f i and j are integers, is i + j an even integer?
(1) i < 10
(2) i = j
B
OG If i and j are integers
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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We need to determine whether i + j is an even integer. Remember:AbeNeedsAnswers wrote:f i and j are integers, is i + j an even integer?
(1) i < 10
(2) i = j
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
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