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At Springfield High, three-fourths of the male students and

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At Springfield High, three-fourths of the male students and [#permalink] New post 14 Nov 2007, 13:13
At Springfield High, three-fourths of the male students and half of the female students speak a foreign language. If the number of males is two-thirds the number of females, what fraction of the students speak a foreign language?

A. 1/3
B. 2/3
C. 1/2
D. 3/4
E. 3/5

M07-15
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 14 Nov 2007, 13:32
bmwhype2 wrote:
at springfield high, 3/4 of males and 1/2F speak a foreign language. If there are 2/3 as many male as female students there, what fractions of the students speal a foreign language?

1/3
3/5
7/7
4/9
4/8


M=2/3(F) assume 3 females in class then 2 males

student speaking foreign language - (3/4)males + 1/2 females

3*2/4+1*2/2=12/4=3

total sudents 3f+2m=5

3/5
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 14 Nov 2007, 13:35
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bmwhype2 wrote:
at springfield high, 3/4 of males and 1/2F speak a foreign language. If there are 2/3 as many male as female students there, what fractions of the students speal a foreign language?

1/3
3/5
7/7
4/9
4/8


The easiest method for me is to pick a number, which divisible by the denominator, to find the answer.

Let f=30

m = 2/3f, so m=20

Total Students
m=20
f=30
--------
50

Foreign Language Speaking Student
3/4m = 3/4(20)=15
1/2f = 1/2(30)=15
---------------------
30

What fractions of the students speak a foreign language?
30/50 = 3/5

-----------

Answer B.
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 14 Nov 2007, 16:36
bmwhype2 wrote:
at springfield high, 3/4 of males and 1/2F speak a foreign language. If there are 2/3 as many male as female students there, what fractions of the students speal a foreign language?

1/3
3/5
7/7
4/9
4/8


Kaplan's picking numbers strategy makes you find speedy answer to this kind of questions.

********BMWHYPE******** you normally leave the posts open to discussion that's fine but do rarely post the OAs. Can you please kindly, regularly, post the OAs as well.

Appreciate
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 18 Nov 2007, 03:17
OA is B.



(3/4)m=foreign speaking males
(1/2)f=foreign speaking females
m=(2/3)f

Total pop = m+f=(2/3)f+f=(5/3)f

Total foreign speaking pop = (3/4)m+(1/2)f=(3/4)(2/3)f+(1/2)f=(1/2)f+(1/2)f=f

(Tot for speak pop)/(tot pop)=f/(5f/3)=3/5
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 18 Nov 2007, 03:18
Ravshonbek wrote:
bmwhype2 wrote:
at springfield high, 3/4 of males and 1/2F speak a foreign language. If there are 2/3 as many male as female students there, what fractions of the students speal a foreign language?

1/3
3/5
7/7
4/9
4/8


Kaplan's picking numbers strategy makes you find speedy answer to this kind of questions.

********BMWHYPE******** you normally leave the posts open to discussion that's fine but do rarely post the OAs. Can you please kindly, regularly, post the OAs as well.

Appreciate


i let the questions sit for a week or so, depending on when i have time to get back to reviewing the question.
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 26 Jun 2014, 22:09
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A table is a good approach in such problems.

Step 1:
Male Female Total
SF 3m/4 f/2
DNF m/4 f/2
Total m f

Step 2: Since m = 2f/3,
Male Female Total
SF f/2 f/2 f
DNF f/6 f/2
Total 2f/3 f 5f/3

Thus, ans. is f/(5f/3) = 3/5
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Re: At Springfield High, three-fourths of the male students and [#permalink] New post 27 Jun 2014, 00:55
Expert's post
bmwhype2 wrote:
At Springfield High, three-fourths of the male students and half of the female students speak a foreign language. If the number of males is two-thirds the number of females, what fraction of the students speak a foreign language?

A. 1/3
B. 2/3
C. 1/2
D. 3/4
E. 3/5

M07-15


The number of males is two-thirds the number of females --> M=\frac{2}{3}F --> M:F=2:3.

Now, say the total number of students is 100, then there are 40 males and 60 females (ratio 40:60=2:3).

So, \frac{3}{4}*40+\frac{1}{2}*60=60 students speak foreign language, which is \frac{60}{100}=\frac{3}{5} of total students.

Answer: E.
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Re: At Springfield High, three-fourths of the male students and   [#permalink] 27 Jun 2014, 00:55
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