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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 gmat740
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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
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
 thephoenix
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s1) WHEN T IS DIV BY 7 REM IS 6>for t^2 remainder will be 36duongthang 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
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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Why is st 2 insuff...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....
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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Why couldn't t^2 = 8, 15, 22, 29, ...?trindadesn wrote:Why is st 2 insuff...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....
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?
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 nonintegers, we could have t= 1, 6, 13, ... which give us a different remainder than their positive counterparts.
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i looked this problem up and the OA is A, but t is a positive integer.
https://www.manhattangmat.com/forums/if ... t4697.html
https://www.manhattangmat.com/forums/if ... t4697.html