If P is a set of integers and 3 is in P, is every positive

[BTGmoderatorDC]

If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.

OA A

Source: Princeton Review

[Jay@ManhattanReview]

If P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

(1) For any integer in P, the sum of 3 and that integer is also in P.
(2) For any integer in P, that integer minus 3 is also in P.

OA A

Source: Princeton Review

Let's first understand the question.

The question says, "If P is a set of integers and 3 is in P, is every positive multiple of 3 in P? "

"every positive multiple of 3" means that all the integers from the set {3, 6, 9, 12, 15, ...}, all the numbers are in Set P. There may or may not be negative multiples and 0 in Set P, but we are not concerned about it.

Let's take each statement one by one.

(1) For any integer in P, the sum of 3 and that integer is also in P.

=> Say x is in Set P, then (x + 3) is also in Set P.

Say x = -3 is in Set P, then -3 + 3 = 0; 0 + 3 = 3; 3 + 3 = 6; onwards are in Set P. Set P: {- 3, 0, 3, 6, 9, 12, 15, ..., ∞}. Sufficient.

(2) For any integer in P, that integer minus 3 is also in P.

Say x = 3, then x - 3 = 0 in the set; 0 - 3 = -3 is in the set; similarly, -6, - 9, -12 are in the set. Since the set may or may not have all the positive multiple of 3, the answer is indeterminable. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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