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Understanding remainders

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Understanding remainders

by detsaw » Thu Mar 26, 2009 8:31 pm
I am taking my GMAT tomorrow and I am still having trouble understanding number properties when it comes to remainders. I've looked over solutions for these kinds over problems again and again but I cant seem to understand why one of these would be insufficient whereas the other is in these 2 qs


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.

A

If p and n are positive integers and p > n, what is the remainder when p^2 - n^2 is divided by 15?

1) The remainder when p + n is divided by 5 is 1.

2) The remainder when p - n is divided by 3 is 1.

E


How do I distinguish?
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by cramya » Thu Mar 26, 2009 9:05 pm
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
Last edited by cramya on Thu Mar 26, 2009 9:19 pm, edited 1 time in total.
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by cramya » Thu Mar 26, 2009 9:10 pm
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
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