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What is the value of b + c? (1) ab + cd + ac + bd = 6 (2) a + d = 4

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Joined: 02 Sep 2009
Posts: 49993
What is the value of b + c? (1) ab + cd + ac + bd = 6 (2) a + d = 4  [#permalink]

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23 Sep 2018, 21:41
00:00

Difficulty:

25% (medium)

Question Stats:

80% (00:56) correct 20% (01:13) wrong based on 50 sessions

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What is the value of b + c?

(1) ab + cd + ac + bd = 6
(2) a + d = 4

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Math Expert
Joined: 02 Aug 2009
Posts: 6958
Re: What is the value of b + c? (1) ab + cd + ac + bd = 6 (2) a + d = 4  [#permalink]

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24 Sep 2018, 05:08
What is the value of b + c?

(1) ab + cd + ac + bd = 6
Four variables, so we will not get our answer but let's simplify the equation..
$$ab+cd+ac+bd=6..........ab+ac+cd+bd=6.........a(b+c)+d (b+c)=6.........(a+d)(b+c)=6$$
Insufficient

(2) a + d = 4
Clearly insufficient

Combined
$$(a+d)(b+c)=6$$
So if a+d=4, 4*(c+b)=6......c+b=6/4=3/2
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of b + c? (1) ab + cd + ac + bd = 6 (2) a + d = 4  [#permalink]

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24 Sep 2018, 05:20
Bunuel wrote:
What is the value of b + c?

(1) ab + cd + ac + bd = 6
(2) a + d = 4

Question: b+c = ?

Statement 1: ab + cd + ac + bd = 6
i.e. (a+d)*(b+c)=6
NOT SUFFICIENT

Statement 2: a + d = 4
NOT SUFFICIENT

Combining the two statements
(a+d)*(b+c)=6
i.e. b+c = 6/4
SUFFICIENT

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Re: What is the value of b + c? (1) ab + cd + ac + bd = 6 (2) a + d = 4 &nbs [#permalink] 24 Sep 2018, 05:20
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