If r, s, and t are integers, is rs + t divisible by 2?

Question

(1) r is divisible by 3, and s is even.

(2) t is divisible by 3.

pushpitkc · Answer

If r, s, and t are integers, is rs + t divisible by 2?
(1) r is divisible by 3, and s is even.
Whatever the value of r, when multiplied by an even number will become even.
But we don't know the value of t. Hence not sufficient

(2) t is divisible by 3.
t can take both odd or even values. Also, we don't have a value for the rs part of the expression
Hence, not sufficient.

On combining both the equations we can determine whether the sum is odd or even,
because of which we cannot say with certainty, if the expression rs + t is divisble by 2.(Option E)

yezz · Answer

the questions asks whether rs+t is even , thus for this to be even rs and t have to be either both even or both odd

from 1

rs = 6m .... insuff

from 2

t = 3k... insuff

both

rs+t = 6m+3k ... thus for this to be even we have to know what k is .... insuff...E

gurmukh · Answer

Both the statements individually are not sufficient because they individually don't say anything about all three variables.
Combining both the statements
rs is a multiple of 6 hence always even
t is divisible by 3 so can be even or odd
Hence rs+t can be even or odd
Therefore we can't say whether rs+t is even or odd. Hence we can't say whether it is divisible by 2 or not.
Therefore option E is the answer

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CrackverbalGMAT · Answer

rs+t will be divisible by 2 if it is EVEN. rs+t can be even in two ways:

If rs = odd and t = odd, rs+t = odd + odd = even. Here, rs can be odd only when both r and s are odd. Even if one of r/s is even, rs will be even.

If rs = even and t = even, rs + t = even + even = even. Here, rs can be even if at least one of r/s is even.

From statement I alone, r is divisible by 3 and s is even. 
So, r can be either odd or even; however, s is even, so rs will definitely be even. But, we do not have any data about t. Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, t is divisible by 3. This means that t is odd or even. But we do not have any data about rs. Statement II alone is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, we have the following:
From statement I,we know that rs is even. From statement II,we know that t is either even or odd. Therefore, even after combining the statements, we cannot conclusively say whether rs+t is even or odd and hence cannot say whether it is divisible by 2. 
The combination of statements is insufficient. Answer option C can be eliminated.

The correct answer option is E .

Hope that helps!

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If r, s, and t are integers, is rs + t divisible by 2?

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If r, s, and t are integers, is rs + t divisible by 2?

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