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# A certain cake has two layers with pieces of fruit on top of

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A certain cake has two layers with pieces of fruit on top of [#permalink]  01 Dec 2012, 04:03
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Dec 2012, 05:59, edited 2 times in total.
Renamed the topic and edited the question.
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Re: DS - A certain cake has two - Gmat Prep Extension Pack [#permalink]  01 Dec 2012, 04:25
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lazarogb wrote:
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 strawberies. 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.

The explanation from the gmat prep is a bit confusing, can anyone make a more direct user-friendly solution??

1)No data on the composition of the layer. Clearly Insufficient.

2)We get that there are 4 strawberries on the second layer.Clearly insufficient.

1 & 2 together. There are a total of 10 strawberries. This constitutes 25% of the total pieces of fruit. So total pieces of fruit over both layers = 40. Layer two has 20. So layer 1 has 40 - 20 = 20. Sufficient.

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Re: DS - A certain cake has two - Gmat Prep Extension Pack [#permalink]  01 Dec 2012, 04:48
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th03 wrote:
lazarogb wrote:
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 strawberies. 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.

The explanation from the gmat prep is a bit confusing, can anyone make a more direct user-friendly solution??

Consider 1)
It is given that 6 are strawberries. We have no idea about the number of other pieces of fruit on the first layer.
Thus, eliminate choices A and D.

Consider 2)
No information is given about the number of pieces of fruit in the first layer.
Thus, eliminate B.

Consider both 1) and 2)
First layer=6 strawberries
Second layer=20% of 20 pieces of fruit are strawberries => 4 strawberry pieces
=> (6 + 4) strawberries totals to 25% as given in the question.
Using this, we can find out the number of pieces of the other fruit.
=> If 25%=10 pieces, 75%=30 pieces

Hence, we can find the solution. The answer is C.

You actually do not need to calculate so much and find the exact number. The moment we arrive at 25%=10 strawberry pieces, we should choose C and move on.

Hope this helps!

Just my two cents...

If the second statement had been something like

Of the pieces of fruit on the second layer, 4 are strawberries. We still would have got 25% = 10. But the statement would still have been insufficient and answer would have been E.
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Re: DS - A certain cake has two - Gmat Prep Extension Pack [#permalink]  01 Dec 2012, 04:29
lazarogb wrote:
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 strawberies. 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.

The explanation from the gmat prep is a bit confusing, can anyone make a more direct user-friendly solution??

Ok we have 2 layers in a cake and on top of each layer we have fruits. Among these fruits 25% is strawberies.
Let x be all the fruits in both the layers.
Question stems tells 25% of X = strawberies
What is X? To find what x is we need to know nos of strawberies in both the layers. ie. 25% of x = strawberies in layer 1 + strawberies in layer 2

Statement 1 says 25% of x = 6 + strawberies in layer 2; we still dont know strawberies in layer 2 so we cant find x.
Statement 2 says 25% of x = strawberies in layer 1 + 4 ; we still dont know strawberies in layer 1 so we cant find x.

Combined we have strawberies in both the layers so we CAN find x.

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Re: DS - A certain cake has two - Gmat Prep Extension Pack [#permalink]  01 Dec 2012, 04:37
lazarogb wrote:
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 strawberies. 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.

The explanation from the gmat prep is a bit confusing, can anyone make a more direct user-friendly solution??

Consider 1)
It is given that 6 are strawberries. We have no idea about the number of other pieces of fruit on the first layer.
Thus, eliminate choices A and D.

Consider 2)
No information is given about the number of pieces of fruit in the first layer.
Thus, eliminate B.

Consider both 1) and 2)
First layer=6 strawberries
Second layer=20% of 20 pieces of fruit are strawberries => 4 strawberry pieces
=> (6 + 4) strawberries totals to 25% as given in the question.
Using this, we can find out the number of pieces of the other fruit.
=> If 25%=10 pieces, 75%=30 pieces

Hence, we can find the solution. The answer is C.

You actually do not need to calculate so much and find the exact number. The moment we arrive at 25%=10 strawberry pieces, we should choose C and move on.

Hope this helps!
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Re: A certain cake has two layers with pieces of fruit on top of [#permalink]  01 Dec 2012, 06:08
Expert's post
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?

Say there are x pieces of fruit on the cake, thus we are given that there are 0.25x pieces of strawberries.

(1) Of the pieces of fruit on the first layer, 6 are strawberries. No info about the second layer. Not sufficient.

(2) 20 percent of the 20 pieces of fruit on the second layer are strawberries --> there are 0.2*20=4 pieces of strawberries on the second layer. No info about the first layer. Not sufficient.

(1)+(2) From above we have that there are total of 6+4=10 pieces of strawberries, thus there are 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.

Hope it's clear.
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Re: A certain cake has two layers with pieces of fruit on top of [#permalink]  17 Jan 2013, 04:46
Is this a venn diagram question?
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Re: A certain cake has two layers with pieces of fruit on top of [#permalink]  17 Jan 2013, 04:51
Expert's post
fozzzy wrote:
Is this a venn diagram question?

No this is not an overlapping sets problem.
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Re: A certain cake has two layers with pieces of fruit on top of [#permalink]  29 Jan 2014, 16:45
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Re: A certain cake has two layers with pieces of fruit on top of   [#permalink] 29 Jan 2014, 16:45
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