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# M07-15

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Math Expert
Joined: 02 Sep 2009
Posts: 54434

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16 Sep 2014, 00:34
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Difficulty:

25% (medium)

Question Stats:

79% (01:35) correct 21% (01:28) wrong based on 66 sessions

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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. $$\frac{1}{3}$$
B. $$\frac{2}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
E. $$\frac{3}{5}$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:34
Official Solution:

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. $$\frac{1}{3}$$
B. $$\frac{2}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
E. $$\frac{3}{5}$$

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

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.

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11 Oct 2016, 13:02
WHY DID I GET A WRONG ANSWER WHEN I TOOK THE TOTAL NUMBER OF STUDENTS AS 30 = 20 MALE,10 FEMALE

3/4*20(BOYS) +1/2(10) GIRLS = TOTAL

15+5=20

RATIO = 20/30

=2/3
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Joined: 02 Sep 2009
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13 Oct 2016, 02:34
yashrakhiani wrote:
WHY DID I GET A WRONG ANSWER WHEN I TOOK THE TOTAL NUMBER OF STUDENTS AS 30 = 20 MALE,10 FEMALE

3/4*20(BOYS) +1/2(10) GIRLS = TOTAL

15+5=20

RATIO = 20/30

=2/3

The ratio between male and female students is 2:3. If there are 30 students then m = 12 boys (not 20) and f = 18 (not 10) --> m:f = 12:18 = 2:3.
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13 Nov 2016, 18:23
Yes , Even i did the same mistake. On re - do Males are 12 and Females are 18 with Total students 30 as the ratio is 2:3
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08 Jul 2017, 03:43
I guess the key take away of this question is picking numbers by carefully reading the questions.

Pick number of female to be a number divisible by 3 and 4. It will make the calculation easier

Let Females = 12.

Males = $$\frac{2}{3}* 12 = 8$$

Total = 20

Males speaking foreign = $$\frac{3}{4} * 8 = 6$$

Females speaking foreign = $$\frac{1}{2} * 12 = 6$$

Total speaking foreign $$= 6+ 6 = 12$$

Required Ratio $$= \frac{12}{20}= \frac{3}{5}$$
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Re: M07-15   [#permalink] 08 Jul 2017, 03:43
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# M07-15

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