A survey was conducted to find out the number of languages spoken by t

Number of employees = 210
Number of employees who did not speak English = 60
So, the number of employees who spoke English = 210 – 60 = 150

Number of employees who did not speak German = 150
So, number of employees who spoke German = 210 – 150 = 60

Number of employees who did not speak French = 170
So, number of employees who spoke French = 210 – 170 = 40

Number of employees who did not speak German or English = 20
So, these employees must speak only French (because it’s given that each employee speaks at least one language)

Number of employees who did not speak French and English = 20
So, these employees must speak only German (because it’s given that each employee speaks at least one language)

To Find: Maximum number of employees who spoke only English

To max the no. who only spoke English we need to reduce as little as possible from 150 (no. who spoke English)
We know French in total is 40, which means that max overlap between French/German/English can be 20. That leaves 20 of german out of the overlapping circles. This 20 needs to get subtracted from 150 of English. Hence max English will be 150-20=130

The explanation will help greatly if you try to understand it with a diagram.

IMO answer has to be 130

According to the data given and venn diagram
c+f+g = 60 .......................1
a+d+g = 150.......................2
a+b+c = 170........................3
g=20
c=20

From 1, f = 20
From 2, a+d = 130
From 3, a+b = 150

Also, a+b+c+d+e+f+g = 210
150 + 20+d+e+20+20 = 210
d=-e
that means both d=e = 0

so, a+d = 130 means a = 130
and b = 20

The no. of people who spoke only english = a = 130
Answer C

the only tricky part in this question is to understand the meaning of the term "only english speaking employee" and what segment it represents in a venn diagram consisting of data like not E, not G, not F etc.. Its actually very simple once we draw the venn diagram (draw it using the data below).

Given:-
Not E = 60 (not English speaking employees)
Not G = 150
Not F = 170
p = not E,G
q = not G,F
r = not E,F
k = not E,G,F
p+k = 20
k+r = 20
N=0

To find :-
q (since q is outside Not E and inside Not G and Not F it is only English speaking employees,
trust me once you draw the venn its very intuitive!)

hard work done! plug in all values and arrive at your answer:-
T-N = not E + not G + not F - (p+q+r) - 2k
210-0 = 60+150+170-(p+k) -(k+r) -q {p+k = 20, k+r = 20, substituting the values in this equantion}
q = 130

Could you share diagram to explain the how you determine 20 should be the minimum value to be subtracted from 150

Can anyone clarify if my concept is right here?

So from the info given we can say that 60-20= 40 people speaks English and french and 40-20=20 people speaks English and German. So from 150 (the number of people who speaks English) we will reduce either 20 or 40 to get maximum and minimum number of English speaking people respectively.

Min number of English speaking people 110 and max number of English speaking people will be 130.

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