GMAT Prep Question - Remainders

Question

Please show your working...

conocieur · Answer

I have the following idea

if t/7 has a remainder of 6 then the number is in the sequence 6,13,20...

such sequence is 7m + 6

if (t^2)/7 has a remainder of 1, such number should be in the sequence

8,15,22,29,36

such sequence is 7n+1

actually I already saw that 36 is there and is the square of 6


so I would go with C

ywilfred · Answer

1) t/7 = q + 6
t = 7q + 6

Substitute into equation t^2 + 5t + 6 gives: 49q^2 + 119q + 72

Divided by 7, the quotient is always 7q^2 + 17q + 10 while the remainder is always 2 

Sufficient.

2) t^2 = 7q+1
t^2 can be 8, 15, 22... ---> t = sqrt(8) = ~3, sqrt(15) = ~4, sqrt(22) = ~5 ...

And the remainder is 1, 6, 3 respectively.

Insufficient.

Ans A

macca · Answer

Anybody who can solve this properly??

M8 · Answer

Definitely 'A'.

From 1) t/7 the reminder is 6. 
t=13, or t=20 does not matter, according to the condition 1) reminder when t^2+5t+6 divided by 7 will always be   2  . 
Sufficient.


From 2) t^2/7 the reminder is 1.
t can be equal to 6 or 8, etc.
According to this reminder r can be equal to 1 or to 5, etc. 
so 2) by itself is insufficient.

Hope it's clear.

macca · Answer

Thanks M8, Picking numbers seems to be the right strategy on questions like these. I'd prefer a more math approach. :cry:

Just have to practice a bit on these :twisted:

jaynayak · Answer

Answer is A.

Picked numbers for this.

1) t=7q + 6 , pick two numbers for q and find T, use T in the equation (t+2)(t+3) and divide by 7 will see that for any two numbers the remainder is 2

2) do the same thing and you will see that remainders differ here.

GMAT Prep Question - Remainders

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