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
What would be the quickest way to solve this?
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- NeilWatson
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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
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
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- Patrick_GMATFix
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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
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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