Question: If a + b + c = 12, what is the value of b ?
- a + b = 8
- b + c = 6
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.
Correct Answer: C
Solution ans Explanation:
Approach Solution 1:
This question can be solved only with 1 approach
The case requires us to find the value of b, if a + b + c = 12. Accordingly, the given two statements are to be evaluated to find the value of b and state whether they are sufficient in relevance to the given case.
The first statement is a + b = 8
There are two cases that can be evaluated for a + b to get the result as 8. This includes-
Case 1- a = 2, b = 6
Case 2- a = 3, b = 5
Since the value of b found is not unique enough, the first statement cannot be considered as sufficient
The second statement is b + c = 6
There are two cases for this statement as well which would help in getting the resultant value as 6.
Case 1- c = 1, b = 5
Case 2- c = 0, b = 6
Even in this information, no unique value for b could be found hence, this statement also cannot be considered sufficient.
By combining both the given statements that are given, implying-
a + b = 8 |b + c = 6| a + b + c = 12
It can be found that the values are- a = 6, b = 2 and c = 4
Thus, a unique value of b could be arrived at which states that combinations of both statements are important and not individually.
“If a + b + c = 12, what is the value of b ? (1)a + b = 8 (2) b + c = 6”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2021". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
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