In a certain company, 25% of the women and 17% of the men participate

MAGOOSH OFFICIAL SOLUTION:

In this problem, it’s very important to realize: when the GMAT say “17% of the men,” it doesn’t mean 16.93% or 17.02%. It means exactly, precisely, 17%. This 17% of M must be a whole number, a positive integer. The only way this can happen is if M equals either 100 or a multiple of 100. That’s a huge insight. Both M and F (the number of female employees) must be multiples of 100 that add up to 600. In other words, there aren’t that many possibilities for the gender breakdown in this company.

Statement #1: M > 100. Well, M could be 200 or 300 or 400 or etc. Many possibilities. This statement, alone and by itself, is not sufficient.

Now, forget about statement #1!

Statement #2: Now, we have to think about the number in the equity program.

If M = 0, and F = 600, then there are 150 in the equity program. A possibility.

If M = 100 & F = 500, then 17 males & 125 females, which results in 142 in the equity program. A possibility.

If M = 200 & F = 400, then 34 males & 100 females, which results in 134 in the equity program. A possibility.

If M = 300 & F = 300, then 51 males & 750 females, which results in 126 in the equity program. This is not possible, and as we add more men and subtract women, this number will drop even lower, so there are no more possible cases.

Right now, we have many possibilities. This statement, alone and by itself, is not sufficient.

Combined: As you probably anticipated, with both statements, things are looking good. If M > 100, then the only case that allows for more than 130 in the equity program is the case with M = 200 & F = 400. We now know that M = 200, so we have definitively answered the prompt question. Combined, the statements are sufficient.

Answer = (C)
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W=600-M

(1) M > 100
as 17% is prime M has to be multiple of 100 .

200,300

insufficient .

(2) more than 130 employees participate in the voluntary equity program

25%(600-M) + 17%M > 130

M<250

M can be 100, 200

insufficient .

Together:


100<M<250 and M has be multiple of 100

M= 200

Answer C

Hi All,

This question involves some subtle Number Property rules that you have to consider to get the correct answer. Those rules, along with TESTing VALUES, can help you to quickly answer the question...

We're told that 25% of the women and 17% of the men participate in the voluntary equity program.

This means that 1/4 of the women participate in the program, which means that the total number of women MUST be a multiple of 4 (you can't have a 'fraction' of a woman, so no other possibilities exist). With 17% of men though, we have an interesting 'limitation': the only way to get an integer number of men is when we multiply by a multiple of 100, so the total number of men MUST be a multiple of 100. These deductions will help you to work through the two Facts much faster....

We're also told that there are 600 total employees. We're asked for the number of male employees.

Fact 1: The number of male employee is > 100

IF....
Males = 200 (a multiple of 100)
Females = 400 (a multiple of 4)
The answer to the question is 200

IF....
Males = 300 (a multiple of 100)
Females = 300 (a multiple of 4)
The answer to the question is 300
Fact 1 is INSUFFICIENT

Fact 2: More than 130 employees participate in the voluntary equity program

IF....
Males = 200 (a multiple of 100)
Females = 400 (a multiple of 4)
.17(200) + .25(400) = 34 + 100 = 134
The answer to the question is 200

IF....
Males = 100 (a multiple of 100)
Females = 500 (a multiple of 4)
.17(100) + .25(500) = 17 + 125 = 142
The answer to the question is 100
Fact 2 is INSUFFICIENT

Combined, we know....
The number of males is > 100
More than 130 employees participate in the voluntary equity program

From our prior work, we can take advantage of a pattern....

Total males COULD be 200, but CANNOT be 100

IF....
Males = 300 (a multiple of 100)
Females = 300 (a multiple of 4)
.17(300) + .25(300) = 126 which does NOT fit the given 'restrictions'
Thus, the total number of males CANNOT be 300 or greater.

The only answer that "fits" is Males = 200
Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Analysis of the question: 17% of M and 25% of W. since we are talking about people, it means that we need a whole number, we cannot get decimals as an answer.

17% is a prime number => possible answers for M are: 100,200,300,400,500 and 600. however, if we have M:600, then W:0, we cannot have W:0, for we end up with M: 100 or 200 or 300 or 400 or 500.

Stmt1 says that m>100... M can still be 200,300,400,500. NS.

Stmt2 says that 17%(M) + 25%(W) > 130.
We can use a chart to see how it will play out

M: 17%(100) = 17 => W: 25%(500) = 125 => 142. fits stmt2. Ok,
M: 17%(200) = 34 => W: 25%(400) = 100 => 134. fits stmt2. Not ok. if I get two different set of number that fit stmt2.
M: 17%(300) = 51 => W: 25%(300) = 75 => 126. does not fit stmt2.

stmt2 works when M is 100 and 200. So it is not suff.

Combining stmt1 and stmt2. M must be higher than 100. and M can be 100 or 200. then 200 must be. C.

I have doubt regarding stmt 2

(2) more than 130 employees participate in the voluntary equity program

Can we deduce that less than 130 employee do not participate, and so get % of employee not participating.
The (100 - %for employee not participating) = % of employee participating
So we get two equation
w+m=600
1/4w+17/100m = 470
Its not resulting in correct answer, but my question is Can we deduce that less than 130 employee do not participate?

This took me a sweet 10 minutes to solve. It would be really helpful if experts could advise on how to solve these types of questions quickly. Thank you.

Hi OreoShake,

Certain questions on Test Day will take you 3 minutes to solve (and that's if you KNOW what you're doing), so you have to be careful about assuming that there's always a 'fast' way to get to the correct answer. Your ability to spot patterns and do basic calculations by hand should help you to speed up, but certain questions require a lot of note-taking and effort to get to the solution. The good news is that the work itself likely won't be that difficult; the bad news is that it will take a lot of work to get the correct answer.

In my prior post (a few posts above this one), I discuss the patterns involved in this prompt and the calculations that you could do to solve it. If you have any questions about that solution (or anything else in this question), then just let me know.

GMAT assassins aren't born, they're made,
Rich
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