GMAT Official Guide 2019 If a + b + c = 12

[BTGmoderatorDC]

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

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

[Jay@ManhattanReview]

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

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

Given: a + b + c = 12

We have to determine the value of b.

Let's take each statement one by one.

(1) a + b = 8

We can get the value of c (= 12 - 8 = 4), but not b. Insufficient.

(2) b + c = 6

We can get the value of a (= 12 - 6 = 6), but not b. Insufficient.

(1) and (2) together

From (1), we get c = 4 and from (2), we get a = 6; thus, from a + b + c = 12, we have b = 2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[Brent@GMATPrepNow]

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

Answer: C

Cheers,
Brent

[AdityaBir]

a+b+c = 12 (i)
1) a+b = 8 (ii)
substituting (ii) in (i) we get c=4 .
but this alone is not sufficient to find b.
2) b+c = 6 (iii)
substituting (iii) in (i) we get a=6
but this alone is not sufficient to find b.
Combining 1) and 2)
from 1) we get c=4 and from 2) we get a=6 .
substituting values of a and c in (i) we get b=2.
so both statements combined are sufficient
Hence option C is correct.