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

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Math Expert
Joined: 02 Sep 2009
Posts: 60727
The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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25 Nov 2019, 01:37
00:00

Difficulty:

55% (hard)

Question Stats:

46% (01:49) correct 54% (01:12) wrong based on 39 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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Joined: 18 Aug 2017
Posts: 5748
Location: India
Concentration: Sustainability, Marketing
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Re: The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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25 Nov 2019, 04:02
1
possible pairs
(0,0) & ( 2,2)
IMO C ; 2

Bunuel 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

Are You Up For the Challenge: 700 Level Questions
VP
Joined: 24 Nov 2016
Posts: 1139
Location: United States
Re: The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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25 Nov 2019, 08:43
Bunuel 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

Couldn't think of any other pairs other than: 0,0 and 2,2 = 2

Ans (C)
Manager
Joined: 10 Dec 2017
Posts: 177
Location: India
Re: The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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26 Nov 2019, 00:29
Bunuel 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

Are You Up For the Challenge: 700 Level Questions

c+d=cd
c/cd+d/cd=1
1/c+1/d=1
(c,d)=(2,2)
B:)
Manager
Joined: 03 Nov 2019
Posts: 54
Re: The total number of integer pairs (c, d) satisfying the equation c + d  [#permalink]

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26 Nov 2019, 03:28
c+d=cd
d=cd-c
d=c(d-1)
c=d/(d-1)
Now when d=0 c=0
d=1 c=not defined
And when d=2 c=2
d=3 c=3/2=1.5
Thus, For every other integer value of d apart from 0 & 2; c is never an integer.
Therefore only two integer pairs of (c,d) are possible i.e.(0,0) and (2,2).

Answer: C

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Re: The total number of integer pairs (c, d) satisfying the equation c + d   [#permalink] 26 Nov 2019, 03:28
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# The total number of integer pairs (c, d) satisfying the equation c + d

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