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What is the remainder when the positive integer x is divided

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What is the remainder when the positive integer x is divided [#permalink] New post 15 Apr 2007, 04:57
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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.

[Reveal] Spoiler:
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: )
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Sep 2014, 08:04, edited 2 times in total.
Edited the question and added the OA.
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Re: What is the remainder when the positive integer x is divided [#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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Re: What is the remainder when the positive integer x is divided [#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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Re: What is the remainder when the positive integer x is divided [#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.
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Re: integer ?? [#permalink] New post 20 Apr 2009, 03:16
tenaman10 wrote:
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.


In many remainders questions, it's enough just to find a couple of numbers that 'work' with the given information, and if you simply list the first few numbers that satisfy each statement, it's easy to judge if the statements together are sufficient:

1) x = 5, 17, 29, 41, 53, 65, 77, 89 ...
2) x = 11, 29, 47, 65, 83, 101 ...

Since 29 and 65 give different remainders when you divide by 8, the answer is E.

More abstractly, when combining two statements like the above, the pattern will be based on the LCM of the two divisors. Here, we can consider dividing x by 36 = LCM(12, 18).

Notice that, if Statement 1 is true, the remainder will be 5, 17 or 29 when x is divided by 36.
If Statement 2 is true, the remainder will be 11 or 29 when x is divided by 36.
If both Statements are true, the remainder therefore must be 29 when x is divided by 36.

That's still not sufficient, as above; x could be 29, or x could be 65.
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Re: What is the remainder when the positive integer x is divided [#permalink] New post 05 Sep 2014, 22:37
ricokevin wrote:
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: )



number plugging -->

1. x = k12+5

k = 0,1,2,3,4.....
x= 5, 17,29,41,53,65...

now x/ 8 --> 5,1,5,1,.....
Not suff

2. x=k18+11
k = 0,1,2,3,4.....
x=11,29,47,65...
nox x/8 --> 3, 5 ,7, 1.....

Not suff..

1+2...

from both we got 29 & 65 are common but still reminders are different.

29 gives rem 5 whereas 65 gives rem 1.

Hence E
Re: What is the remainder when the positive integer x is divided   [#permalink] 05 Sep 2014, 22:37
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