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is 5n an integer?

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by sanju09 » Thu Jul 17, 2014 4:06 am
If n is not an integer, is 5n an integer?
(1) 3n + 2 is an integer divisible by 10.
(2) 6n - 1 is an integer divisible by 5.


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by GMATinsight » Thu Jul 17, 2014 10:26 am
If n is not an integer, is 5n an integer?
(1) 3n + 2 is an integer divisible by 10.
(2) 6n - 1 is an integer divisible by 5
Question : Is 5n an Integer?

Statement 1) 3n+2 is an integer divisible by 10

i.e. 3n + 2 is a Multiple of 10
therefore possible values of (3n + 2) = 10, 20, 30, 40, 50, .... and so on

Therefore values of n = 8/3, 18/3, 28/3 .....and so on respectively

For each value of n obtained above, 5n is never an Integer. Consistent solution therefore SUFFICIENT

Statement 2) 6n-1 is an integer divisible by 5

i.e. 6n - 1 is a Multiple of 5
therefore possible values of (6n - 1) = 5, 10, 15, 20, 25 .... and so on

Therefore values of n = 1 (not acceptable being integer), 11/6, 8/3, 7/2, 13/3 .....and so on respectively

for n = 11/6, 5n is NOT an Integer
for n = 8/3, 5n is NOT an Integer and so on

For each value of n obtained above, 5n is never an Integer. Consistent solution therefore SUFFICIENT

Answer : Option D
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