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# What is the value of C + B?

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Senior Manager
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What is the value of C + B? [#permalink]

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05 Feb 2014, 16:36
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Difficulty:

55% (hard)

Question Stats:

65% (02:06) correct 35% (01:39) wrong based on 51 sessions

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What is the value of C + B?

(1) A + B = C + D = E + F
(2) (E + F) = (D – B)

OE
[Reveal] Spoiler:
For (1), pick some numbers.
A = 7, B = 3, C = 4, D = 6 → C + B = 7
A = 1, B = 9, C = 3, D = 7 → C + B = 12
No single value
Insufficient.

For (2), It does not even contain the variable C.
Insufficient.
Combined:
Notice in this problem that there are several sets of 2 variable terms and they're all equal.
From (2), (D – B) = (E + F) → C + D = D–B.
Add B to both sides and subtract D from both sides
→ C + B = 0.
Sufficient.

Hi, I want to know if we can solve Statement (1) without pick number, please.
I think it does not have C + B in equation, it is insufficient.
[Reveal] Spoiler: OA
Manager
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Re: What is the value of C + B? (1) A + B = C + D = E + F [#permalink]

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05 Feb 2014, 17:20
1
KUDOS
Let me try,

We can rearrange the equations:

C = E+F - D
B = E+F - A

All 3 equalities given would boil down to this,

C+B = 2 (E+F) - (A+D)

So C+B depends on 4 different variables which are still unknown. In other words there are infinitely many number of possibilities for C+B when the Statement 1 alone is considered.

I hope this helps.
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Re: What is the value of C + B? (1) A + B = C + D = E + F [#permalink]

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05 Feb 2014, 21:52
2
KUDOS
Expert's post
goodyear2013 wrote:
What is the value of C + B?
(1) A + B = C + D = E + F
(2) (E + F) = (D – B)

OE
[Reveal] Spoiler:
For (1), pick some numbers.
A = 7, B = 3, C = 4, D = 6 → C + B = 7
A = 1, B = 9, C = 3, D = 7 → C + B = 12
No single value
Insufficient.

For (2), It does not even contain the variable C.
Insufficient.
Combined:
Notice in this problem that there are several sets of 2 variable terms and they're all equal.
From (2), (D – B) = (E + F) → C + D = D–B.
Add B to both sides and subtract D from both sides
→ C + B = 0.
Sufficient.

Hi, I want to know if we can solve Statement (1) without pick number, please.
I think it does not have C + B in equation, it is insufficient.

You don't really need to do anything in statement (1)

(1) A + B = C + D = E + F
Each equation you can make has 4 different variables in it. We don't have the value of any variable. Hence, there is no way you can find the value of B+C.
B and C could innumerable values and their sum could be anything.

Using both statements together,
A + B = C + D = E + F
(E + F) = (D – B), focus on B and C and eliminate as many variables as you can

you get C + D = D - B
B + C = 0

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Senior Manager
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Re: What is the value of C + B? (1) A + B = C + D = E + F [#permalink]

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05 Feb 2014, 23:02
VeritasPrepKarishma wrote:
goodyear2013 wrote:
What is the value of C + B?
(1) A + B = C + D = E + F
(2) (E + F) = (D – B)

OE
[Reveal] Spoiler:
For (1), pick some numbers.
A = 7, B = 3, C = 4, D = 6 → C + B = 7
A = 1, B = 9, C = 3, D = 7 → C + B = 12
No single value
Insufficient.

For (2), It does not even contain the variable C.
Insufficient.
Combined:
Notice in this problem that there are several sets of 2 variable terms and they're all equal.
From (2), (D – B) = (E + F) → C + D = D–B.
Add B to both sides and subtract D from both sides
→ C + B = 0.
Sufficient.

Hi, I want to know if we can solve Statement (1) without pick number, please.
I think it does not have C + B in equation, it is insufficient.

You don't really need to do anything in statement (1)

(1) A + B = C + D = E + F
Each equation you can make has 4 different variables in it. We don't have the value of any variable. Hence, there is no way you can find the value of B+C.
B and C could innumerable values and their sum could be anything.

Using both statements together,
A + B = C + D = E + F
(E + F) = (D – B), focus on B and C and eliminate as many variables as you can

you get C + D = D - B
B + C = 0

Statement 1 and 2 both are insufficient to get the value C-B..

St(1) and st(2) togather..

A+B=C+D=E+F
E+F=D-B
So,

A+B=C+D=D-B

A+B+B=C+D-B=D
A+2B=C+D-B=D
A+2B-D=C+D-D-B=0
A+2B-D=C-B=0

so C-b=0..so both statement togather are sufficient..

Is this correct ?? experts?
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Re: What is the value of C + B? (1) A + B = C + D = E + F [#permalink]

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05 Feb 2014, 23:13
Hi Sanjoo, the question stem says "C+B = ?" not "C-B"

So if we combine S1 and S2 together
A+ B = C+D = E+F = D - B

C + D =D - B
which leaves us with C + B = 0
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Re: What is the value of C + B? (1) A + B = C + D = E + F [#permalink]

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05 Feb 2014, 23:38
[quote="goodyear2013"]What is the value of C + B?
(1) A + B = C + D = E + F
(2) (E + F) = (D – B)

Combining the statement we get:

C + D = D - B which means C = - B

C + B = -B + B = 0
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Re: What is the value of C + B? (1) A + B = C + D = E + F   [#permalink] 05 Feb 2014, 23:38
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# What is the value of C + B?

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