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What is the remainder when the positive integer x is divided

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Senior Manager
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What is the remainder when the positive integer x is divided [#permalink] New post 15 Apr 2007, 04:57
00:00
A
B
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D
E

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(N/A)

Question Stats:

50% (01:01) correct 50% (00:55) wrong based on 4 sessions
What is the remainder when the positive integer x is divided by 8?
(1) When x is divided by 12, the remainder is 5.
(2) When x is divided by 18, the remainder is 11.

OA: E

When a number must satisfy two different divisible and remainder conditions, you could use what is known as "the Chinese remainder theorem" that uses modular arithmetic. Does anyone know how to apply that theorem to solve this problem?

Or how would you guys solve this in 2 min? :?

(I picked numbers :oops: )
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 [#permalink] New post 15 Apr 2007, 07:24
Picking numbers is a great way to go!

Clearly, neither is sufficient

We know that x=12k+5 so that x € {5,17,29,42,53,65...}

Also x=18m+11 so that x€ {11,29,47,65...}

29 and 65, both possible values of x, yield different remainders
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 [#permalink] New post 15 Apr 2007, 08:10
Ok guys this E..

here is why..remember PRIMES...

x=8M + R? where M and R are some integers...

1) x=12M+5; well..12 has 2^2 and 3... 8 has 2^3 so..we dont have enuff 2s to make any decision.. INSUFF

2) x=18M+11; well again look at the primes, 18 has 2 and 3^2; again not enuff 2s ..so Insuff..

together..INSUFF..we still dont have enuff 2s..we need a term that has at least 3 2s ..
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 [#permalink] New post 15 Apr 2007, 09:41
kevincan wrote:
Picking numbers is a great way to go!

Clearly, neither is sufficient

We know that x=12k+5 so that x € {5,17,29,42,53,65...}

Also x=18m+11 so that x€ {11,29,47,65...}

29 and 65, both possible values of x, yield different remainders


I agree with kevincan. i pick E

Javed.

Cheers!
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 [#permalink] New post 18 Apr 2007, 00:46
hey fresinha,
could u explain ur explanation in detail? I dont know the rule of primes in this case.
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 [#permalink] New post 18 Apr 2007, 01:01
I have used the picking numbers method, could not think of anything else other than this. I agree with Kevincan.
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 [#permalink] New post 18 Apr 2007, 11:47
OK, in order to know the remainder..we need to make sure that the statement provide us enuff info to compare with the question stem..

we are asked with is the remainder when X is divided by 8..well 8 has 3 2s..right!

OK statement 1) says X divided by 12 remainder is 5..well...we know that 12 has 2 2s..which is not the same as having 3 2s...so this statement is going to be insuff..

OK statement 2) says x divided by 18, remainder is 11...well 18 again has only 1 2 as a prime factor..again we need some number that has 3 2s...to conclusively anything..so Insuff

combined..again we dont know if the X has 3 2s or not..insuff..

shahrukh wrote:
hey fresinha,
could u explain ur explanation in detail? I dont know the rule of primes in this case.
  [#permalink] 18 Apr 2007, 11:47
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