M47-201

Question

At a charity event, 80 volunteers were assigned to exactly one of two roles: setup crew or check-in desk. If one volunteer is selected at random from the 80 volunteers, is the probability greater than \(\frac{3}{10}\) that the selected volunteer is a woman on the setup crew?

(1) There were 45 men among the 80 volunteers.

(2) There were 22 volunteers on the setup crew.

Show Answer

Official Answer

B

(1) There were 45 men among the 80 volunteers.
 
(2) There were 22 volunteers on the setup crew.

Bunuel · Answer

Official Solution:

At a charity event, 80 volunteers were assigned to exactly one of two roles: setup crew or check-in desk. If one volunteer is selected at random from the 80 volunteers, is the probability greater than  \frac{3}{10}  that the selected volunteer is a woman on the setup crew? 
 
The question asks:
 
Is  \frac{\{	ext{women on setup crew}\}}{80} > \frac{3}{10} ?
 
Is  \{	ext{women on setup crew}\} > 24 ?
 
Thus, the question is equivalent to asking whether there were more than 24 women on the setup crew.
 
(1) There were 45 men among the 80 volunteers.
 
So there were:
 
 80 - 45 = 35  women
 
But we do not know how many of these women were on the setup crew. The number of women on the setup crew could be more than 24 or not more than 24.
 
Not sufficient.
 
(2) There were 22 volunteers on the setup crew.
 
Since there were only 22 volunteers on the setup crew in total, the number of women on the setup crew could not possibly be more than 22. So the number of women on the setup crew was definitely not more than 24. The answer to the question is NO.
 
Sufficient.
 
Answer: B

M47-201

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