Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that

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

Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that

by BTGmoderatorDC » Wed Apr 29, 2020 6:19 pm

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Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that Ann bought was twice the number of oranges and if the number of pears that Ann bought was the same as the number of apples and oranges combined, what fraction of the total number of pieces of fruit that Ann bought were pears?

(1) Ann bought a total of 18 pieces of fruit.
(2) Ann bought 5 bananas.

OA E

Source: GMAT Prep

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 29, 2020 6:19 pm

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

Re: Ann bought five different kinds of fruit: apples, oranges, pears, mangoes, and bananas. If the number of apples that

by deloitte247 » Sun May 03, 2020 3:56 am

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Let apples = a; orange = y; pears = p; mangoes = m; bananas = b
a = 2y and p = a + y
Since a = 2y; p = 2y + y = 3y

Target question => What fraction of the total number of pieces of fruit that Ann bought were pears?
$$i.e\ fraction\ of\ pear\ =\ \frac{total\ pear}{sum\ of\ all\ fruits}$$
$$\ \frac{3y}{y+2y+3y+m+b}$$
$$Find\frac{3y}{6y+m+b}$$

Statement 1 => Ann bought a total of 18 pieces of fruit
$$i.e\ 6y+m+b=18\ \ \ and\ fraction\ of\ p\ =\frac{3y}{18}$$
y is unknown, so target question cannot be answered. Statement 1 is NOT SUFFICIENT

Statement 2 =>Ann bought 5 bananas
$$b=5\ \ and\ \ fraction\ of\ p\ =\frac{3y}{6y+m+5}$$
m and y are unknown, so target question cannot be answered and statement 2 is NOT SUFFICIENT

Combining both statements together =>
$$6y+m+b=18\ and\ b\ =\ 5$$
$$6y+m+5=18$$
$$\frac{6y}{6}=\frac{18-5-m}{6}$$
$$y=\frac{13-m}{6}$$
$$fraction\ of\ p\ =\frac{3y}{18}$$
$$where\ y=\frac{13-m}{6}$$
$$=\frac{13-m}{6}\cdot\frac{1}{18}=\frac{13-m}{6\left(18\right)}$$
The value of m still remains unknown and target question cannot be answered. Therefore, both statements combined together are NOT SUFFICIENT

Answer = E