Of the $48$ students in a class, $16$ like to study History. What percentage of the girls in the class do not like

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Wed Sep 23, 2020 5:48 am

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Of the $48$ students in a class, $16$ like to study History. What percentage of the girls in the class do not like to study History?

(1) One-third of the boys in the class like to study History.

(2) The number of girls who like History is $50$ percent of the number of girls who do not like History.

Answer: D

Source: e-GMAT

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Source: Beat The GMAT — Data Sufficiency | Wed Sep 23, 2020 5:48 am

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

Re: Of the $48$ students in a class, $16$ like to study History. What percentage of the girls in the class do not li

by deloitte247 » Sat Oct 03, 2020 9:18 am

Total number of students = 48
Students who like history = 16
Students who do not like history = 48 - 16 = 32

Target question => What percentage of the girls in the class do not like to study history?
$$i.e\ \frac{what\ is\ the\ number\ of\ girls\ who\ do\ not\ like\ history\ }{Total\ number\ of\ girls}\cdot\frac{100}{1}$$
Let the number of girls who do not like history = x
Let the total number of girls = y
Girls who like history = y - x
Total number of boys = 48 - y
Boys who like history = 16 - (y - x) = 16 - y + x
Boys who do not like history = 32 - x

$$Statement\ 1=>\ one-third\ of\ the\ boys\ in\ class\ like\ to\ study\ history$$
$$16-y+x=\frac{1}{3}\cdot\left(48-y\right)$$
$$16-y+x=\frac{48}{3}-\frac{y}{3}$$
$$16-y+x=16-\frac{y}{3}$$
$$-y+x=\frac{-y}{3}$$
$$x=\frac{-y}{3}+\frac{y}{1}=\frac{-y+3y}{3}=\frac{2y}{3}$$
$$\exp res\sin g\ it\ in\ terms\ of\ \frac{x}{y};\ divide\ through\ by\ y$$
$$x\div y=\frac{2y}{3}\div y$$
$$x\cdot\frac{1}{y}=\frac{2y}{3}\cdot\frac{1}{y}$$
$$\frac{x}{y}=\frac{2}{3}$$
$$\%\ of\ girls\ who\ don't\ like\ history\ =\ \frac{2}{3}\cdot100\ =\ 67\%$$
$$Statement\ 1\ is\ SUFFICIENT$$

$$Statement\ 2\ =>\ The\ number\ of\ girls\ who\ like\ history\ is\ 50\%\ of\ the\ number\ of\ girls\ who\ do\ not\ like\ history$$
$$y-x=50\%\ of\ x$$
$$y-x=\frac{50}{100}\cdot x$$
$$y-x=\frac{x}{2}$$
$$2\left(y-x\right)=x$$
$$\left(\exp res\sin g\ it\ in\ terms\ of\ \frac{x}{y}\right)$$
$$2y-2x=x$$
$$2y=x+2x$$
$$\frac{2y}{y}=\frac{3x}{y}$$
$$2=\frac{3x}{y}$$
$$2\div3=\frac{3x}{y}\div3$$
$$2\cdot\frac{1}{3}=\frac{3x}{y}\cdot\frac{1}{3}$$
$$\frac{2}{3}=\frac{x}{y}$$
$$\%\ of\ girls\ who\ don't\ like\ history=\frac{2}{3}\cdot100=67\%$$
$$statement\ 2\ is\ SUFFICIENT$$

$$Since\ each\ statement\ alone\ is\ SUFFICIENT,$$
$$Answer\ =\ D$$

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