If 2/5 of the students at College C are business majors, wha

I hope you will be patient with me since it's been a long morning, but here is my reasoning, even after sifting through the various related threads:

We are given that 2/5 of the students are business majors so (2/5)(Males+Females) = Business majors. Expanded, we have Business majors = (2/5)(Males)+(2/5)(Females) = Business majors. Therefore 2/5 males are business majors and 2/5 females are business majors.

Statement 1 just repeats that (2/5)(Males) are business majors

Statement 2 says that 200 females are business majors. We can equate that (2/5)(Females) = 200 from the expanded information provided and have the final form be Females = (5/2)(200) = 500.

For the life of me I cannot see how statement 2 is insufficient unless I am confused about how the information they gave us is constructed as stated.

The red part is not correct. 2/5 (40%) of the students are business majors does not mean that 40% of males and 40% of females are business majors.

For example: say there are 300 males and 200 females (total of 500 students), then there will be 2/5*500=200 business majors. So, it could be that 100% of females and 0% of males are business majors.

Hope it's clear.

I can see how that situation will make what I said incorrect, but then I do not know how I would setup a question like this in the future. I was under the impression that students = males + females. Therefore if 2/5 students are business majors, then 2/5 (males + females) are business majors. What rule did I violate to cause me to tunnel vision into thinking that the aforementioned equation could be expanded into (2/5)(males) + (2/5)(females)?

Again: 2/5(Female+Male)=Business Majors CAN be expanded as 2/5*F+2/5*M=Business Majors, but it does not mean that 2/5 of males and 2/5 of females are business majors.

Ah, I ended up thinking of variables as words. Thank you for the clarification.

Assume male students =X
Female students = y

total Biz majors = (2/5)(X+y)
non-Biz majors =(1- 2/5)(X+Y) = (3/5)(x+y)

statement 1: 2/5 of males students are business majors ..which means 3/5 of male students are non-business majors
= 3X/5
non-biz females=(3/5)(X+Y)-3X/5=(3/5)Y

no information on actual number of students

not sufficient

statement 2: 200 female students are business majors.

no information on non-biz majors female students

not sufficient

statement 1&2: 3/5 of male students are non-biz majors and 200 female students are biz majors
non-biz females= (3/5)Y
biz females = Y-(3/5)Y=(2/5)Y
(2/5)Y=200
=>Y=500
thus females are 500


sufficient

Hence C

Look at Picture:
Statement 1: Not Enough Info, but we can infer that Total Females = (X-Y)
Statement 2: Not Enough Info

Both statements Together:

\(\frac{2}{5}\)Y + 200 = \(\frac{2}{5}\)X

200 = \(\frac{2}{5}X\) - \(\frac{2}{5}Y\) (Factor out \(\frac{2}{5}\))

200 = \(\frac{2}{5}(X-Y)\)

\(200*\frac{5}{2} = (X-Y)\)

\(500 = (X-Y)\)

Statement 1:
40% OF THE MALE STUDENTS are business majors.
When the female students are added in, we get the information given in the prompt:
40% OF ALL THE STUDENTS are business majors.
Since the percentage does not change when the female students are included, the percentage for the female students must be the same as the percentage for the male students.
Thus:
40% OF THE FEMALE STUDENTS must be business majors.
No way to determine the number of female students.
INSUFFICIENT.

Statement 2:
If 100% of the female students are business majors, then the total number of female students = 200.
If 50% of the female students are business majors, then the total number of female students = 400.
Since the total number of female students can be different values, INSUFFICIENT.

Statements combined:
Since the 200 female business students represent 40% of the total number of female students, we get:
200 = 0.4F
2000 = 4F
500 = F
SUFFICIENT.

Lets say Total students = x
BM = 2x/5
NBM = 3x/5
M(Males) + F(Females) = x

Statement 1 :
(2M/5)+F(BM)=(2x/5) = Not sufficient

Statement 2 :
M + 200 = 2x/5 = Not Sufficient

Combining the 2

2M/5 + 200 = 2x/5
Multiplying by 5/2

M + 500 = X

No. of females = 500

Sufficient.

Therefore C is the correct answer

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