Data Sufficiency

If t is a postive integer and r is the remainder when t-squared+5t+6 is divided by 7, what is the value of r?

1) When t is divided by 7, the remainder is 6.
2) When t-squared is divided by 7, the remainder is 1.

How to solve this without taking heaps of time?

Thank you!


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(t^2 + 5t+6)/7 = t^2/7 + 5t/7 + 6/7

Looking at both 1 and 2 they are not enough , the only option is to combine them
from second statement t^2/7 has remainder 1 and 6/7 has remainder 6 so combining them (6+1) /7 will leave 0 remainder,

So if we find the remainder for 5t/7 we solve the puzzle

from statement 1, t= 7k + 6
Multiply by 5 => 5t = 35k + 30
5t/7=35k/7 + 30 /7
will always have remainder 2 as 30/7 leaves remainder 2

Choice C

the answer was A... and I didn't really follow your solution. I was thinking that maybe the equation should be factored or something?

Refer to

https://www.beatthegmat.com/t-2-5t-6-t20195.html


Morgoth has posted an excellent explanation (one of the best solutions that I have seen in this forum)

thank you!

Patiod,
Please post OA's using SPOILER function if possible at the same time that u post the questions.


Let me know if u still have any questions on the actual DS question also!

Regards,
Cramya

patio-d wrote:If t is a postive integer and r is the remainder when t-squared+5t+6 is divided by 7, what is the value of r?

1) When t is divided by 7, the remainder is 6.
2) When t-squared is divided by 7, the remainder is 1.

How to solve this without taking heaps of time?

Thank you!


[/img]

well if I understand you correctly, you already know how to solve this problem but you are looking for a faster approach.

Question wants you to find R:

t-squared+5t+6 = 7(integer) + R

so in other words, if you can change the left side of the question into 7A+R format, R is your answer!

and you need to see that t-squared+5t+6 = (t+3)(t+2) in case!

1) t = 7a+ 6

(7a+9)(7a+8)divided by 7

(7a+7+2)(7a+7+1) ; so the remainder will always be 2.

SUFF



2) t-squared = 7b+1

t-squared - 1 = 7b

(t-1)(t+1) = 7b

t will have two values, and for each T value the Remainder will change

Insuf

IMO, hence A

It might be D , if I missed something in statement 2

It is A and u did not miss D.

Building upon what was said above just as a double check....

(t+1) (t-1) = 7 (some integer)

Either t-1 is a multiple of 7 or t+1 is a multiple of 7

Lets say t+1 is a multiple of 7 ASSUME t=6

(t+1) (t-1) = 7 * 5 = 7 (some integer which is 5) The remainder for t+3 t+2 divided by 7 here would be 9 * 8 /7 REMIANDER 2

Lets say t-1 is a multiple of 7 ASSUME t=8

(t+1) (t-1) = 9 * 7 = 7 (some integer which is 9) The remainder for t+3 t+2 divided by 7 here would be 11 * 10 /7 REMAINDER 5

TWO VALUES FOR REMAINDERS JUST BY LOOKING AT 2 CASES DONT KNOW WHICH ONE STMT IS INSUFF TO ANSWER THE QUESTION

what are OA's and what is the spoiler function? sorry i'm brand new...

Sorry for not being more specific.

OA's are official answers that you know are right for a given problem

SPOILER function (its one of the message body icons just below the subject) is just used to hide the OA so that we dont know the answer before we solve a problem (may also influence our thought process in solving the problem)

Eg: [spoiler]OA: whatever the correct choice is[/spoiler]

cramya wrote:It is A and u did not miss D.

Building upon what was said above just as a double check....

(t+1) (t-1) = 7 (some integer)

Either t-1 is a multiple of 7 or t+1 is a multiple of 7

Lets say t+1 is a multiple of 7 ASSUME t=6

(t+1) (t-1) = 7 * 5 = 7 (some integer which is 5) The remainder for t+3 t+2 divided by 7 here would be 9 * 8 /7 REMIANDER 2

Lets say t-1 is a multiple of 7 ASSUME t=8

(t+1) (t-1) = 9 * 7 = 7 (some integer which is 9) The remainder for t+3 t+2 divided by 7 here would be 11 * 10 /7 REMAINDER 5

TWO VALUES FOR REMAINDERS JUST BY LOOKING AT 2 CASES DONT KNOW WHICH ONE STMT IS INSUFF TO ANSWER THE QUESTION

Beautiful