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(n - 1) (n + 1) is divided by 24

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(n - 1) (n + 1) is divided by 24

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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

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Sanjeev K Saxena
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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.

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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.

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Nailya's nice; mals24's marvelous!!

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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

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what is the remainder when 0/24 ?

i thought it would be 0/24= quiotent 0 dividend 24 remainder 24

if n=1 (not a multiple of 2 or 3 )

(n-1)(n+1)=0

0/24 = 0 R 24

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J N wrote:
what is the remainder when 0/24 ?

i thought it would be 0/24= quiotent 0 dividend 24 remainder 24
0 is divisible by every number.
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.

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