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16 Sep 2014, 00:22
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What is the value of non-negative integer \(x\)?
(1) \(x!\) is odd
(2) \(x\) is even
(1) \(x!\) is odd
(2) \(x\) is even
16 Sep 2014, 00:22
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Official Solution:
What is the value of non-negative integer \(x\)?
(1) \(x!\) is odd.
Two values satisfy this condition: 0 and 1. \(0!=1\) and \(1!=1\). Not sufficient.
(2) \(x\) is even.
\(x\) can be any even number. Not sufficient.
(1)+(2) Since from (1), \(x\) can be either 0 or 1, and (2) states that \(x\) is even, then \(x=0\), which is even. Sufficient.
Answer: C
What is the value of non-negative integer \(x\)?
(1) \(x!\) is odd.
Two values satisfy this condition: 0 and 1. \(0!=1\) and \(1!=1\). Not sufficient.
(2) \(x\) is even.
\(x\) can be any even number. Not sufficient.
(1)+(2) Since from (1), \(x\) can be either 0 or 1, and (2) states that \(x\) is even, then \(x=0\), which is even. Sufficient.
Answer: C
General Discussion
15 Jul 2016, 02:15
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ZERO:
1. Zero is an INTEGER.
2. Zero is an EVEN integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.
3. Zero is neither positive nor negative (the only one of this kind).
4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).
5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x).
6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).
7. Division by zero is NOT allowed: anything/0 is undefined.
8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))
9. \(0^0\) case is NOT tested on the GMAT.
10. If the exponent n is positive (n > 0), \(0^n = 0\).
11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.
12. \(0! = 1! = 1\).
1. Zero is an INTEGER.
2. Zero is an EVEN integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.
3. Zero is neither positive nor negative (the only one of this kind).
4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).
5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x).
6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).
7. Division by zero is NOT allowed: anything/0 is undefined.
8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))
9. \(0^0\) case is NOT tested on the GMAT.
10. If the exponent n is positive (n > 0), \(0^n = 0\).
11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.
12. \(0! = 1! = 1\).
