Maths logic question

Practice Question Solving
1

Year 9s have an option to choose 1 or 2 out of 4 languages – French, German, Russian or Mandarin to learn at Layton High School. There are 180 students in year 9. 1/3 of students take 2 languages, the rest only learn 1.

There are twice as many students studying Russian as there are Mandarin. 60 students study French which is 2/3 the amount that study Russian.

Which of the following statements is true about the number of students who study German?

A The number of students studying German is the same as French
B The number of students studying German is the same as Mandarin
C The number of students studying German is the same as Russian
D The number of students studying German is half the number of students studying French

it should be answer B but i don’t understand how you solve this.

2

Let’s tag the language-taking students as Rs for Russian, Fs for French, Gs for German, Ms for Mandarin and T for total number of students.

Since Fs=60=2/3 Rs —> Rs=90
Since Rs=2 . Ms = 90 —> Ms=45
So, Ms + Rs + Fs = 45 + 90 + 60 = 195 (I)

Now, we have to consider how many times the languages have been taken in total:
1/3 . T take 2 languages —> 1/3 . 180 = 60 —> 60 . 2 = 120
2/3 . T take 1 language —> 2/3 . 180 = 30 —> 120 . 1 = 120
so, 120 + 120 = 240 times languages have been chosen. (II)

From I and II we conclude that students who took German - as the only left language in our calculation - were:
II - I = 240 - 195 = 45
which is the same number as Ms.

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