60 employees.19 degree,18 diploma,50 cpa,13 degree and diploma,11 diploma and cpa,13 degree and cpa, 9 degree , diploma and cpa

Question

a) none of the three qualifications b) only cpa c) degree and diploma and not cpa d) only one of the three qualifications e) only two of the qualifications

Answer 1

This can be solved using a Venn diagram (below).

 

A=Employees without the named qualifications.

B=Only degree

C=Only CPA

D=Only diploma

E=Degree+diploma only

F=CPA+diploma only

G=CPA+degree only

H=All three qualifications

Now we can put in some numbers.

A+B+C+D+E+F+G+H=60 (employees)

B+E+G+H=19 (degree)

D+E+F+H=18 (diploma)

C+F+G+H=50 (CPA)

H=9

E+H=G+H=13, so E=G=13-H=4; F+H=11, so F=2; C=50-2-4-9=35; D=18-4-2-9=3; B=19-4-4-9=2.

A=60-2-35-3-4-2-4-9=1.

(a) A=1 employee with none of the qualifications.

(b) C=35 employees with CPA only.

(c) E=4 employees with degree and diploma only.

(d) B+C+D=2+35+3=40 employees with only one qualification.

(e) E+F+G=4+2+4=10 employees with only two qualifications.