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# Q is a certain positive integer. If Q is divided by 5, then

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Q is a certain positive integer. If Q is divided by 5, then [#permalink]  05 Mar 2003, 04:03
Q is a certain positive integer.

If Q is divided by 5, then the remainder is 3
If Q is divided by 7, then the remainder is 5

What is Q?

Consultant
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Is this a DS problem????
SVP
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simple problem solving
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Ans [#permalink]  05 Mar 2003, 08:56
Q = 68
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the answer is 33 not 68 boss!

sac22 is not quite at it better luck next time
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Expert's post
the answer is 33 not 68 boss!

sac22 is not quite at it better luck next time

Well, both 68 and 33 work.

There is no mentioning that Q is the smallest possible number.....
SVP
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forgive me guys, I meant 33 - the smallest Q
SVP
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My approach:

Q=5X+3
Q=7Y+5

Q+2=5X+5=5(X+1)
Q+2=7Y+7=7(Y+1)

Thus, Q+2 is evenly divisible both by 5 and by 7. Thus, since we need the smallest Q, we need to do Q=LCM (5, 7)–2=35–2=33.
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Re: Q [#permalink]  25 Mar 2004, 00:11
stolyar wrote:
Q is a certain positive integer.

If Q is divided by 5, then the remainder is 3
If Q is divided by 7, then the remainder is 5

What is Q?

from the first, Q = 5k+3
from the second, 5k+3 = 5 (7)

5(k-1) = 4 (7)

k-1 = 5 (mod 7)
k = 6 (7)

Q = 5(7m+6) +3 = 35m+33 = 35n -2 where n is an integer
Re: Q   [#permalink] 25 Mar 2004, 00:11
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