If t is a positive integer and r is the remainder when t^2+5t+6 is divided by7, what is the value of r?
1) when t is divided by 7 the remainder is 6.
2) when t^2 is divided by 7 the remainder is 1.










remainder problems usually show patterns after a very, very small number of plug-ins.

statement (1):
it's easy to generate t's that do this: 6, 13, 20, 27, ... (note that 6 is a member of this list, and an awfully valuable one at that; it's quite easy to plug in)

try 6: 36 + 30 + 6 = 72; divide by 7 --> remainder 2
try 13: 169 + 65 + 6 = 240; divide by 7 --> remainder 2
try 20: 400 + 100 + 6 = 506; divide by 7 --> remainder 2

by this point i'd be convinced.
note that 3 plug-ins is NOT good enough for a great many problems, esp. number properties problems. however, as i said above, remainder problems don't keep secrets for long.

sufficient.



statement (2):


the first two perfect squares that do so are 1^2 = 1 and 6^2 = 36.
if you don't recognize that 1 ÷ 7 gives remainder 1, then you'll have to dig up 6^2 = 36 and 8^2 = 64

1 + 5 + 6 = 12 --> divide by 7; remainder = 5
36 + 30 + 6 = 72 --> divide by 7, remainder = 2

Insuff...

Ans : A