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remainder problem

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by gmat009 » Wed Oct 01, 2008 10:59 pm
What is the remainder when the sum of the positive integers x and y is divided by 6?
(1) When x is divided by 6, the remainder is 3.
(2) When y is divided by 6, the remainder is 1.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |
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by rdxb » Wed Oct 01, 2008 11:27 pm
The answer would be C i guess, as we'd need both statements a and b to proceed with the problem. M looking for a nice way to do these problems, as I just used the substitution method...

From what little I understand, problems like these are best solved by using the equation:
x=6q+ 3----------------(1)
y=6z+ 1----------------(2)

Now , adding both, we'd get
x+y= 6(q+z) +4 ----------------(3)
If we divide the above by 6, we'd get a remainder of 4 for any positive value(even zero) of q and z

I would like some of you guys to explain how to proceed , once we reach till equation (3) i.e the remainder concept.
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