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What is the remainder when the positive integer X is divided by 12? [#permalink]
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Updated on: 17 Dec 2014, 06:34
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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
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Originally posted by uday1409 on 15 Dec 2014, 09:54.
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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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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17 Dec 2014, 06:33
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: manhattanremainderproblem93752.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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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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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: rulesforpostingpleasereadthisbeforeposting133935.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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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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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 ... spartii/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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