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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?

Re: What is the remainder when the positive integer x is divided [#permalink]

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22 Apr 2016, 07:20

1

This post received KUDOS

calinerie wrote:

Thanks for the explanation! I was wondering if there is any short cut to solve these types of questions? It took me a while to compile all the numbers + I could have easily missed 65 as it is down the line...

I did it this way:

(1) \(12q + 5 = x\) insuf

(2) \(18b + 11 = x\) insuf

Together: \(12q + 5 = 18b +11\)

\(12q - 18b = 6\)

\(6(2q - 3b) = 6\)

This leads us to \(2q - 3b = 1\)

I replace q by b in equation 1:

\(12(\frac{1 + 3b}{2}) +5 = x\)

\(18b + 11 = x\)

Statement 1 becomes equal to statement 2 : Hence insufficient.

Re: What is the remainder when the positive integer x is divided [#permalink]

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18 Apr 2007, 12:47

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.

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:

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]

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05 Sep 2014, 23:37

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?

Re: What is the remainder when the positive integer x is divided [#permalink]

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02 Mar 2016, 06:38

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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?

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 )

Hi, and welcome to GMAT Club.

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked. C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked. D. EACH statement ALONE is sufficient to answer the question asked. E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Re: What is the remainder when the positive integer x is divided [#permalink]

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14 Mar 2016, 15:12

Thanks for the explanation! I was wondering if there is any short cut to solve these types of questions? It took me a while to compile all the numbers + I could have easily missed 65 as it is down the line...

luckyme17187 wrote:

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?

What is the remainder when the positive integer x is divided [#permalink]

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23 May 2016, 09:38

Icecream87 wrote:

calinerie wrote:

Thanks for the explanation! I was wondering if there is any short cut to solve these types of questions? It took me a while to compile all the numbers + I could have easily missed 65 as it is down the line...

I did it this way:

(1) \(12q + 5 = x\) insuf

(2) \(18b + 11 = x\) insuf

Together: \(12q + 5 = 18b +11\)

\(12q - 18b = 6\)

\(6(2q - 3b) = 6\)

This leads us to \(2q - 3b = 1\)

I replace q by b in equation 1:

\(12(\frac{1 + 3b}{2}) +5 = x\)

\(18b + 11 = x\)

Statement 1 becomes equal to statement 2 : Hence insufficient.

What happens when they are equal?

My understanding is that if we add both the equation it will be 0. And if we just take "18b + 11 = x" then we can various values. So insufficient.

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