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

Question

If 2/5 of the students at College C are business majors, what is the number of female students at College C?

(1) 2/5 of the male students at College C are business majors.
(2) 200 of the female students at College C are business majors.

Bunuel · Accepted Answer

If 2/5 of the students at College C are business majors, what is the number of female students at College C?

Given:  2/5(Female+Male)=Business Majors . Question:  Female=?

(1) 2/5 of the male students at College C are business majors -->  2/5*M=Male Business Majors . Not sufficient.

(2) 200 of the female students at College C are business majors -->  Female Business Majors=200 . Not sufficient.

(1)+(2)  {Business Majors}={Male Business Majors}+{Female Business Majors}  -->  2/5(F+M)=2/5*M+200  -->  2/5*F=200  -->  F=500 . Sufficient.

Answer: C.

bschooladmit · Answer

C it is.

Given: 2/5 students Business majors

1. 2/5 BM = Male . =>3/5 of BM Female. Insuff
2. BM Female = 300

c combine the two 300=(2/5)(3/5) Students

Injuin · Answer

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.

Bunuel · Answer

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.

Injuin · Answer

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)?

Bunuel · Answer

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.

Injuin · Answer

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

anairamitch1804 · Answer

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

Jsound996 · Answer

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)

GMATGuruNY · Answer

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.

C

Gmat202023 · Answer

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

siddhantvarma · Answer

KarishmaB I still can't wrap my head around this. 2/5(M+F) can be opened as 2/5M + 2/5F and yet we can't equate 2/5F to female business majors? Can you please explain what I am missing conceptually here?

Bunuel · Answer

2/5(M + F) means 2/5 (40%) of the total students are business majors. It does not automatically mean 40% of the female students are business majors. It only means that the number of business majors equals 40% of the males plus 40% of the females. For example, suppose M = 50 and F = 50, so M + F = 100. Then 2/5 of 100 is 40, so there are 40 business majors total. This could happen with 30 male business majors and 10 female business majors. That is 30/50 = 60% of males and 10/50 = 20% of females, but overall it is still 40/100 = 40%, even though it is not true that 40% of the females are business majors.

Hope it's clear.

Hope it's clear.

siddhantvarma · Answer

I think I'm getting somewhere, thanks, Bunuel. One thing, though - " It only means that the number of business majors equals 40% of the males plus 40% of the females. " This is a little contradictory, don't you think? When you say "number of business majors equals 40% of the males plus 40% of the females." => 40% of total females are business majors, which isn't true. Did I get that right or am I misinterpreting your statement here?

Bunuel · Answer

I’m not sure why this is so confusing. I think you are overcomplicating it. 2/5(M + F) means 40% of the total student body are business majors. Expanding it to 2/5M + 2/5F is just algebra.

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