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Is r+ s+ t an even number?

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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Jan 12, 2017 6:13 am
NandishSS wrote:Is r+ s+ t an even number?

(1) rs is an odd number.
(2) t is an even number.
Statements combined:

Case 1: r=1, s=1, t=2
In this case, r+s+t = 1+1+2 = 4, which IS an even number.

Case 2: r=0.5, s=2, t=2
In this case, r+s+t = 0.5 + 2 + 2 = 4.5, which is NOT an even number.

Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Brent@GMATPrepNow » Thu Jan 12, 2017 11:33 am
The trap in this question is that many people will assume that r, s and t are integers.
This is a common mistake that students make with Data Sufficiency question.
This common mistake and others are highlighted in the following videos:
- Avoiding Common Mistakes - Part I: https://www.gmatprepnow.com/module/gmat ... video/1097
- Avoiding Common Mistakes - Part II: https://www.gmatprepnow.com/module/gmat ... video/1105

IF it were the case that r, s and t are integers, then the correct answer would be C


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by [email protected] » Thu Jan 12, 2017 2:30 pm
Hi NandishSS,

We're asked if R+S+T is an EVEN number. This is a YES/NO question and it can be solved by TESTing VALUES. However, it's worth noting that we are NOT told anything about the 3 variables. They might be integers or non-integers and that is an important distinction here - we would need to be given really specific information about the three variables to definitively answer this question.

1) (R)(S) is an ODD number.

This tells us nothing about T, so there's no way to know whether the sum is an even or not.
Fact 1 is INSUFFICIENT

2) T is an EVEN number.

This tells us nothing about R and S, so there's no way to know whether the sum is an even or not.
Fact 2 is INSUFFICIENT

Combined, we know that...
(R)(S) is an ODD number.
T is an EVEN number.

IF....
R=1
S=1
T=0
Then the sum is 2 and the answer to the question is YES.

IF....
R=1/2
S=2
T=0
Then the sum is 2.5 and the answer to the question is NO.
Combined, INSUFFICIENT

Final Answer: E

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by Jay@ManhattanReview » Sun Jan 22, 2017 1:10 am
NandishSS wrote:Is r+ s+ t an even number?

(1) rs is an odd number.
(2) t is an even number.

OA:E

Source:Math Revolution
Whenever we deal with even/odd numbers, we deal with integers. Note that the sum of two numbers can be even/odd even though none is even/odd. For example. 2.5 + 0.5 = 3 (odd) and 1.5 + 0.5 = 2 (even).

We have to see whether r+ s+ t is an even or not. If r+ s+ t is not an even number, it does not mean that it must be odd. it may be a real number.

With these concepts in mind, let's see each statement one by one.

S1: rs is an odd number.

"rs is an odd number" means that either r and s each are odd or they are real. Say if r = 1/2 and s = 2. Moreover, we do not know the value of t. So this statement can be dumped on account of a couple of reasons.

S2: t is an even number.

Clearly, insufficient.

S1 & S2:

Case 1: r (Odd) + s (Odd) + t (Even) = Even. Answer is YES.
Case 2: r (fraction = 1/2) + s (2) + t (Even) = Odd. Answer is NO. No unique answer.

Answer: E

Hope this helps!

-Jay
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