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tanviet: Legendary Member; Posts: 1404; Joined: Tue May 20, 2008 6:55 pm; Thanked: 18 times; Followed by:2 members

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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Source: Beat The GMAT — Data Sufficiency | Fri Jan 22, 2010 8:49 pm

gmat740: MBA Student; Posts: 1194; Joined: Sat Aug 16, 2008 9:42 pm; Location: Paris, France; Thanked: 71 times; Followed by:17 members; GMAT Score:710

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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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 am; Thanked: 137 times; Followed by:5 members

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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tanviet: Legendary Member; Posts: 1404; Joined: Tue May 20, 2008 6:55 pm; Thanked: 18 times; Followed by:2 members

by tanviet » Sat Jan 23, 2010 1:19 am

this is from GMATprep

why 2) is not sufficient

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trindadesn: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Jul 23, 2009 4:23 am; Location: bombay; Thanked: 1 times

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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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » 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.