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

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New post 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.

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

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New post 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.

Answer: C.


pushpitkc hello

can you help me please :) sos :) cant understand the logic of Bunuel`s 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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New post 24 Apr 2018, 08:21
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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.

Answer: C.


pushpitkc hello

can you help me please :) sos :) cant understand the logic of Bunuel`s 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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New post 05 Jul 2018, 10:49
Hi

GMATPrepNow your solution to this question.
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Re: What is the value of b + c ?  [#permalink]

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New post 05 Jul 2018, 11:31
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Walkabout wrote:
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

Answer: C

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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