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# If A + B = 5, B + C = 4, and C + D = 6, then AB + CD + AC + BD is:

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Director
Joined: 30 Sep 2017
Posts: 955
GMAT 1: 720 Q49 V40
GPA: 3.8
If A + B = 5, B + C = 4, and C + D = 6, then AB + CD + AC + BD is:  [#permalink]

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Updated on: 10 Sep 2019, 04:30
2
5
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:34) correct 20% (02:52) wrong based on 61 sessions

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If A + B = 5, B + C = 4, and C + D = 6, then AB + CD + AC + BD is:

A) 11
B) 12
C) 15
D) 28
E) 48

Originally posted by chondro48 on 07 Aug 2019, 10:45.
Last edited by chondro48 on 10 Sep 2019, 04:30, edited 3 times in total.
Manager
Joined: 10 May 2018
Posts: 75
Re: If A + B = 5, B + C = 4, and C + D = 6, then AB + CD + AC + BD is:  [#permalink]

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07 Aug 2019, 11:03
1
1
AB + CD + AC + BD
=> B(A+D) + C(A+D)
= (B+C)(A+D)

From the given equaation:
A + B -(B + C)+C + D = 5 - 4 + 6

A+D=7

therefore

(B+C)(A+D)
=4*7
=28
Ans D
Intern
Status: Classified
Joined: 19 Jun 2019
Posts: 33
Re: If A + B = 5, B + C = 4, and C + D = 6, then AB + CD + AC + BD is:  [#permalink]

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07 Aug 2019, 22:07
1
No constraints on $$A$$, $$B$$, $$C$$ or $$D$$.

So, let $$A=5$$, $$B=0$$, $$C=4$$ and $$D=2$$.
$$\implies AB+CD+AC+BD = 28$$

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Re: If A + B = 5, B + C = 4, and C + D = 6, then AB + CD + AC + BD is:   [#permalink] 07 Aug 2019, 22:07