hard question from GMATPrep

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hard question from GMATPrep

by tanviet » Fri Jan 22, 2010 8:49 pm
Pls, help with this

r in remainder when t^2+5t+6 is divided by 7, what is 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

pls, help,thank

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by gmat740 » Fri Jan 22, 2010 9:33 pm
Given : t^2+5t+6 = 7k +r

where k = any constant number
Statement 1:

t = 7M+6
m = another constant number

Now put the value of t in the given equation

(7M+6)^2 + 5*(7M+6) + 6

49M^2+ 119M + 72

7M(7M + 17 + 10) + 2

So, 7M(7M + 17 + 10) = Multiple of 7

so r= 2

Only 1 is sufficient

Hope this Helps

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by thephoenix » Fri Jan 22, 2010 10:22 pm
duongthang wrote:Pls, help with this

r in remainder when t^2+5t+6 is divided by 7, what is 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

pls, help,thank
s1) WHEN T IS DIV BY 7 REM IS 6----->for t^2 remainder will be 36
and for 5t remainder will be 30
and for 6 rem is 6
tot is 72 and when 72 is div by 7 rem is 2 hence r =2( suff)

s2) we dnt know about t hence insuff....

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by tanviet » Sat Jan 23, 2010 1:19 am
this is from GMATprep

why 2) is not sufficient

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by trindadesn » Sat Jan 23, 2010 4:35 am
thephoenix wrote:
s1) WHEN T IS DIV BY 7 REM IS 6----->for t^2 remainder will be 36
and for 5t remainder will be 30
and for 6 rem is 6
tot is 72 and when 72 is div by 7 rem is 2 hence r =2( suff)

s2) we dnt know about t hence insuff....
Why is st 2 insuff...

for t^2 to leave a remainder of 1 when divided by 7, t^2 must be: 1, 36, 169, 400 ......which give corresponding values of t= 1,6,13,20 respectively.

this when plugged into the eq gives remainder = 1 only.

IMO st 2 is also suff and ans should D.

what is the OA?

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by [email protected] » Sun Jan 24, 2010 1:59 am
trindadesn wrote:
thephoenix wrote:
s1) WHEN T IS DIV BY 7 REM IS 6----->for t^2 remainder will be 36
and for 5t remainder will be 30
and for 6 rem is 6
tot is 72 and when 72 is div by 7 rem is 2 hence r =2( suff)

s2) we dnt know about t hence insuff....
Why is st 2 insuff...

for t^2 to leave a remainder of 1 when divided by 7, t^2 must be: 1, 36, 169, 400 ......which give corresponding values of t= 1,6,13,20 respectively.

this when plugged into the eq gives remainder = 1 only.

IMO st 2 is also suff and ans should D.

what is the OA?
Why couldn't t^2 = 8, 15, 22, 29, ...?

Remember, we can't assume anything in DS - nowhere does it say that t is an integer.

If you let t = root8, for example, you get a different answer to the question.

Also, we don't know the sign of t; even ignoring non-integers, we could have t= -1, -6, -13, ... which give us a different remainder than their positive counterparts.
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by rahul.s » Wed Feb 24, 2010 5:43 am
what's the OA?

for statement (1), why can't we consider t = 6?
Last edited by rahul.s on Wed Feb 24, 2010 5:53 am, edited 1 time in total.

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by rahul.s » Wed Feb 24, 2010 5:45 am
i looked this problem up and the OA is A, but t is a positive integer.

https://www.manhattangmat.com/forums/if- ... t4697.html