Is x an integer?

Question

Is x an integer?

(1) 5x is an integer.
(2)  \frac{5}{x}  is an integer.

KS15 · Answer

Statement 1:5x is an integer. We can have x=1 or x=1/5. Insufficient
Statement 2:5/x is an integer. Again, we can have x=1 or x=1/5. Insufficient.

Even using both, we can have x=1 or 1/5. Answer E

tapabrata · Answer

From statement 1 alone
5x is an integer 
For x=1/5, 5x is an integer (x is not an integer)
For x=1, 5x is an integer (x is an integer)
Hence we can't answer the question from Statement 1 with a definite 'yes' or 'no'

From statement 2 alone
for x= 1,  \frac{5}{x}  is an integer (x is an integer)
for x=1/5,  \frac{5}{x}  is an integer (x is not an integer)
Hence we can't answer the question from Statement 2 with a definite 'yes' or 'no'

Combining both statements
If x=1, then 5x is an integer and 5/x is also an integer (x is an integer)
if x=1/5, then 5x is an integer and 5/x is also an integer (x is not an integer)

Even by combining both the statements, we cannot answer the question with a definite 'yes' or 'no'

Answer E

NandishSS · Answer

1)5x is an integer. Test the values-

Put x=1 gives Yes

Put x=(1/5) gives No

1) Is not Sufficient

2) \frac{5}{x}  is an integer

Put x=1 gives Yes

Put x=(1/5) gives No

Combining both still gives

Put x=1 gives Yes

Put x=(1/5) gives No

Hence E

TheUltimateWinner · Answer

Statement 1:
if,
5x=5
-->x=1
-->YES

again,
if,
5x=1
-->x=1/5
-->NO
So, Insufficient

Statement 2:
if,
5/x=5
-->x=1
-->YES

again,
if,
5/x=25
-->x=1/5
-->NO
So, insufficient

Combining Statement 1 and 2:
after combining Statement 1 and 2 it still gives x=1 and 1/5. So,  the correct answer is E , to me. If my answer doesn't match with the official answer, I request to  chetan2u  not to give the solution so that we can give trial again.
Thank you  chetan2u

Is x an integer?

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GMAT Data Sufficiency (DS) Questions

Is x an integer?

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