Is the integer p divisible by 4?

[Vincen]

Is the integer p divisible by 4?

(1) p < 123
(2) p is the product of 5 consecutive positive integers.

The OA is B.

Clearly statement (1) is not sufficient. But, how can I ensure the statement (2) is sufficient?

[Jay@ManhattanReview]

Is the integer p divisible by 4?

(1) p < 123
(2) p is the product of 5 consecutive positive integers.

The OA is B.

Clearly statement (1) is not sufficient. But, how can I ensure the statement (2) is sufficient?

Statement 2: p is the product of 5 consecutive positive integers.

If you take any five consecutive positive integers, you are sure to get minimum two EVEN positive integers. Since every even number is a multiple of 2, we get at least two 2s. Thus, p = Product of 5 consecutive positive integers is divisible by 4. Sufficient.

Example:

Case 1: Say the five consecutive positive integers are: 1, 2, 3, 4, 5. We see that the product of 2*4 = 8, thus, p = Product of 5 consecutive positive integers is divisible by 4.

Case 2: Say the five consecutive positive integers are: 17, 18, 19, 20, 21. We see that the product of 18*20 = 8*45, thus, p = Product of 5 consecutive positive integers is divisible by 4.

Hope this helps!

-Jay

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[Matt@VeritasPrep]

If you're multiplying five consecutive integers together, then at least two of them must be even. Since you've got at least two evens, you've got:

2*something * 2*something else =>

4*something*something else =>

a multiple of 4