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

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.

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.

Answer: C.

Hope it's clear.

Is this a venn diagram question?

No this is not an overlapping sets problem.

Should we assuming that both layers have the same amount of fruit on them? I know how to calculate total pieces but how would we know how they are divided amount the layers?

No.. There is no reason to information in the question that suggests that the two layers have the same number of fruits.. Statement B states that there are 20 pieces of fruit on the second layer and we can calculate the total number of fruits. So from that information we can calculate the total number of fruits in he first layer.

St. 1 -- NS. There is no relation between total SB % and number of fruits in first layer only
St. 2 -- NS. This gives us number of strawberries in the 2nd layer but depending upon number of strawberries, total number of fruits (and hence number of fruits in first layer) could vary.

C is the correct answer since combining gives us the total number of SB i.e. 10. That gives us the total number of fruits (10/25% = 40) and the number of fruits in the first layer (total - number in second layer).

(1) We can't determine the number of strawberries on the second layer; INSUFFICIENT.

(2) We can't determine the number of fruit on the first layer; INSUFFICIENT.

(1&2) We're told the pieces of fruit = 25% strawberries.

4 out of the 20 pieces of fruit on the second layer are strawberries. As well, we know that 6 strawberries are on the first layer. We can create the following equation

\(\frac{10}{20+x} = \frac{1}{4}\)

\(x = 20\)

There are 20 pieces of fruit on the first layer of the cake. SUFFICIENT.

Answer is C.

Bunuel, can you please clarify what does it indicate in the second statement that 20 is the total # of fruits on the second layer?

Check the highlighted part:

(2) 20 percent of the 20 pieces of fruit on the second layer are strawberries.

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