Question

A charitable association sold an average of $66$ raffle tickets per member. Among the female members, the average was $70$ raffle tickets. The male to female ratio of the association is $1:2$. What was the average number of tickets sold by the male members of the association?

• A. $55$
• B. $58$
• C. $60$
• D. $50$

Answer 1

Answer: (B)

$58$

You can answer this question without doing a lot of calculation. Women sold an average of $70$ raffle tickets, which is $4$ higher than the total average of $66$. Each woman is selling, therefore, an average of $+4$ tickets over the group average. You also know that the ratio of men to women is $1:2$. There are twice as many women and the total amount of extra tickets that the women sell needs to be canceled out by lower-than-average sales from the men. The positive difference from the average for women multiplied by $2$ must cancel with the negative difference from the average for men multiplied by $1$. If you call the difference from the average for men m then:
$1\times m+2\times (+4)=0$
$m+8=0$
$m=-8$
The men sold an average of $8$ fewer tickets than the total average so subtract: $66-8=58$.