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11 Nov 2023, 06:33
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C
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Difficulty:
65%
(hard)
Question Stats:
53% (01:51) correct
47%
(01:51)
wrong
based on 109
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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.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
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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. \(0! = 1! = 1\).
