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

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Magoosh

In a certain company, 25% of the women and 17% of the men participate in the voluntary equity program. Let M be the number of male employees. If there are 600 employees total, what is the value of M?

1) M > 100
2) More than 130 employees participate in the voluntary equity program.

OA C

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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.

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

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: C

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

[Jay@ManhattanReview]

Magoosh

In a certain company, 25% of the women and 17% of the men participate in the voluntary equity program. Let M be the number of male employees. If there are 600 employees total, what is the value of M?

1) M > 100
2) More than 130 employees participate in the voluntary equity program.

OA C

Given there are M numbers of male employees, we have (600 - M) numbers of female employees.

Thus, total number of employees who participated in the program

= 17% of M + 25% of (600 - M)

= 0.17M + 150 - 0.25M

= 150 - 0.08M

We have to get the value of M.

Let's take each statement one by one.

1) M > 100

Certainly insufficient. M can have many qualified values.

2) More than 130 employees participate in the voluntary equity program.

=> 150 - 0.08M > 130

20 > 0.08M

M < 250

We must not reject Statement 2 the way we rejected Statement 1. In Statement 1, we had no limit for the values of M; however, with Statement 2 (M < 250), we have a limited number of values of M. Let's check if there is only one qualified value for M.

Note that we are given that 17% of men participated in the program, thus, 17% of M must be a positive integer.

Since 17% of M = 17M/100 and 17 and 100 are co-prime, M must be a multiple of 100.

With M < 250, we have M = 100 or 200. No unique value of M. Insufficient.

(1) and (2) together

From both the statements, we have 100 < M < 250.

Keeping the constraint that 17% of men participated in the program, thus, 17% of M must be a positive integer, we have only one eligible value of M, i.e. M = 200.

However, we must see another constraint that 25% of women participated in the program, thus, (600 - 25% of M) must be a positive integer.

We see that 25% of M = 25% of 200 = 50, a positive integer.

Thus, we have a unique answer, M = 200. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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