Data Sufficiency

if t is a positive integer and r is the remainder when t^2+5t+6 is divided by 7, what is the value of r?

A) when t is divided by 7, the remainder is 6

B) when t^2 is divided by 7, the remainder is 1


OA is A

statement 1 : t = 7x+6, where x=1,2,3,4,5

(7x+6)^2 + 5(7x+6) + 6
= 49x^2 + (2*7*6 + 5*7)x + some constant term without x.

First two terms are divisible by 7, Third term is contant, we can find out remainder, Suff

Statement 2 : (t^2+1) is divisible by 7
t^2 + 5t + 6
=(t^2+1) + 5(t+1)

We know first term is divisible by 7
we have to find out the remainder when 5(t+1) is divided by 7........

I'm stuck here....... help plz
but in actual test if i have to take a guess between A and D. I'll go with A

EDIT : i realized my mistake (in red)
statement 2 : (t^2 - 1) is divisible by 7
(t+1)(t-1) is divisible by 7
Possible values of t are (6,8, 13,15 ....... )

check with 6, 8, remainder is diff...... Insuff.

(t^2+5t+6)/7
=> (t+2)(t+3)/7

1) says t/7 remainder is 6; so (t+1) has a remainder of 0; and (t+2) has a remainder of 1 and (t+3) has a remainder of 2

=> so, remainder of (t+2)(t+3)/7 will be 2

2) (t^2+1)/7, has a remainder of 1, this is not sufficient to answer the problem.

We can also do this problem by picking nos.
i) Since t/7 gives remainder 6 and t is a postive no, choose t= 13, 20, ..
Substitute in original equation from the stimulus and we get a consistent value of 2 for r.
==> sufficient.

ii) Since (t^2)/7 gives remainder 1, choose t= 6, 8 (try for atleast 2-3 values when picking nos)
Hence t^2 = 36, 64 which gives remainder 1 when divided by 7.
However on putting t= 6 and 8 in the equation in the stimulus, we get two different values for r i.e. 2 and 5
==> Not sufficient.

Ans: A