficient.

Let me know if this helps

Hi grandh01,

This problem is a great illustration of the important of analyzing the question stem before you move onto the statements. After all, look at those statements--statement 2), in particular, if a huge, messy number with a bunch of prime terms raised to high powers!

But if you stop for a moment, you can make some key deductions before you move on to either statement. First, the question asks if an integer's units digit is zero. Well, what's that mean? It ends in zero, which is a giveaway--the question is really asking if the number is a multiple of ten!

So, statement 1 gives us 35 and 14 as factors of N. But to be divisible by 35, N must be divisble by 5. So be divisible by 14, N must be even. And an even number divisible by 5 does divide by 10 and ends in 0. Sufficient--done!

An 2) is similar. It looks like a mess, but all that matters is the 2 and the 5. N has at least one 2 and at least one 5, so it ends in at least one 0. (of course, you don't even need to make THAT deduction; you have an exact value for N which will always be sufficient!)

The answer is definitely (D), and we're done.

grandh01 wrote:If N is a positive integer, is the units digit of N equal to zero?

1) 14 and 35 are factors of N.
2) N=(2^5)(3^2)(5^7)(7^6)

We need to determine whether the units digit of a positive integer N is zero. If N has a units digit of zero, then N must be divisible by 10. In other words, N must be divisible by both 2 and 5.

Statement One Alone:

14 and 35 are factors of N.

Since 14 is divisible by 2 and 35 is divisible by 5, N is divisible by both 2 and 5, and thus it has a units digit of zero. Statement one alone is sufficient. We can eliminate answer choices B, C, and E.

Statement Two Alone:

N = (2^5)(3^2)(5^7)(7^6)

We see that N is divisible by both 2 and 5 and thus has a units digit of zero. Statement two alone is also sufficient.

Answer: D