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What is the value of positive integer x?

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by BTGmoderatorLU » Mon Oct 23, 2017 3:36 pm
What is the value of positive integer x?

(1) Units digit of x is 5.
(2) x, x-3 and x+2 are all prime numbers

The OA is B.

Can any expert help me with this DS question please? Thanks.
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by Jay@ManhattanReview » Wed Oct 25, 2017 1:28 am
LUANDATO wrote:What is the value of positive integer x?

(1) Units digit of x is 5.
(2) x, x-3 and x+2 are all prime numbers

The OA is B.

Can any expert help me with this DS question please? Thanks.
(1) Unit digit of x is 5.

We only know that the units digit of x is 5. x can be any number; for example, 5, 15, 2345, 34565, etc. Insufficient.

(2) x, x-3 and x+2 are all prime numbers.

We see that except '2,' all the prime numbers are odd. If x is odd, (x + 2) would be odd, and (x - 3) would be even. Thus, among x, x - 3 and x + 2, there is an even prime number.

Since (x -3) is the smallest among x, x-3 and x+2, we have x - 3 = 2 (smallest prime number) => x = 5.

This gives that x = 5, x-3 = 2 and x+2 = 7 are all prime numbers.

Thus, x = 5. Sufficient.

The correct answer: B

Hope this helps!

-Jay

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