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The sums of three integers taken in pairs are 12, 17, and 19. What is

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The sums of three integers taken in pairs are 12, 17, and 19. What is  [#permalink]

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18 Apr 2019, 00:16
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The sums of three integers taken in pairs are 12, 17, and 19. What is the middle number?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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The sums of three integers taken in pairs are 12, 17, and 19. What is  [#permalink]

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Updated on: 18 Apr 2019, 06:17
Bunuel wrote:
The sums of three integers taken in pairs are 12, 17, and 19. What is the middle number?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

a+b=12
b+c=17
c+a=19
solve for b
we get b=5 other terms 7,12
IMO D

Originally posted by Archit3110 on 18 Apr 2019, 04:18.
Last edited by Archit3110 on 18 Apr 2019, 06:17, edited 1 time in total.
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Re: The sums of three integers taken in pairs are 12, 17, and 19. What is  [#permalink]

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18 Apr 2019, 06:15
x+y=12
y+z=17
x+z=19
so, x+y+z=48/2 => 24
Hence, the three numbers are 5,7 & 12
Middle number => 7
IMO ans is D

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Re: The sums of three integers taken in pairs are 12, 17, and 19. What is  [#permalink]

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23 Apr 2019, 19:50
Bunuel wrote:
The sums of three integers taken in pairs are 12, 17, and 19. What is the middle number?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

We can let x, y, and z be the three integers (such that x < y < z). So we have:

x + y = 12

x + z = 17

and

y + z = 19

If we add the three equations together, we have:

2x + 2y + 2z = 48

x + y + z = 24

If we subtract the first, second, and third equations from x + y + z = 24, we have:

z = 12, y = 7 and x = 5, respectively

So the middle integer is 7.

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Re: The sums of three integers taken in pairs are 12, 17, and 19. What is  [#permalink]

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24 Apr 2019, 06:14
ScottTargetTestPrep What does the actual question mean? I'm not sure why I'm soo confused about such a simple question. I understand assigning variables but why do you have to do add x to z? is this some sort of method?
Re: The sums of three integers taken in pairs are 12, 17, and 19. What is   [#permalink] 24 Apr 2019, 06:14
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