In a certain school, there are 160 boys and 240 girls. If 15

This is a weighted average problem, where 15% and 25% are the averages of each group. We can draw a number line with the three averages:

---15------------A------25---

Since the ratio of boys to girls is 2 to 3, the overall average A will divide the total distance above in a 3 to 2 ratio, so the larger distance, from 15 to A, is 3/5 of the total distance between 15 and 25, so that distance is 6 and A = 15 + 6 = 21.

I'm using a weighted average method sometimes called 'alligation' here - someone unfamiliar with that method might not follow the logic above, but can read about the method by googling that term.

For this particular problem, it's straightforward to solve arithmetically, though the method above is a better method for harder questions. Here we have (3/20)(160) = 24 lefthanded boys, (1/4)(240) = 60 lefthanded girls, and 400 students in total, so the answer is (24+60)/400 = 84/400 = 21/100 = 21%.

BTGmoderatorDC wrote:In a certain school, there are 160 boys and 240 girls. If 15 percent of the boys are left-handed and 25 percent of the girls are left-handed, what percent of the school`s entire student population is left-handed?

A. 18
B. 20
C. 21
D. 23
E. 24

OA C

Source: Magoosh

160 x 0.15 = 24 left-handed boys

240 x 0.25 = 60 left-handed girls

Thus, 84/400 x 100 = 21/100 x 100 = 21 percent of the entire population is left-handed.

Answer: C