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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Feb 28, 2019 11:39 pm

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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

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Source: Beat The GMAT — Problem Solving | Thu Feb 28, 2019 11:39 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sat Mar 02, 2019 4:21 am

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%.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Mar 02, 2019 4:37 am

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

Left-handed boys = 15% of 160 = 24.
Left-handed girls = 25% of 240 = 60.
(total left-handed)/(total students) = (24+60)/(160+240) = 84/400 = 21/100 = 21%.

The correct answer is C.

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Tue Mar 05, 2019 4:59 am

Total no of boys = 160
Left handed boys = 15% of the total boys
=24 boys $$=\frac{15}{100}\cdot160$$

Total no of girls = 240
Left hande girls = 25% of the total girls.
$$=\frac{25}{100}\cdot240\ =60girls$$ $$=\frac{25}{100}\cdot240\ =60girls$$

Total left handed students in the school = Left handed boys + Left handed girls = 24 + 60 = 84 students
Students entire population = 160 + 240 = 400
% of left handed students in the school
$$\frac{84}{100}\cdot100=21\%$$

$$answer\ is\ Option\ C$$

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Mar 06, 2019 6:54 pm

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

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