When dealing with remainders and equations, it is often helpful to translate the words into formulas.

"When x is divided by 2, remainder is 1" --> This means that x is 1 more than a multiple of 2 --> \(x = 2a+1\), where \(a\) is an integer.
"y is divided by 8, remainder is 2" --> This means that y is 2 more than a multiple of 8 --> \(y = 8b+2\), where \(b\) is an integer.

Now if we plug those expressions into 2x + y we get:

\(2x + y = [2(2a+1)] + [8b+2]\)
\(= 4a+2 + 8b+2\)
\(= 4(a+2b+1)\)

So 2x + y = 4*(some integer), and is therefore a multiple of 4. The only answer choice that is a multiple of 4 is C) 12.

Answer: C
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Dave de Koos
GMAT aficionado

Hi,

Apart from the method stated above..
lesser error prone way would be
1) if x is divided by 2, the remainder is 1, that is x is odd..
if the same x multiplied by 2, ( 2x), and divided by 4 will give a remainder 2..

now if y divided by 8 leaves a remainder 2, y when divided by 4 will also give a remainder of 2..
so if 2x+y is divided by 4, it should give us a remainder of 2+2=4, meaning 2x+y should be div by 4..
only C fits in
C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

Hi Hari,

2 is a valid choice for y because when you divide 2 by 8, the answer is 0 with remainder 2.

In general, any time you divide a smaller integer by a larger integer, the result will be 0 with the remainder equal to the smaller number. If integer \(a\) is smaller than integer \(b\), then \(\frac{a}{b}\) = 0 with remainder \(a\).

I hope that helps!

Cheers,
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Dave de Koos
GMAT aficionado

I had to go back to the good old number testing method for this
\(2x + y\)
pick numbers for x and y that fulfils the conditions given.
2(3) + 2
6 + 2
8. Not in the option!

raise x to the next level
2(5) + 2
10 + 2
12
That's in the option!
Defnily their CANNOT be more than one possible value for \(2x + y\) in the options.
C.

next to least value of x=5
least value of y=2
2*5+2=12
C