Is p divisible by 8?

When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

(1) p is divisible by 2 and 3
(2) p < 100[/list]


Answer is E


Numbers which satisfy the condition of "remainder 2 when divided by 2" are

9,16,23,30,37,44,51,58,

1) P is divisible by 2 and 3..

It can be 30,72

30 is not divisible by 8 whereas 72 is .

Insuff

2) Insuff

Same reasoning as above..

1) P divided by 2 and 3 is similar to saying the number is divisible by 6. Without a range here, there is more than one possibility that P is divisible by 6 when the remainder will be 2 when divided by 7. Insufficient.

2) P < 100. Not enough information.

Together: Same as the above, yet there are two numbers under 100 that are divisible by 6 and have remainder 2 when it is divided by 7 (i.e. 30 and 72). Insufficient.

I choose E.

4meonly wrote:When integer p is divided by 7, the remainder is 2. Is p divisible by 8?

(1) p is divisible by 2 and 3
(2) p < 100

1) p is divisible by 2 and 3. so it is a multiple of 6
6,12,18,24,30,36,42,48,54,60,66,72...
here 30/7 and 72/7 both give reminder 2
30 is not divisible by 8 but 72 is...
so insuff

2) insuff as there are several numbers
combing both too we will have same problem as in (1)
Insuff

so E

any simple method??