Data Sufficiency

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.

Please provide explanation on your answers.

kashefian wrote: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.

Please provide explanation on your answers.

Is it A?

I am not sure though. If it is Not A then please do not follow the below explanation as my thought process my be wrong.

Here is what I think,

3C -> 2P => C = (2/3)P Or P = (3/2)C. percent of the entire crew are carpenters or painters?

Option 1:

18% of Crew --> Carpainters. So percentage of Carpainters is known.

Say total crew members are 100 then 18 C and thus 18*(2/3) = 12P

Say total crew members are 150 then 27 C and thus 18 P.

When consider any number of crew member as total, to get 18% of so a WHOLE number that WHOLE number will definitely be divisible by 3. As u see when I take 100 or 150 as whole numbers we have 18 and 27 respectively. As 18 and 27 are divisible by 3 we can find 2/3 which will give us the Number of Painters.

Basically what I mean is suppose you consider total number of crew members are 125.
Then 18% of 125 = 22.5.
This is practically not possible as we cannot have 0.5 Carpainter.

Thus, it is SUFFICIENT as we can always determine the percentage of Painters when we know the Percentage of Carpainters as 18.

Option 2:
12% of Crew --> Painters. So we know the percentage of P.

Say total crew members are 100 then 12 P and thus 12*(3/2) = 18C

Say total crew members are 150 then 18 P and thus 18*(3/2) = 27C

But when we consider,
Say total crew members are 125 then 125(12%) = 15 P and thus 15*(3/2) = 22.5 C which is not feasible as we cannot have 0.5 Carpainter.

Thus, it is INSUFFICIENT as we cannot always determine the percentage of Car painters when we know the Percentage of Painters as 12.

Rahul@gurome wrote:

kashefian wrote: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.

Please provide explanation on your answers.

In first glance it may appear that the question itself (without the statements) is sufficient to answer the it. But nowhere it is mentioned that there are only painters and carpenters in the construction crew. There may be other kinds of crew present.

Statement 1: 18% of the crew are carpenters.
Say total number of crew = 100x
Thus, total number of carpenters = 18x
For 3 carpenter -> 2 painter
For 18x carpenter -> (2/3)*(18x) = 12x painter
Percentage of painter = 12%

Thus, (12 + 18)% = 30% of the entire crew are carpenters or painters.

Sufficient.

Statement 2: 12% of the crew are painters.
Proceeding similarly as above, percentage of carpenter = 18%

Thus, (12 + 18)% = 30% of the entire crew are carpenters or painters.

Sufficient.

The correct answer is D.

Hi Rahul,

Can you please let me know on my approach to the Option 2?

Option 2:
12% of Crew --> Painters. So we know the percentage of P.

Say total crew members are 100 then 12 P and thus 12*(3/2) = 18C

Say total crew members are 150 then 18 P and thus 18*(3/2) = 27C

But when we consider,
Say total crew members are 125 then 125(12%) = 15 P and thus 15*(3/2) = 22.5 C which is not feasible as we cannot have 0.5 Carpainter.

Thus, it is INSUFFICIENT as we cannot always determine the percentage of Car painters when we know the Percentage of Painters as 12.

Thanks,
Shovan

I was wondering how do we know that none of the crew is both a painter and a carpenter. In this case none of the choices are sufficient and the answer would be E.

I was wondering how do we know that none of the crew is both a painter and a carpenter. In this case none of the choices are sufficient and the answer would be E.

I Dont think u have to worry about that cause..
The Question clearly states that there are 3 Carpenters for every 2 painters.(Besides i never thought of this possibility, but its worth to know that there is such a possiblity too)
The only thing u have to worry is whether there are people other than painter and carpenter in the crew.

Note in the choices:
1. You are given percentage in the choices. Because u are specifically given a percentage, u can offcourse decide on the number of the rest of the people.

If u were given a number for both the choices, then, both of them would be unsufficient , even together..(because u can only count only the number of carpenters and painters, not the rest of the number of people in the crew..).

Hope it helps.

junegmat221 wrote:I was wondering how do we know that none of the crew is both a painter and a carpenter. In this case none of the choices are sufficient and the answer would be E.

Hi junegmat221,

Actually, this IS a good question. It's reasonable to assume that people only have one job, but the GMAT will never require you to make that assumption--and I've flagged this problem for revision, so future printing will specify that each person has only one profession.

Also, there will be cases where you CAN'T assume that. People generally only have one profession, but they may work on more than on project; on a GMAT problem that told you that there was a 3:2 ratio among workers building the house and workers painting it, than the answer would be (E) because there could be overlap.

Thanks for asking this question, and I hope I was able to clear it up!