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OG If i and j are integers

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Source: — Data Sufficiency |

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by [email protected] » Thu Aug 24, 2017 6:08 pm
Hi AbeNeedsAnswers,

We're told that I and J are integers. We're asked if(I + J) is an even integer. This is a YES/NO question. We can solve it by TESTing VALUES.

1) I < 10

IF... I = 9 and J = 1, then the answer to the question is YES.
I = 9 and J = 2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) I = J

Fact 2 tells us that I and J are the SAME integer, so (I+J) can be rewritten as either 2I or 2J. Since the product of any integer and 2 results in an EVEN integer, the answer to the question is ALWAYS YES. You can also prove it with examples:
I = 1 and J = 1 ... total = 2
I = 2 and J = 2 ... total = 4
I = 3 and J = 3 ... total = 6
Etc.
Fact 2 is SUFFICIENT

Final Answer: B

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Rich
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by Scott@TargetTestPrep » Sun Jul 22, 2018 5:13 pm
AbeNeedsAnswers wrote:f i and j are integers, is i + j an even integer?

(1) i < 10
(2) i = j
We need to determine whether i + j is an even integer. Remember:

even + even = even

odd + odd = even

Thus, if we can determine that i and j are either both even or both odd, we will be able to answer the question.

Statement One Alone:

i < 10

Knowing that i is less than 10 is not enough to determine whether i + j is an even integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

i = j

Since we know i = j, we know that i and j are both even or both odd. Following our addition rules for even and odd numbers, we see that i + j must be even.

Statement two alone is sufficient to answer the question.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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