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If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2?

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Bunuel
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If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink] New post   07 Jul 2016, 05:55
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If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2?

A. 4.
B. 8.
C. 12.
D. 16.
E. 64.
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D
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Re: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink] New post   07 Jul 2016, 06:01
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A-B-C+D = 13 -- equation 1

A+B-C-D = 5 -- equation 2

Adding 1 and 2 , we get
2A - 2C = 18
=> A-C = 9 -- equation 3

Using equation 3 in 2 , we get
B-D = 5 - 9 = -4
=>(B-D)^2 = 16

Answer D
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Re: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink] New post   10 Jul 2016, 02:09
Add both eq => A-C = 9. Then use A-C to get B-D in 2nd eq = -4. B-D^2 = 16 ,so D
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If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink] New post   14 Jul 2016, 15:23
EQ1: A - B - C + D = 13
EQ2: A + B - C - D = 5

(1) Subtract EQ1 from EQ2

A - B - C + D = 13
- A +B - C - D = 5
------------------------
-2B + 2D = 8

(2) Simplify

-B + D = 4
B - D = -4
(B-D)^2 = (-4)^2 = 16


My answer: D
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Re: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink] New post   14 Jul 2016, 22:01
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Bunuel wrote:
If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2?

A. 4.
B. 8.
C. 12.
D. 16.
E. 64.


A-B-C+D = 13
A+B-C-D = 5

On subtracting both the equations,
A-B-C+D = 13
-A-B+C+D = -5

-2(B-D) = 8
B-D = 4
(B-D)^2 = 16

Correct Option: D
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Re: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink] New post   06 Dec 2020, 02:31
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Re: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2? [#permalink]
06 Dec 2020, 02:31
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