I would say the answer is D, r =2

I got this by plugging in possible values of t in the equation.

Pls confirm if the answer is correct.

Also if any one can suggest a better way than plugging in values would appreficate it

thanks a lot

Q says t^2 + 5t + 6 is divided by 7 with remainder r

stmt 1: when t is divided by 7, the remainder is 6

so we can say let t-6 (t -reminder) = x (where x will be divisible by 7)

so t =x + 6

putting this in eqn we have (x + 6) ^ 2 + 5(x+6) + 6 / 7
i.e (x^2 +17x + 72) / 7
i.e x^2/7 + 17x/7 + 72/7

now here the first two fractions will yield an integer value (no remainder as x is divisile by 7)

so 72/7 will produce the remainder

so the remainder is 2 SUFF

stmt 2: t ^ 2 / 7 gives 1 as remainder

working with t^2 will produce a root in the above eqn
so we have

let t - a (remainder of t/7) = x

so t = x+ a
i.e t^2 = (x +a) ^2
i.e. x^2 + a^2 + 2ax
divide this by 7
so we have x ^2/ 7 will be an integer
2ax /7 wll be an int

so remainder is produced by a^2/7 and this should be 1

so possible values of "a" can be 1-6 if you check with these
u will get 1/7 will give remainder 1
& 6^2 / 7 will give remaider 1

so a can be 1 or 6

so we can say that we t is divided by 7 it will give remainder 1 or 6
so t^2 will give remainder as 1

you can check this with 8 & 13
now as we calculated for stmt 1 t/7 with remainder 6, same value is here so we can say that if a =6 then remainder for eqn is 2

now for a=1
we can say
t-1 =x
so t=x +1

put in eqn provided
i.e (x +1 )^2 +5(x+1) +6/7

solving we get

x^2/7 + 7x/7 +12/7

now here again first two fractions will yield a integer value only remaider will be added coz of 12/7 which will be 5

so we have two remainders here henec INSUFF

so ans must be A

You are right again. The answer is A. Thanks again.

TT

Ans should be A

I agree with Samir's explanantion of stmt 1.

For stmt 2 - I solved like this (I think this is faster)

t^2-1 = 7n => t^2 = 7n+1 => t = sqrt(7n+1)

Fitting this into equation given in Q we get
(t^2+6)/7 will have remainder 0. t^2 gives remainder 1. 6+1 = 7

now, we need to find what is the remainder of [5*sqrt(7n+1)]/7.. putting values which are easy to calulcate

Say, n = 5 gives 30/7 remainder 2
Say, n = 9 gives 40/7 remainder 5

So, stmt 2 is NOT SUFF

Yes Kajcha,
Your approach would be little faster, I did not use it because I thought it would be better of to work without the square root sign (mentioned it in my post).

After thinking over it again, I realised we really don't have to use sqrt at all... this approach will be even faster

t^2 + 6 will give remainder 0

We just need to calculate for 5*t/7 ... substitue values

t = 6 remainder is 2
t = 8 remainder is 5

PS: I chose 6 and 8 to satisfy stmt 2 .

Kajcha,
If anyone gets this kind of a problem on the GMAT he/she will definitely remember u while solving it. Thanks for these shortcuts.