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What is the remainder when the positive integer x is divided

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Director
Joined: 29 Oct 2004
Posts: 851
What is the remainder when the positive integer x is divided [#permalink]

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19 Feb 2005, 21:35
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What is the remainder when the positive integer x is divided by 8?

(1) When x is divided by 12, the remainder is 5.

(2) When x is divided by 18, the remainder is 11.
Director
Joined: 19 Nov 2004
Posts: 556
Location: SF Bay Area, USA

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19 Feb 2005, 22:01
1)x = 12K1 +5

Can't really say what remainder we get when x is divided by 8 with this

2) x = 18K2 +11
Can't really say what remainder we get when x is divided by 8 with this

Together
12K1 +5 = 18K2 +11
2K1 = 3K2 +1

Plugging in values for K1 and K2 that satisfies the above eqn., we get X= 29(K1=2, K2=1), 65 (K1=5, K2=3) , ... where both the statements are satisfied.

29/8 leaves a remainder 5
65/8 leaves a remainder 1

E)
VP
Joined: 25 Nov 2004
Posts: 1483

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19 Feb 2005, 22:06
MA wrote:
C.

oh, i miscalculated.....................

agreed, it is E.

Last edited by MA on 19 Feb 2005, 22:34, edited 1 time in total.
VP
Joined: 18 Nov 2004
Posts: 1433

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19 Feb 2005, 22:15
"E"

State 1...insuff....x = 12n+5....x = 17/8 = remainder 1....29/8= 5.....insuff

State 2....insuff....x = 18m+11.....x = 29/8 = remainder 5...47/8 = 7....insuff

Combine

12n+5 = 18m+11
12n-18m = 6

2n-3m = 1
2(n+1) = 3(m+1)

So n-1 has to be a multiple of 3 and m+1 of 2

n = 3t-1

So
x = 36t -12+5 = 36t -7

29/8 = 5
72-7 = 65/8 = 1......again insuff
19 Feb 2005, 22:15
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