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If x and n are +ve integers and when (n+1)(n-1) is divided

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If x and n are +ve integers and when (n+1)(n-1) is divided [#permalink] New post 23 Sep 2006, 09:06
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If x and n are +ve integers and when (n+1)(n-1) is divided by 24 the quotient is x and remainder is r . r= ??

a)2 is not the factor of n
b)3 is not the factor of n
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 [#permalink] New post 23 Sep 2006, 09:23
for me (C)

Statment 1: 2 is not the factor of n

o n=3
(n+1)*(n-1) = 4*2=8
=> 8 = 0*24 + 8
Remainder = 8

o n=5
(n+1)*(n-1) = 6*4=24
=> 24 = 1*24 + 0
Remainder = 0

INSUFF

Statment 2: 3 is not the factor of n

o n=2
(n+1)*(n-1) = 1*3=3
=> 3 = 0*24 + 3
Remainder = 3

o n=5

(n+1)*(n-1) = 6*4=24
=> 24 = 1*24 + 0
Remainder = 0

INSUFF

(1) & (2) together:
o n=1
(n+1)*(n-1) = 0*2=0
=> 0 = 0*24 + 0
Remainder = 0

o n=5
(n+1)*(n-1) = 6*4=24
=> 24 = 1*24 + 0
Remainder = 0

o n=7
(n+1)*(n-1) = 8*6
=> 2*(8*3) = 2*24 + 0
Remainder = 0

o n=11
(n+1)*(n-1) = 10*12
=> 5*(2*12) = 5*24 + 0
Remainder = 0
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 [#permalink] New post 23 Sep 2006, 09:50
If x and n are +ve integers and when (n+1)(n-1) is divided by 24 the quotient is x and remainder is r . r= ??

a)2 is not the factor of n
b)3 is not the factor of n

N^2-1 = 24X+R

N^2 = 24X+R+1

FRO A N IS ODD { 5,9..} NOT 3 OR 1 BECAUSE X IS NOT ZERO

IF N^2 = 25 THUS R+1 = 1 THUS R= 0
IF N?^2 = 81 THUS R+1 = 3 THUS R = 2.........INSUFF

FROM TWO

N { 5,7,11,8 ....}


IF N^2 = 25 THUS R+1 = 1 THUS R= 0
IF N^2 = 49 THUS R+1= 1 THUS R = 0

IF N^2 = 121 THUS R+1 = 1 THUS R=0

IF N^2 = 64 THUS R+1 = R = 13 INSUFF

FROM ONE AND TWO R =0 MY ANSWER IS C
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 [#permalink] New post 23 Sep 2006, 10:15
Answer: C
n^2 -1 = 24*x + r

S1: n = 3, 5, 7 ...
n^2-1= 8, 24, 48
r = 8,0,0
Not sufficient..

S2: n = 2,4,5,7
n^2-1=3, 15, 24, 48
r = 3, 15, 0,0
Not sufficient.

S1 & S2:n=5,7,11,13
n^2-1= 24, 48, 120, 168
r = 0,0,0,0
Sufficient.

Answer: C
  [#permalink] 23 Sep 2006, 10:15
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