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# If t is a positive integer and the r is the remainder when

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If t is a positive integer and the r is the remainder when [#permalink]

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03 Jun 2006, 23:21
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If t is a positive integer and the r is the remainder when t^2+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^2 is divided by 7, the remainder is 1.
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05 Jun 2006, 06:37
amansingla4 wrote:
C.....

Please explain how you got C.
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05 Jun 2006, 07:17
(t+2)(t+3) = 7K + r

(1) let t=6, 13, ...
t^2+5t+6 = 72, 240, ...
Remainder = 2
Sufficient

(2) same way as with (1) sufficient

Hence D
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05 Jun 2006, 07:33
dinesh8 wrote:
If t is a positive integer and the r is the remainder when t^2+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^2 is divided by 7, the remainder is 1.

I came up with C.

Statement 2: We know t^2 when divided by 7 gives remainder 1

e.g. 36, 64, 139 (i.e. 6^2, 8^2, 13^2)

So,

t^2 + 6 must be divisible by 7 (if you add the remainder 1 to 6)

But we do not know anything about 5t hence INSUFF.

St.1: When t is divided by the remainer is 6. INSUFF

Together,

From 1 we know t^2 + 6 gives remainder 0
From 2 we know 5t gives remainder 6

Hence the remainder for t^2 + 5t + 6 = 6

Took me close to 4 mins to get this by the way. What is the OA?
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05 Jun 2006, 07:45
tapan22 wrote:
dinesh8 wrote:
If t is a positive integer and the r is the remainder when t^2+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^2 is divided by 7, the remainder is 1.

I came up with C.

Statement 2: We know t^2 when divided by 7 gives remainder 1

e.g. 36, 64, 139 (i.e. 6^2, 8^2, 13^2)

So,

t^2 + 6 must be divisible by 7 (if you add the remainder 1 to 6)

But we do not know anything about 5t hence INSUFF.

St.1: When t is divided by the remainer is 6. INSUFF

Together,

From 1 we know t^2 + 6 gives remainder 0
From 2 we know 5t gives remainder 6

Hence the remainder for t^2 + 5t + 6 = 6

Took me close to 4 mins to get this by the way. What is the OA?

I agree with gmatmba the answer should be D and remainder is always 2.

P.S. I am having a wretched day today. Seems like all answers I posted today were wrong.
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07 Jun 2006, 07:47
A..
t=8, the remainder you get is 5.
t=6, the remainder is 2
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09 Jun 2006, 03:05
It is A.

Eqn (2) gives different answers for t=1 & t=6 so not sufficient.

OA time.....................
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09 Jun 2006, 04:32
xsports wrote:
A..
t=8, the remainder you get is 5.
t=6, the remainder is 2

Agree with A.
1)
(t+2)(t+3)
T divided by 7 gives remainder 6
Remainder for t+2 = 1
Remainder for t+3 = 2
Hence remainder = 2

2) t^2 gives remainder 1. 6 and 8 both satisfy the equation.
when t=6, remainder of eq = 2
when t= 8, remainder of eq = 5
hence not suff

09 Jun 2006, 04:32
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