Samwong wrote:

If there is a remainder of 2 when integer P is divided by 7, is P divisible by 8?

1. P is divisible by 2 and 3

2. P<100

Can somone please explain how do to do this problem? I don't know how to handle "remainder of 2." Thanks.

When positive integer p is divided by 7 the remainder is 2: \(p=7q+2\), so p can be: 2, 9,

16, 23, 30, 37, 44, 51, 58, 65,

72, ...

(1) p is divisible by 2 and 3 --> p is a multiple of 6 --> p can be 30 (answer NO) or 72 (answer YES). Not sufficient.

(2) p<100. Clearly insufficient.

(1)+(2) p can still be 30 (answer NO) or 72 (answer YES). Not sufficient.

Answer: E.

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