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# What is the value of b + c ?

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What is the value of b + c ?  [#permalink]

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06 Dec 2012, 05:04
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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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Joined: 02 Sep 2009
Posts: 47978
Re: What is the value of b + c ?  [#permalink]

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06 Dec 2012, 05:10
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]

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24 Apr 2018, 07:57
Bunuel wrote:
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.

pushpitkc hello

can you help me please sos cant understand the logic of Bunuels solution...

how from this $$b(a+d)+c(a+d)=6$$ he gets this $$(a+d)(b+c)=6$$

Alsi $$a+d=1$$ how can a+d equal to 1 why a = 0.5 and d = 0.5 ?

and he says if $$b+c=6$$ ... but first statement says that whole expression is 6 ----> ab + cd + ac + bd = 6

and from combing two statements how can $$b+c=1.5$$. why decimal and not integers and why 1.5
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Re: What is the value of b + c ?  [#permalink]

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24 Apr 2018, 08:21
1
dave13 wrote:
Bunuel wrote:
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.

pushpitkc hello

can you help me please sos cant understand the logic of Bunuels solution...

how from this $$b(a+d)+c(a+d)=6$$ he gets this $$(a+d)(b+c)=6$$

Alsi $$a+d=1$$ how can a+d equal to 1 why a = 0.5 and d = 0.5 ?

and he says if $$b+c=6$$ ... but first statement says that whole expression is 6 ----> ab + cd + ac + bd = 6

and from combing two statements how can $$b+c=1.5$$. why decimal and not integers and why 1.5

Hey dave13

To begin with, $$b(a+d)+c(a+d)$$ can also be written as $$(b+c)(a+d)$$
because if you take (a+d) as common, you will get the expression (b+c)

Whenever you have trouble with such expression - put some random values for a,b,c, and d

If a=1,b=2,c=3, and d=4
The right-hand side $$b(a+d)+c(a+d)$$ is $$2(1+4) + 3(1+4) = 2*5 + 3*5 = 25$$
Similarly,the left hand side $$(b+c)(a+d)$$ is $$(2+3)(1+4) = 5*5 = 25$$ and we can prove the same

Coming to the second part of your question, in Bunuel's solution it has been given
If $$a+d=1$$ then $$b+c=6$$ since in statement 1 it is written that $$(a+d)(b+c) = 6$$
The reason it is not sufficient is there is a second possibility when $$a+d=6$$ and $$b+c=1$$
So, (b+c) can have two values - 1 or 6

Hope this helps clear your confusion!
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Re: What is the value of b + c ?  [#permalink]

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05 Jul 2018, 10:49
Hi

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Re: What is the value of b + c ?  [#permalink]

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05 Jul 2018, 11:31
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Top Contributor
What is the value of b + c ?

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

Target question: What is the value of b + c ?

Statement 1: ab + cd + ac + bd = 6
Rearrange terms: ab + ac + bd + cd = 6
Factor the a out of the first two terms to get: a(b + c) + bd + cd = 6
Factor the d out of the last two terms to get: a(b + c) + d(b + c) = 6
Rewrite as: (a + d)(b + c) = 6

There are infinitely many values of a, b, c and d that satisfy the equation (a + d)(b + c) = 6. Here are two:
Case a: a + d = 1 and b + c = 6. In this case, the answer to the target question is b + c = 6
Case b: a + d = 2 and b + c = 3. In this case, the answer to the target question is b + c = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a + d = 4
Since we're given NO INFORMATION about b and c, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that (a + d)(b + c) = 6
Statement 2 tells us that a + d = 4

Take the first equation and replace a + d with 4
We get: (4)(b + c) = 6
So, is MUST be the case that b + c = 1.5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: What is the value of b + c ? &nbs [#permalink] 05 Jul 2018, 11:31
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# What is the value of b + c ?

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