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What is the remainder when the positive integer X is divided by 12?

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What is the remainder when the positive integer X is divided by 12? [#permalink]

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What is the remainder when the positive integer X is divided by 12?

(1) When X is divided by 3 the remainder is 2
(2) When X is divided by 4 the remainder is 3
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Dec 2014, 06:34, edited 1 time 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 by 12? [#permalink]

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New post 15 Dec 2014, 10:01
i think the ans is C.


1) reminder when x/3=2
so x can take 5,8,11,14,17,20,23,26,29,32,35,..
Then reminder of x/12= 5,8,11,2,5,8,11...
insufficient

2) reminder when x/4=3
so x can take 3,7,11,15,19,23,27,31,35,39....
Then reminder of x/12= 3,7,11,3,7,11
insufficient
1+2) Common values for x that satify both stmt's are 11,23,35
Then reminder of x/12= 11,11,11
sufficient

Ans C
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Re: What is the remainder when the positive integer X is divided by 12? [#permalink]

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What is the remainder when the positive integer X is divided by 12?

(1) When X is divided by 3 the remainder is 2 --> x = 3q + 2 --> x could be 2, 5, 8, 11, 14, ... If x is 2, then the remainder upon division x by 12 will be 2 but if x is 5, then the remainder upon division x by 12 will be 5. Not sufficient.

(2) When X is divided by 4 the remainder is 3 --> x = 4p + 3 --> x could be 3, 7, 11, 15, 19, ... If x is 3, then the remainder upon division x by 12 will be 3 but if x is 7, then the remainder upon division x by 12 will be 7. Not sufficient.

(1)+(2) x = 3q + 2 and x = 4p + 3 implies that x = 12n + 11 (for more about deriving general formula check: manhattan-remainder-problem-93752.html#p721341), thus x divided by 12 gives the remainder of 11. Sufficient.

Answer: C.
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What is the remainder when the positive integer x is divided by 12? [#permalink]

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New post 23 May 2016, 09:45
What is the remainder when the positive integer x is divided by 12?

(1) When x is divided by 3, the remainder is 2.
(2) When x is divided by 4, the remainder is 3.

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Re: What is the remainder when the positive integer X is divided by 12? [#permalink]

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New post 23 May 2016, 10:22
bimalr9 wrote:
What is the remainder when the positive integer x is divided by 12?

(1) When x is divided by 3, the remainder is 2.
(2) When x is divided by 4, the remainder is 3.


Topic merged. Please do a thorough search before posting. Thank you.

Rules for posting: rules-for-posting-please-read-this-before-posting-133935.html#p1092822

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Re: What is the remainder when the positive integer X is divided by 12? [#permalink]

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New post 23 May 2016, 20:19
For remainder questions, you solve such questions by: direct substitution  find the first number that two numbers have in common as multiples  add the least common multiple of the numbers you divide by.

There is 1 variable (x) in the original condition. In order to match the number of variables to the number of equations, we need 1 equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer.

In the case of the condition 1), if we directly substitute, we get x=3p+2=2,5,8,11… Then, 2=12*0+2-->2, 5=12*0+5-->5. The answer is not unique and the condition is not sufficient.
In the case of the condition 2), if we directly substitute, we get x=4q+3=3,7,11..... Then, =12*0=3-->3, 7=12*0+7-->7. The answer is not unique and the condition is not sufficient.

Using the condition 1) and the condition 2), we find the x=11 (the first the number that two have in common as multiple). Then, we add the least common multiple of 3 and 4, which is 12. Then we get x=11, 23, 35,..... Since =12*0+11, 23=12*1+11, 35=12*2+11, we always get 11. The answer is unique and the condition is sufficient. Therefore, the correct answer is C.
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Re: What is the remainder when the positive integer X is divided by 12? [#permalink]

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New post 23 May 2016, 22:42
uday1409 wrote:
What is the remainder when the positive integer X is divided by 12?

(1) When X is divided by 3 the remainder is 2
(2) When X is divided by 4 the remainder is 3


Here is a post discussing how to solve such questions:
http://www.veritasprep.com/blog/2011/05 ... s-part-ii/

It is obvious that neither stmnt alone can be sufficient since we are considering divisibility by 12. We need to find the divisibility by both 3 and 4.

Stmnt 1: X = 3a + 2
Stmnt 2: X = 4b + 3

Try b = 0, 1 , 2... When b = 2, X = 11 which is also of the form 3a + 2.
So X can take the smallest value of 11.
Next values of X will be 12n + 11 where n is a positive integer. In all these cases, the remainder will be 11.

Answer (C)
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Re: What is the remainder when the positive integer X is divided by 12? [#permalink]

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Re: What is the remainder when the positive integer X is divided by 12?   [#permalink] 30 Sep 2017, 07:03
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