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

Question

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

uday1409 · Answer

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

Bunuel · Answer

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.

Kurtosis · Answer

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MathRevolution · Answer

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.

KarishmaB · Answer

Here is a post discussing how to solve such questions: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/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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What is the remainder when the positive integer X is divided by 12?

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