Question

A survey of a group’s viewing habits over the last year revealed the following information: (i) 28% watched gymnastics (ii) 29% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and baseball (v) 12% watched baseball and soccer (vi) 10% watched gymnastics and soccer (vii) 8% watched all three sports. Calculate the percentage of the group that watched none of the three sports during the last year. (A) 24% (B) 36% (C) 41% (D) 52% (E) 60%

Answer 1

Answer: D) 52%

Step-by-step explanation:

G = gymnastics

B = baseball

S = soccer

G = 28%

BA = 29%

S = 19%

G and BA = 14%

BA and S = 12%

G and S = 10%

GBS = 8%

So, as we can see at the Venn diagram attached (consider every number in %)

GBS = 8

A = G and S - GBS = 10 - 8 = 2

B = G and BA - GBS = 14 - 8 = 6

C = BA and S - GBS = 12 - 8 = 4

Only G = G - A - B - GBS = 28 - 2 - 6 - 8 = 12

Only BA = BA - B - C - GBS = 29 - 6 - 4 - 8 = 11

Only S = S - A - C - GBS = 19 - 2 - 4 - 8 = 5

So, 2+6+4+12+11+5+8 = 48

100 - 48 = 52%