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11 Nov 2023, 06:33
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
52% (01:51) correct
48%
(01:51)
wrong
based on 107
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If n is an integer, is (n - 1)(n + 1) a multiple of 24?
(1) n is odd.
(2) n is not divisible by 3.
(1) n is odd.
(2) n is not divisible by 3.
Updated on: 14 Nov 2023, 00:43
Originally posted by VibhuAnurag on 14 Nov 2023, 00:09.
Last edited by VibhuAnurag on 14 Nov 2023, 00:43, edited 1 time in total.
Last edited by VibhuAnurag on 14 Nov 2023, 00:43, edited 1 time in total.
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Edited and corrected:
The answer should be (C).
(1) n is odd:
Let n = 3 --> (n - 1)(n + 1) = 2*4 --> No
Let n = 23 --> (n - 1)(n + 1) = 22*24 --> Yes
Conflicting answers, hence, insufficient.
(2) n is not divisible by 3 (we can take the same numbers again for the sake of simplicity):
Let n = 2 --> (n - 1)(n + 1) = 1*3 --> No
Let n = 23 --> (n - 1)(n + 1) = 22*24 --> Yes
Conflicting answers, hence, insufficient.
Combined:
n is odd and not divisible by 3.
Let n = 1 --> (n - 1)(n + 1) = 0*2 --> Yes
Let n = 5 --> (n - 1)(n + 1) = 4*6 --> Yes
Let n = 7 --> (n - 1)(n + 1) = 6*8 --< Yes
We always get yes. Hence, sufficient.
The answer should be (C).
(1) n is odd:
Let n = 3 --> (n - 1)(n + 1) = 2*4 --> No
Let n = 23 --> (n - 1)(n + 1) = 22*24 --> Yes
Conflicting answers, hence, insufficient.
(2) n is not divisible by 3 (we can take the same numbers again for the sake of simplicity):
Let n = 2 --> (n - 1)(n + 1) = 1*3 --> No
Let n = 23 --> (n - 1)(n + 1) = 22*24 --> Yes
Conflicting answers, hence, insufficient.
Combined:
n is odd and not divisible by 3.
Let n = 1 --> (n - 1)(n + 1) = 0*2 --> Yes
Let n = 5 --> (n - 1)(n + 1) = 4*6 --> Yes
Let n = 7 --> (n - 1)(n + 1) = 6*8 --< Yes
We always get yes. Hence, sufficient.
14 Nov 2023, 00:29
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VibhuAnurag
0 is a multiple of every integer.
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. \(0! = 1! = 1\).
