Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcel

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcel

by Vincen » Wed Nov 18, 2020 11:09 am

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Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller parcels are the same size, what is the number of acres in one of the smaller parcels?

(1) The combined size of the larger parcel and one of the smaller parcels is 416 acres.
(2) The size of the larger parcel is 312 acres.

Answer: D

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Wed Nov 18, 2020 11:09 am

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

Re: Josie's land is to be divided into three parcels. If the larger parcel is 60 percent of the total and the smaller pa

by deloitte247 » Fri Nov 20, 2020 3:40 pm

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Let total = t; larger parcel = l; small parcel = s
Since samller parcels are the same size = s + s = 2s
$$l=60\%\ of\ t=\frac{60}{100}t=\frac{3}{5}t$$
$$2s=40\%\ of\ t=\frac{40}{100}t=\frac{2}{5}t$$
$$s=\frac{\frac{2}{5}t}{2}=\frac{1}{5}t$$
Target question: what is the number of acres in one of the smaller parcels?
Statement 1: The combined size of the larger parcel and one of the smaller parcels is 416 acres.
l+s = 416
$$i.e\ \frac{3}{5}t+\frac{1}{5}t=416$$
$$\frac{4}{5}t=416$$
$$t=\frac{416\cdot5}{4}=520$$
$$Therefore,\ s=\frac{1}{5}\cdot520=104\ acres$$
Therefore, statement 1 is SUFFICIENT

Statement 2: The size of the larger parcel is 312 acres.
l=312
$$Hence,\ \frac{3}{5}t=312,\ and\ t=312\cdot\frac{5}{3}=520$$
This is similar to the information established in statement 1.
Hence, s=104 areas; therefore, statement 2 alone is SUFFICIENT.

Since each statement alone is SUFFICIENT, then, option D is the correct answer.