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# What is the value of b + c ?

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What is the value of b + c ? [#permalink]  06 Dec 2012, 04:04
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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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Re: What is the value of b + c ? [#permalink]  06 Dec 2012, 04:10
Expert's post
What is the value of b + c ?

(1) ab + cd + ac + bd = 6 --> $$(ab+bd)+(cd+ac)=6$$ --> $$b(a+d)+c(a+d)=6$$ --> $$(a+d)(b+c)=6$$ --> if $$a+d=1$$, then $$b+c=6$$ but if $$a+d=6$$, then $$b+c=1$$. Not sufficient.

(2) a + d = 4. Nothing about $$b$$ and $$c$$. Not sufficient.

(1)+(2) From (1) we have that $$(a+d)(b+c)=6$$ and from (2) we have that $$a + d = 4$$, thus $$4(b+c)=6$$ --> $$b+c=1.5$$. Sufficient.

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Re: What is the value of b + c ?   [#permalink] 06 Dec 2012, 04:10
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