What is the remainder when a three-digit number ABC (where A, B and C

Question

What is the remainder when a three-digit number ABC (where A, B and C are its hundreds, tens and units digit respectively) is divided by 6?

(1) A + B + C = 3K + 13 where K is a positive integer.
(2) A + B + C = 19

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AryaSwagat · Answer

(1) A + B + C = 3K + 13 where K is a positive integer
If K is even then 3K is already divisible by 6, and 13 when divided by 6 leaves a remainder 1. 
If K is odd then 3K will leave a remainder 3 when divided by 6. So 3+13=16 when divided by 6 leaves a remainder of 4. 
Not Sufficient.
(2) A + B + C = 19
Alone not sufficient as 883 and 838 leave different remainders when divided by 6. 
Not Sufficient.

Combining Both.
We can see 19=3*2+13. So all the numbers in which sum of digits are 19 can be written in 3K+13 form. Any two we can test and verify if they leave different remainders.
883=870+13 and 838=825+13 leave different remainder when divided by 6.
Even combined not sufficient.

IMO   E

babyulikeit · Answer

Bunuel 
Can you please explain the solution?

Bunuel · Answer

There isn’t much to add here.

For a number ABC, we can express it as ABC = 6q + r, where r is the remainder when divided by 6. The sum of the digits is given as 19. If the number is odd, the remainder will be odd, and if the number is even, the remainder will be even. For instance, if the number is 199, the remainder when divided by 6 is 1, but if the number is 298, the remainder is 4. Therefore, even with both statements combined, they are not sufficient to determine the exact remainder.

Jon22 · Answer

Both statements independently show that ABCABCABC is not divisible by 6. Therefore, we can summarize that the number will have a remainder when divided by 6, but we don't know what the remainder is from these statements alone; they both confirm the same outcome.
Since both statements indicate that A+B+CA + B + CA+B+C is not divisible by 3, the remainder when ABCABCABC is divided by 6 will be  1  or  2 , depending on whether CCC is odd or even, respectively.
Thus, both statements are sufficient to conclude that the number ABCABCABC is not divisible by 6.
The final answer is:  Both statements are sufficient.

What is the remainder when a three-digit number ABC (where A, B and C

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GMAT Data Sufficiency (DS) Questions

What is the remainder when a three-digit number ABC (where A, B and C

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