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a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +

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V
Joined: 02 Sep 2009
Posts: 49544
a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

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New post 05 Jul 2018, 04:41
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (02:30) correct 33% (02:24) wrong based on 31 sessions

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Concentration: Technology, Nonprofit
WE: Analyst (Non-Profit and Government)
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Re: a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

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New post 05 Jul 2018, 04:59
Given:
ab + c = 7 -- (eq. 1)
ac + b = 5 -- (eq. 2)
a + b + c = 6 -- (eq. 3)

Add eq. 1 and 2
(a+1)(b+c) = 12
Substitute b+c = 6 - a from eq. 3
(a+1)(6-a) = 12
This gives a = 2, 3

Pick a value. Say a = 3
Substitute in eq. 1 and 2
3b + c = 7
3c + b = 5
==> b = 2 and c = 1
a*b*c = 3*2*1 = 6

Answer: B
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Re: a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

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New post 05 Jul 2018, 05:12
Bunuel wrote:
a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b + c = 6. What is the value of abc ?

A. 2
B. 6
C. 9
D. 12
E. 18


Going from the answer options can be advantageous in this kind of problem.

A. 2 = 2*1 | a = 2,b = c = 1
Whichever way we go about the numbers, we can't get a sum s.t a + b + c = 6

B. 6 = 2*3 | a = 2,b = 3,c = 1
In this case a + b + c = 6. Also, ab + c = 6 +1 = 7 and ac + b = 2 + 3 = 5.

Therefore, Option B(6) is the value of abc.
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Re: a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b + &nbs [#permalink] 05 Jul 2018, 05:12
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