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16 Sep 2014, 00:44
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If \(x\) is an integer and \(|1-x| \lt 2\), then which of the following must be true?
A. \(x\) is not a prime number
B. \(x^2+x\) is not a prime number
C. \(x\) is positive
D. Number of distinct positive factors of \(x+2\) is a prime number
E. \(x\) is not a multiple of an odd prime number
A. \(x\) is not a prime number
B. \(x^2+x\) is not a prime number
C. \(x\) is positive
D. Number of distinct positive factors of \(x+2\) is a prime number
E. \(x\) is not a multiple of an odd prime number
16 Sep 2014, 00:44
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Official Solution:
If \(x\) is an integer and \(|1-x| \lt 2\), then which of the following must be true?
A. \(x\) is not a prime number
B. \(x^2+x\) is not a prime number
C. \(x\) is positive
D. Number of distinct positive factors of \(x+2\) is a prime number
E. \(x\) is not a multiple of an odd prime number
\(|1-x|\) is just the distance between 1 and \(x\) on the number line. We are told that this distance is less than 2:
--(-1)----1----3-- so, \(-1 < x < 3\). Since it is given that \(x\) is an integer, then \(x\) can be 0, 1 or 2.
A. \(x\) is not a prime number. Not true if \(x=2\).
B. \(x^2+x\) is not a prime number. Not true if \(x=1\).
C. \(x\) is positive. Not true if \(x=0\).
D. Number of distinct positive factors of \(x+2\) is a prime number. True for all three values of \(x\).
E. \(x\) is not a multiple of an odd prime number. Not true if \(x=0\), since zero is a multiple of every integer.
Answer: D
If \(x\) is an integer and \(|1-x| \lt 2\), then which of the following must be true?
A. \(x\) is not a prime number
B. \(x^2+x\) is not a prime number
C. \(x\) is positive
D. Number of distinct positive factors of \(x+2\) is a prime number
E. \(x\) is not a multiple of an odd prime number
\(|1-x|\) is just the distance between 1 and \(x\) on the number line. We are told that this distance is less than 2:
--(-1)----1----3-- so, \(-1 < x < 3\). Since it is given that \(x\) is an integer, then \(x\) can be 0, 1 or 2.
A. \(x\) is not a prime number. Not true if \(x=2\).
B. \(x^2+x\) is not a prime number. Not true if \(x=1\).
C. \(x\) is positive. Not true if \(x=0\).
D. Number of distinct positive factors of \(x+2\) is a prime number. True for all three values of \(x\).
E. \(x\) is not a multiple of an odd prime number. Not true if \(x=0\), since zero is a multiple of every integer.
Answer: D
27 Sep 2022, 03:41
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ZERO:
1. Zero is an INTEGER.
2. Zero is an EVEN integer.
3. Zero is neither positive nor negative (the only one of this kind).
4. Zero is divisible by EVERY integer except 0 itself (\(\frac{0}{x} = 0\), 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.
3. Zero is neither positive nor negative (the only one of this kind).
4. Zero is divisible by EVERY integer except 0 itself (\(\frac{0}{x} = 0\), 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. \(0! = 1! = 1\).
