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# What is the value of b – 2c ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
What is the value of b – 2c ?  [#permalink]

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23 Jun 2017, 08:27
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Difficulty:

25% (medium)

Question Stats:

79% (01:33) correct 21% (01:38) wrong based on 80 sessions

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What is the value of $$b – 2c$$?

(1) $$ab – 2cd + bd – 2ac = 8$$

(2) $$a = 4 – d$$

_________________
Intern
Joined: 18 Aug 2013
Posts: 3
Re: What is the value of b – 2c ?  [#permalink]

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23 Jun 2017, 11:49
2
Bunuel wrote:
What is the value of $$b – 2c$$?

(1) $$ab – 2cd + bd – 2ac = 8$$

(2) $$a = 4 – d$$

The best way to do this sort of problem is usually to try to isolate what we're being asked to solve for.

Statement 1:

$$ab - 2cd + bd - 2ac = 8$$

Let's try get all the "b" terms together and all the "2c" terms together:

$$ab + bd - 2ac - 2cd = 8$$

Now we can factor out the b in the first two terms and a negative 2c in the second two terms (be careful to change the signs properly):

$$b(a + d) -2c (a + d) = 8$$

Finally, we can divide by (a+d):

$$b - 2c = \frac{8}{a+d}$$

At this point, we're stuck. We can't solve for $$b-2c$$ without knowing the value of $$a+d$$
Insufficient.

Statement 2:
Statement 2 doesn't give us any information about b or about c.
Insufficient.

Combined:
We can rewrite Statement 2 as:

$$a+d = 4$$

Now we can substitute in our rewritten first equation:

$$b - 2c = \frac{8}{4}$$

$$b - 2c = 2$$
Sufficient.

C.
Manager
Joined: 05 Nov 2014
Posts: 102
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21
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Re: What is the value of b – 2c ?  [#permalink]

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24 Jun 2017, 06:06
What is the value of b–2cb–2c?

(1) ab–2cd+bd–2ac=8ab–2cd+bd–2ac=8

(2) a=4–d

Solution:

Statement 1: Rearranging,
we get a(b-2c)+ d(b-2c)=8
Taking out the common factor, (b-2c) (a+d)=8.
We can't find the unique value of either of terms as infinite values are possible.

Statement 2: Insufficient on its own.

Combining St1 and St2,
We get a unique value of b-2c. We get 4 as the value.
Therefore, the answer is Option C.
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the value of b – 2c ?  [#permalink]

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19 Feb 2019, 01:08
Bunuel wrote:
What is the value of $$b – 2c$$?

(1) $$ab – 2cd + bd – 2ac = 8$$

(2) $$a = 4 – d$$

After manipulating both options A and B, combining we get

b(a+d) -2c (a+d) = 8

b-2c (a+d) = 8

from 2) a+d = 4

b-2c = 2

C
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Re: What is the value of b – 2c ?   [#permalink] 19 Feb 2019, 01:08
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