BTGModeratorVI wrote: ↑

Mon Jun 08, 2020 12:04 pm

If n is a positive integer, is n odd?

(1) When n is divided by 3, the remainder is 1.
(2) When n is divided by 8, the remainder is 1.

Answer: B
Source: GMAT prep

Target question: Is n odd?

---------------ASIDE------------------
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
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Statement 1: When n is divided by 3, the remainder is 1.
So, some possible values of n are: 1, 4, 7, 10, 13, . . .
If n = 1, the answer to the target question is YES, n is odd
If n = 4, the answer to the target question is NO, n is not odd
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 8, the remainder is 1.
Some possible values of n are: 1, 9, 17, 25, 33, 41, 49, ...
So it certainly LOOKS LIKE n must be odd

Alternatively, statement 2 is telling us that n is 1 greater than some multiple of 8
Since all multiples of 8 are EVEN, we know that n is 1 greater than some EVEN integer. This means n must be odd

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent