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Math Expert V
Joined: 02 Sep 2009
Posts: 60459
If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Question Stats: 89% (00:43) correct 11% (00:44) wrong based on 790 sessions

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If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

NEW question from GMAT® Official Guide 2019

(DS04605)

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examPAL Representative P
Joined: 07 Dec 2017
Posts: 1155
Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

NEW question from GMAT® Official Guide 2019

(DS04605)

To answer the question, we need to know the value of a + c.
We'll look for an answer that gives us this information, a Logical approach.

(1) does not tell us a+c.
Insufficient.

(2) does not tell us a + c.
Insufficient.

Combined: Combining the two equations gives us a + c (as a + 2b + c = 14 --> a + c = 14 - 2b).
Sufficient.

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Joined: 26 Feb 2016
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If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

NEW question from GMAT® Official Guide 2019

(DS04605)

1. a + b = 8
Case 1: a = 2, b = 6
Case 2: a = 3, b = 5
Since we cannot find a unique value of b, the information
present in this statement is not enough.(Insufficient)

2. b + c = 6
Case 1: c = 1, b = 5
Case 2: c = 0, b = 6
Since we cannot find a unique value of b, the information
present in this statement is not enough.(Insufficient)

On combining the information present in the two statements,
a + b = 8 | b + c = 6 | a + b + c = 12. Here, a=6,b=2, & c=4.
We can arrive at an unique value of b. (Sufficient - Option C)
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Joined: 06 Jan 2015
Posts: 713
Location: India
Concentration: Operations, Finance
GPA: 3.35
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Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

Given a + b + c = 12, b=?

(1) a + b = 8 This implies c= 4 but we don't know what is the value of b? Also, b might be positive or negative

(2) b + c = 6 This implies a= 6 but we don't know what is the value of b? Also, b might be positive or negative

Form 1 & 2 a+2b+c = 14 & a+b+c =12

Hence b = 2

C
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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3203
Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Solution

Given:
• The value of a + b + c = 12

To find:
• The value of b

Analysing Statement 1
• As per the information given in statement 1, a + b = 8
o From this, we cannot separately say what is the value of b, as we don’t know the value of a

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in statement 2, b + c = 6
o From this, we cannot separately say what is the value of b, as we don’t know the value of c

Hence, statement 2 is not sufficient to answer

Combining Both Statements
Combining both the statements, we can write:
• a + b = 8
• b + c = 6

If we add these two equations, we get a + 2b + c =14

Substituting the value of a + b + c = 12 in the previous equation, we get 12 + b = 14
• Or, b = 2

Hence, the correct answer is option C.

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Joined: 12 Sep 2015
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Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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1
Top Contributor
Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

Target question: What is the value of b ?

Given: a + b + c = 12

Statement 1: a + b = 8
We can take a + b + c = 12 and rewrite it as (a + b) + c = 12
Now replace a+b with 8 to get: (8) + c = 12
Solve: c = 4
Now that we know the value of c, can we find the value of b?
No.
Let's TEST some values that satisfy statement 1. Here are two:
Case a: a = 1, b = 7 and c = 4. In this case, the answer to the target question is b = 7
Case b: a = 0, b = 8 and c = 4. In this case, the answer to the target question is b = 8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b + c = 6
We can take a + b + c = 12 and replace b+c with 6 to get: a + 6 = 12
Solve: a = 6
Now that we know the value of a, can we find the value of b?
No.
Let's TEST some values that satisfy statement 2:
Case a: a = 6, b = 5 and c = 1. In this case, the answer to the target question is b = 5
Case b: a = 6, b = 4 and c = 2. In this case, the answer to the target question is b = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that c = 4
Statement 2 tells us that a = 6
We can take a + b + c = 12 and replace c and a with 4 and 6 to get: 4 + b + 6 = 12
Solve: b = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
Brent
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Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

NEW question from GMAT® Official Guide 2019

(DS04605)

We need value of b, so if we have value of a+c, we can get the value of b.
St-1: will give value of c only - Insufficient.
St-2: will give value of a only - Insufficient.

Combined, we can get the value of a+c, so OA is C.
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Joined: 31 Oct 2013
Posts: 1494
Concentration: Accounting, Finance
GPA: 3.68
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Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

NEW question from GMAT® Official Guide 2019

(DS04605)

Given,

a+b+c = 12

We are asked to determine the value of b.

Statement 1: a+b = 8. Clearly not stuff.

Statement 2 : b+c = 6. Clearly not sufficient.

Combining 1 and 2:

a+b+c = 12
8 +c = 12
c = 4

Now put the value of c in statement 2.

b+c = 6
b + 4 = 6
b = 2.

Thus the best answer is C.
Intern  B
Joined: 03 Mar 2018
Posts: 30
GMAT 1: 620 Q44 V31
Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Bunuel wrote:
If a + b + c = 12, what is the value of b ?

(1) a + b = 8
(2) b + c = 6

NEW question from GMAT® Official Guide 2019

(DS04605)

Statement 1: a + b = 8

Since we need the value of a + c; Statement 1 is insufficient.

Statement 2: b + c = 6

Since we need the value of a + c; Statement 2 is insufficient.

Together

a + b + c = 12
b + c = 6

a + 6 = 12; a = 6
a + b = 8
a + 6 = 8; a = 2. Therefore, Sufficient.

Intern  B
Joined: 01 Jun 2017
Posts: 19
Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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1) a+b=8
therefore, c=4 but we dont know what is b

2) b+c=6
therefore, a=6 but we dont know what is b

on combining 1and 2, we know 6+b+4=12.
therefore b=2
hence sufficient

Ans. C
Intern  B
Joined: 01 May 2017
Posts: 34
Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6  [#permalink]

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Statement 1: a+b = 8. Clearly not stuff.

Statement 2 : b+c = 6. Clearly not sufficient.

Combining 1 and 2:

a+b+c = 12
8 +c = 12
c = 4

Now put the value of c in statement 2.

b+c = 6
b + 4 = 6
b = 2.

Thus the best answer is C. Re: If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6   [#permalink] 24 Jan 2019, 20:39
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