If t is an integer, is t odd?

Question

(1) t/3 is not an integer
(2) (t-1)/3 is not an integer

CrackverbalGMAT · Answer

Statement 1:   t/3 is not an integer

From this we can say that t is not divisible by 3.

t = 2, then t is not divisible by 3.

t = 5, then t is not divisible by 3

So t can be even or odd.

Therefore Statement 1 Alone is Insufficient  . Answer options could be B, C or E.

Statement 2:   (t-1)/3 is not an integer

Here t - 1 is not divisible by 3

t = 6, then t - 1 = 5 which is not divisible by 3.

t = 5, then t - 1 = 4 is not divisible by 3

So t can be even or odd.

Therefore Statement 2 Alone is Insufficient  . Answer Options could be C or E

Combining Both Statements:   t/3 and t - 1 are both not divisible by 3.

t = 8, then t and t - 1 = 7 are not divisible by 3.

t = 5, then t and t - 1 = 4 are not divisible by 3

So t can be even or odd.

Therefore Both Statements together are Insufficient  .

Option E

Arun Kumar

TestPrepUnlimited · Answer

Statement 1:

t is not a multiple of 3, then either t + 1 or t + 2 must be a multiple of 3. Insufficient.

Statement 2:

t - 1 is not a multiple of 3, then we have either t is a multiple of 3 or t + 1 is a multiple of 3. Insufficient.

Combined:

Combined we know t + 1 must be a multiple of 3. If we have t + 1 = 3, then t is even. If t + 1 = 6, then t is odd. Insufficient.

Ans: E

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