The easiest way to solve this problem would require the below knowledge

Odd+Odd=Even

Even+Even=Even

Odd+Even=Odd

Even+Odd=Odd

Now the first question just states that a,b,c are integers. We still do not know whether they are even or odd. To be divisible by 4, one of the below 2 scenarios need to occur

1. Either 2 numbers are even

2. One number is a multiple of 4

Now let's take the given statements one by one

1. This tells us that

a+b+2c is even. Since, 2c is always even irrespective of whether c is even or odd, we have no information about c. However, since 2c is even, we know that a+b also needs to be even for the sum to be even. This gives rise to two scenarios

i. a=even, b=even

ii. a=odd and b= odd

Since, we have no further information to determine which of the two is true, we cannot proceed with this. INSUFFICIENT.

2. This tells us that a+2b+c=odd

Since, we know that 2b is always even irrespective of whether b is even or odd, we have no idea about b. However, since 2b is even and the sum is odd, a+c needs to be odd since only a sum of even and odd adds up to an odd number. This can happen only in two ways

i. a=odd and c=even

ii a=even and c=odd

Since, again we have no further info, we cannot proceed further with these statements. INSUFFICIENT.

Together, we still get the four conclusions that we got from 1 and 2.

i. a=even, b=even

ii. a=odd and b= odd

i. a=odd and c=even

ii a=even and c=odd

However, there is no overlap between these four distinct scenarios. Hence, INSUFFICIENT.

Answer=E

This approach might initially confuse you but the more you practice this approach, the lesser time this will take to solve such problems.

Hope it helps!

alexpavlos wrote:

If a + b+ c are integers, is abc divisible by 4?

1) a + b + 2c is even

2) a + 2b + c is odd

Can anyone please show me what is the festet and most "elegant" way of solving this? Do you just try each scenario?

Thanks!

Alex

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Kris

Instructor at Aspire4GMAT

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