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A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25

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by BTGmoderatorDC » Thu Aug 04, 2022 1:42 am

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A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25 percent are strawberries. How many pieces of fruit are on the first layer of the cake?

(1) Of the pieces of fruit on the first layer, 6 are strawberries.
(2) 20 percent of the 20 pieces of fruit on the second layer are strawberries.


OA C

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Source: — Data Sufficiency |
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Re: A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25

by swerve » Sun Aug 07, 2022 11:36 am
BTGmoderatorDC wrote: ↑
Thu Aug 04, 2022 1:42 am
 A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25 percent are strawberries. How many pieces of fruit are on the first layer of the cake?

(1) Of the pieces of fruit on the first layer, 6 are strawberries.
(2) 20 percent of the 20 pieces of fruit on the second layer are strawberries.


OA C

Source: GMAT Prep
Say there are \(x\) pieces of fruit on the cake, thus we are given that there are \(0.25x\) pieces of strawberries.

From 1
No info about the second layer. Not sufficient. \(\Large{\color{red}\chi}\)

From 2
There are \(0.2\cdot 20=4\) pieces of strawberries on the second layer. No info about the first layer. Not sufficient. \(\Large{\color{red}\chi}\)

Combining 1 & 2
There are a total of \(6+4=10\) pieces of strawberries, thus there are a total of \(40\) pieces of fruit on the cake (from \(0.25x=10\)). Since from (2) we have that there are \(20\) pieces of fruit on the second layer, then there are \(40-20=20\) pieces of fruit on the first layer. Sufficient. \(\Large{\color{green}\checkmark}\)

Therefore, C
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