Question: On a certain construction crew there are 3 carpenters for every 2 painters. What percent of the entire crew are carpenters or painters?
(1) Eighteen percent of the crew are carpenters.
(2) Twelve percent of the crew are painters.
A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.
Approach Solution 1
18%: x% (painters/entire crew)=3:2
Painters make up 12% of the whole team.
Carpenters and painters make up a combined total of 30% (18+12) of the overall team.
Second assertion: twelve percent of the team is comprised of painters.
Using the same method described up top will allow you to determine the percentage of carpenters.
Each individual assertion is sufficient on its own.
The answer is D.
Approach Solution 2
From the given ratio of carpenters to painters (3:2), we can deduce that the ratio of carpenters to the entire crew is also 3:5 (since 3 out of 5 parts represent carpenters). If 18% of the crew are
carpenters, we can find the percentage of the entire crew that are either carpenters or painters as follows:
18% (carpenters) + 5/5 * 12% (painters) = 18% + 12% = 30%
So, statement 1 alone is sufficient to determine that 30% of the entire crew are either carpenters or painters.
Statement 2: Twelve percent of the crew are painters.
Using the same reasoning as before, if 12% of the crew are painters, we can find the percentage of the entire crew that are either carpenters or painters:
3/3 * 18% (carpenters) + 12% (painters) = 18% + 12% = 30%
So, statement 2 alone is also sufficient to determine that 30% of the entire crew are either carpenters or painters.
Therefore, each statement alone is sufficient to answer the question.
The correct answer is D.
Approach Solution 3
Statement 1: Eighteen percent of the crew are carpenters.
If 18% of the crew are carpenters, we can write it as:
(3x / 5x) * 100 = 18%
Simplifying the equation:
3x / 5x = 18 / 100
3 / 5 = 0.18
This implies that x = 5.
Therefore, the crew size is 5 * 5 = 25.
Statement 2: Twelve percent of the crew are painters.
If 12% of the crew are painters, we can write it as:
(2x / 5x) * 100 = 12%
Simplifying the equation:
2x / 5x = 12 / 100
2 / 5 = 0.12
This implies that x = 5.
Therefore, the crew size is 5 * 5 = 25.
From both statements, we have determined that the crew size is 25. With this information, we can calculate the percentage of the entire crew that are either carpenters or painters.
Percentage of crew that are carpenters = (3x / 5x) * 100 = (3/5) * 100 = 60%
Percentage of crew that are painters = (2x / 5x) * 100 = (2/5) * 100 = 40%
The combined percentage of carpenters and painters in the entire crew is 60% + 40% = 100%.
Therefore, each statement alone is sufficient to answer the question.
The correct answer is D.
“On a certain construction crew there are 3 carpenters for every 2 painters" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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