Another GMAT Question - Please crack this?

Question

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?

Are either of these sufficient?

Given A: When "t" is divided by 7, the remainder is 6.
Given B: When t^2 is divied by 7, the remainder is 1.

(side note when you plug in 13, or 26 in for "t" the remainder is 1, but if you plug 21 for t, the remainder is not 1. Yet GMAT says A is sufficient. ) Can you guys crack it

Answer 1

Saying t divided by 7 has a remainder of 6 means that t=7p+6, for some nonnegative integer p.

Plug that into t^2+5t+6 and you get

49p^2 + 119p + 72.

Now divide this by 7. 49 is divisible by 7, and so is 119, so they won't contribute to a remainder. So you just need the remainder of 72 when divided by 7.

Note: your remainder for 13 is wrong. Also, 26 doesn't have a remainder of 6 when divided by 7.

Answer 2

yes

Given A (When "t" is divided by 7, the remainder is 6.) means that
t ≡ -1 (mod 7)
therefore t^2 ≡ 1 (mod 7)
so t^2 + 5t + 6 ≡ 1 - 5 + 6 ≡ 2 (mod 7)
and R = 2.

(Double-checking,
13 ≡ 6 (mod 7), and
13^2 + 5*13 + 6 = 169 + 65 + 6 = 240
240 / 7 = 34 R=2
Also,
27 ≡ 6 (mod 7), and
27^2 + 5*27 + 6 = 729 + 135 + 6 = 870
870 / 7 = 124 R=2
)

But given B (When t^2 is divied by 7, the remainder is 1) means that t^2 ≡ 1 (mod 7), so it could be that t ≡ 1 (mod 7)
or t ≡ -1 (mod 7). Therefore the remainder of t^2 + 5t + 6 when divided by 7 is indeterminant, since R could equal 5 [1 + 5 + 6 (mod 7)] or 2 [1 - 5 + 6 (mod 7)].

Answer 3

GMAT now asks this kind of questions???
It is even tougher than GRE.

A. t ≡ 6 ≡ -1 (mod 7), t^2 ≡ 1 (mod 7)
plug into the eqn: R=1-5+6 =2
So A alone is sufficient.

B. t^2 ≡ 1 (mod 7), t ≡ 1 or 6 (mod 7)
cannot uniquely determine value of t, and thus value of R

Answer 4

What is GMAT?