At Springfield High, Three-Fourths of the Male Students and Half of the Female Students Speak a Foreign Language GMAT Problem Solving

Question: 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?

1. \(\frac{1}{3}\)
2. \(\frac{2}{3}\)
3. \(\frac{1}{2}\)
4. \(\frac{3}{4}\)
5. \(\frac{3}{5}\)

“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?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1

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.

Correct option: E

Approach Solution 2

Pick the number of females to be a number divisible by 3 and 4. This will make the calculations easier.

Let number of females = 12

Then 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 = \(\frac{12}{20}=\frac{3}{5}\)

Correct option: E

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