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by NeilWatson » Tue Feb 18, 2014 7:08 pm
I believe this problem might be pretty straight forward, but I got it wrong :/

If N is a positive integer, is the units digit of N equal to 0?
1) 14 and 35 are factors of N

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

I know the answer but would like a formal explanation.

Thanks
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Source: — Data Sufficiency |
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by dimochka » Tue Feb 18, 2014 9:22 pm
Hi NeilWatson,

Looking at (1) we know that N is divisible by 14 and 35.
If a number is divisible by 14, it's divisible by both 2 and 7
If a number is divisible by 35, it's divisible by both 5 and 7
Since N is divisible by 2 and by 5, it has to be divisible by 2*5 = 10, and therefore must end with a 0.
Sufficient

(2) Same logic applies. As it is divisible by at least one 2 and one 5, it is divisible by 10 and will therefore end with at least one 0.
Sufficient
Please feel free to private message me with any questions; I don't check the forums regularly, whereas PMs go straight to my email.
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by Patrick_GMATFix » Tue Feb 18, 2014 9:38 pm
An integer with a units digit of 0 must be divisible by 10. An integer is divisible by 10 if it has 2 and 5 among its factors.

Rephrase: Are 2 and 5 both factors of N?

(1) 2 must be a factor because 14 (2*7) is. 5 must be a factor because 35 is. SUFFICIENT

(2) This gives us the exact value of N, so it must be SUFFICIENT.

Answer is D

-Patrick
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