PCAT Math Question

[217933]

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Can someone show me the work to solve this problem? The book describes it in written language and I still don't understand the equation they set up.

In a class of 40 students, 30 speak French and 20 speak German. What is the lowest possible number of students who speak both languages?

A. 5
B. 20
C. 15
D. 10

 

[Transformer]

Ok I like this problem.

Here is how I solved it.

The answer choices are:
5
20
15
10

What is the lowest number of students who speak both languagues
(30 spoke French and 20 spoke German)
(There is Total of 40 students in the class)

Lets take the value: 10

If the 10 people spoke French and German. Subtract 10 from the total
30 - 10 = 20 (this is the number of students left who speak French)
20 - 10 = 10 (number of students left who speak German)

20 + 10 = 30 (total number of students left who separately spoke each language)

Also, note that there are a total of 40 people in the class so subtract 10 from 40 students
40 - 10 = 30 students are left


30 and 30 matches so ...10 is the lowest possible number of students who speak both languages

Use the above process for all the other choices (3,20,15) and you'll see that only 10 makes sense.

 

[ufdlim]

(30-x) + (20-x) + x = 40
50 - x = 40
x = 10

 

[cdpiano27]

Easy formula

From basic statistics

total number is A union B

A union B = A + B - A intersect B

A = number of students who speak French
B = number of students who speak German
A intersect B = number of students who speak both languages

A union B = total number of students

40 = 30 + 20 - x

x = 10

Review these basic probability formulas