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# The total number of integer pairs (c, d) satisfying the equation c + d

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Director
Joined: 08 Jun 2013
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The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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Updated on: 15 Aug 2018, 13:24
2
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:28) correct 50% (01:16) wrong based on 44 sessions

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The total number of integer pairs (c, d) satisfying the equation c + d = cd is

A) 0
B) 1
C) 2
D) 3
E) 4

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Originally posted by Helium on 15 Aug 2018, 05:19.
Last edited by Bunuel on 15 Aug 2018, 13:24, edited 1 time in total.
Renamed the topic.
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Joined: 03 Apr 2012
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Re: The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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15 Aug 2018, 06:12
2 pairs...

(2,2) and (0,0)

2+2=2*2 and 0+0=0*0
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Re: The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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15 Aug 2018, 07:20
Harshgmat wrote:
The total number of integer pairs (c, d) satisfying the equation c + d = cd is

A) 0
B) 1
C) 2
D) 3
E) 4

Given, c+d=cd
Or, cd-(c+d)=0
Or, cd-c-d=0
Or, cd-c-d+1=1
Or, c(d-1)-1(d-1)=1
Or, (d-1)(c-1)=1*1
So, d-1=1 or c-1=1
Or, d=2, c=2-------------(1 pair)

(d-1)(c-1)=(-1)*(-1)
Or, d-1=-1, c-1=-1
Or, d=0, c=0-------------(1 pair)

So, total 2 pairs of (c,d) satisfies the given condition.

Ans. (C)
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Re: The total number of integer pairs (c, d) satisfying the equation c + d   [#permalink] 15 Aug 2018, 07:20
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