If n is a positive integer and r is the remainder when (n - 1) (n + 1) is divided by 24, what is the value of r?
(1) n is not divisible by 2.
(2) n is not divisible by 3.
OA C
(n - 1) (n + 1) is divided by 24
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- sanju09
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- Nailya
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Try picking numbers
1) n is not divisible by 2
n=3 (3-1)(3+1)=8 8:24=0+8 r=8
n=5 (5-1)(5+1)=24 24:24=1+0 r=0
Two different values of r, this means that the condition is insufficient
2) n is not divisible by 3
n=2 (2-1)(2+1)=3 3:24=0+3 r=3
n=5, as we know already r=0
Two different values, means condition is insufficient
1 and 2) n is not divisible by 2 and 3
n=5 r=0
n=7 (7-1)(7+1)=48 48:24=2 r=0
n=11 (11-1)(11+1)= 120 120:24=5 r=0
We can try other numbers and the result will yield to r=0, therefore answer is C.
1) n is not divisible by 2
n=3 (3-1)(3+1)=8 8:24=0+8 r=8
n=5 (5-1)(5+1)=24 24:24=1+0 r=0
Two different values of r, this means that the condition is insufficient
2) n is not divisible by 3
n=2 (2-1)(2+1)=3 3:24=0+3 r=3
n=5, as we know already r=0
Two different values, means condition is insufficient
1 and 2) n is not divisible by 2 and 3
n=5 r=0
n=7 (7-1)(7+1)=48 48:24=2 r=0
n=11 (11-1)(11+1)= 120 120:24=5 r=0
We can try other numbers and the result will yield to r=0, therefore answer is C.
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(n-1), n, (n+1) are consecutive numbers.
24 = 3*(2^3)
St 1: n is odd
That means (n-1) and (n+1) are even
48*50 when divided by 24 the remainder is 0
26*28 when divided by 24 the remainder is not 0
Insuff
St 2: n is not divisible by 3
which means either (n-1) or (n+1) is divisible by 3, because if there are 3 consecutive numbers then one of the numbers is divisible by 3.
25*27 when divided by 24 the remainder is not 0
24*26 when divided by 24 the remainder is 0
Insuff
Combining 1 and 2
We know (n-1) and (n+1) are even and one of them is divisible by 3.
36*38 when divided by 24 remainder is 0
72*74 when divided by 24 remainder is 0
Suff
Answer is C.
24 = 3*(2^3)
St 1: n is odd
That means (n-1) and (n+1) are even
48*50 when divided by 24 the remainder is 0
26*28 when divided by 24 the remainder is not 0
Insuff
St 2: n is not divisible by 3
which means either (n-1) or (n+1) is divisible by 3, because if there are 3 consecutive numbers then one of the numbers is divisible by 3.
25*27 when divided by 24 the remainder is not 0
24*26 when divided by 24 the remainder is 0
Insuff
Combining 1 and 2
We know (n-1) and (n+1) are even and one of them is divisible by 3.
36*38 when divided by 24 remainder is 0
72*74 when divided by 24 remainder is 0
Suff
Answer is C.
- sanju09
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Nailya's nice; mals24's marvelous!!
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- Atekihcan
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0 is divisible by every number.J N wrote:what is the remainder when 0/24 ?
i thought it would be 0/24= quiotent 0 dividend 24 remainder 24
So, when 0 is divided by any number, the remainder is 0.
Apart from that, when an integer M is divided by some integer N, then the resulting operation will be of the form M = qN + r, where q and r are also integers and M = dividend, N = divisor, q = quotient, and r = remainder. And r < q < M.
In this case, 0 = 0*24 + 0
As we are dividing 0 by 24, the resulting remainder cannot be greater than 0 - this should have been your clue that remainder cannot be 24.