What is the value of x?
(1) x! is odd
(2) x is even
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What is the value of x?
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Brent@GMATPrepNow
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Target question: What is the value of x?himu wrote:What is the value of x?
(1) x! is odd
(2) x is even
Statement 1: x! is odd
First, x cannot be an integer greater than 1, because 2!, 3!, 4!, 5!(etc) all have a 2 in their product, so they all evaluate to be even.
So, x could equal 1 (since 1! = 1, which is odd)
Or x could equal 0 (since 0! = 1, which is odd)
Why does 0! = 1? Well, it's basically something that mathematicians need to agree on so that other mathematical concepts (involving factorials) work out nicely.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is even
Lots of possible values for x (x = 0, 2, 4, 6, etc.)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 tells us that x = 0 or x = 1
Statement 2 says x is even, so x must equal 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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send2dar
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for all x >= 2, x! will be even (as 2 is a factor in the x!).
x! is odd only when x = 0 or 1 (so statement 1 is not sufficient)
There is a multitude of solutions to statement 2 so (stmt 2 is not sufficient)
combine both statements, x = 0 is the only answer. So solution is C
x! is odd only when x = 0 or 1 (so statement 1 is not sufficient)
There is a multitude of solutions to statement 2 so (stmt 2 is not sufficient)
combine both statements, x = 0 is the only answer. So solution is C
Thanks
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