If a + b + c = 12, what is the value of b? (1) a + b = 8 (2) b + c = 6

Video solution from Quant Reasoning:

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.

(C) is our answer.

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)

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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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.

Answer: C
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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

Answer: C

Cheers,
Brent

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.

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.

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.

Answer is C.

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

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.

Answer: Option C

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1) b = 8-a, insufficient since no info on a
2) b = 6-c, insufficient since no info on 7

Combined

Approach 1:

Notice
1) + 2) gives us

a + 2b + c = 14

We can subtract

a + b + c =12 from 1) + 2) and get

b=2

1) and 2) are sufficient

Approach 2 if you didn't noice Approach 1:
Use results from 1) and 2)
b-b=0=(8-a)-(6-c)=2-a+c=0
a=c+2
Sub in original equation

(c+2)+b+c=12
b+2c=10

b=10-2c

Combine with
b=6-c

We can get c, then a, and then b. Sufficient.

1) and 2) are sufficient.

I am sure there are more ways to solve this question algebraically.

Solution:

Question Stem Analysis:

We need to determine the value of b, given that a + b + c = 12.

Statement One Alone:

Since a + b = 8, we know that c = 12 - 8 = 4. However, since we don’t have the value of a, we can’t determine the value of b. Statement one alone is not sufficient.

Statement Two Alone:

Since b + c = 6, then a = 12 - 6 = 6. However, since we don’t have the value of c, we can’t determine the value of b. Statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that a = 6 and c = 4, so b = 12 - 6 - 4 = 2.

Alternatively, if we add the two equations in the statements, we have a + 2b + c = 14. Subtracting the equation from the problem stem from this, we will also have b = 2.

Both statements together are sufficient.

Answer: C
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