Data Sufficiency

HI,


OA is A.. but Can anyone explain pls?

dunkin77 wrote:HI,


OA is A.. but Can anyone explain pls?

Hello,

The correct answer is [A] indeed. Here is why:

t^2 + 5t + 6 can also be written as
(t+3)(t+2)

Statement (1) says

t-6 is divisible by 7. Adding 7...
t+1 is also divisible by 7.
t+2 will leave a remainder of 1.
t+3 will leave a remainder of 2.
(t+2)(t+3) will leave a remainder of 1 * 2 = 2 = r SUFFICIENT

This is a nice formula worth generalizing:
"when a/d leaves a remainder of m and b/d leaves a remainder of n, a.b/d leaves a remainder of m.n" ......... (I)

proof of (I) by plugging in some numbers...
try it, t = 6
t+1 = 7, divisible by 7
t+2 = 8, remainder 1
t+3 = 9, remainder 2
(t+2)(t+3) = 8 * 9 = 72, remainder 2

try it, t = 13
t+1 = 14, divisible by 7
t+2 = 15, remainder 1
t+3 = 16, remainder 2
(t+2)(t+3) = 15 * 16 = 240, remainder 2

Statement (2) obviously is not sufficient.

ANSWER [A]