Understanding remainders

Q 1)

t divided by 7 remainder is 6 can be expressed as

t = 7q+6

Eg:

50/7 quotient is 7 remiander is 1

50 = 7*quotient +remainder
= 7*7+1



Stmt I

t = 7q+6

Substitue this in the expression t^2+5t+6

(7q+6)^2+5(7q+6) + 6

49q^2+36+84q+35q+30+6

36+6 = 42

so it becomes

49q^2+42+84q+35q+30

We can see that all terms excepting 30 are divisible by 7 so the remainder will be 0+0+0+0+2

=2

All integers of this form will give a remainder 2

SUFF

Another approach:

In easier problems try to express whatever is given in the form t(or whatever is given i.e. dividend) = nq+r where n is divisor(7 in this problem) and q->quotient which can take values from 0,1,2... and r is the remainder.

Pick q=0,1,2,3.. and see if u get different remainders. Thsi would tell u that the stament is INSUFF if its asking for a single remainder value


Eg: t= 7q+6 when q=0 t=6 and t^2+5t+6 = 96 remainder->2
when q=1 t=13 and t^2+5t+6 = 240 remainder->2
when q=2 t = 20 and t^2+5t+6 = 506 remainder->2

Clearly see a pattern that the remainder is going to be 2



Stmt II

t^2/7 remainder is 1

Pick t=6 t^2+5t+6 gives a remiander 2 when divided by 7

Pick t=8 t^2+5t+6 gives a remiander 5 when divided by 7

INSUFF

Choose A

For prob 2 check this out:

https://www.beatthegmat.com/gmat-prep-p- ... 24991.html

and/or

https://www.beatthegmat.com/remainders-t22704.html#95683

2 different approaches-> Pick on the approach that u feel most comfortable with.

Good luck!

Regards,
CR