Fiona picks 30 apples and puts them in her basket. The apples have

Question

Fiona picks 30 apples and puts them in her basket. The apples have either one of two colors and either one of two flavors. She picks apples that are either red or sweet or both red and sweet. If there are 20 green apples in the basket, how many sweet red apples are in the basket?

(1) Of the apples in the basket, 26 apples are sweet.

(2) There are 4 red apples in the basket that are not sweet.

(1) Of the apples in the basket, 26 apples are sweet.

(2) There are 4 red apples in the basket that are not sweet.

Tough word problem.

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gmatophobia · Answer

We can plot the information from the premise in a 2 * 2 matrix as shown below - Note: Because Fiona picks apples that are either red or sweet or both red and sweet, she will not pick any green non sweet apples. 1.jpg Statement 1 We can fill in the matrix with the information provided in statement 1. Once we have filled in the details, we can find the information in the required cell as shown. 2.jpg Hence the statement is sufficient. We can eliminate B, C and E Statement 2 We can fill in the matrix with the information provided in statement 2. Once we have filled in the details, we can find the information in the required cell as shown. 3.jpg Statement 2 is also sufficient. Option D

GmatKnightTutor · Answer

Hello, people. This is an interesting one which can seem ovewhelming, but if we use algebra to first sort things out and focus clearly on what we need, things may be easier to process.

First, we're told there are 4 types of apples: red apples that are sweet, red apples that are not sweet, green apples that are sweet, and green apples that are not sweet.

Let's give them algebraic values: a, b, c, d (e.g. "a" applies to red apples that are sweet inside Fiona's basket)

We're told Fiona picks 30 apples and puts them in her basket. This means that:

a + b + c + d = 30

She only picks apples that are red or sweet or both red and sweet. This means she does not pick any green apples that are not sweet. Basically, this means d = 0.

Therefore, a + b + c = 30

We're then told there are 20 green apples in the basket.

Since the only green apples in the basket are green apples that are sweet, we know c = 20

a + b = 10

Whew! We're nearly there.

Now the question asks us how many sweet red apples are in the basket. Basically, what is the value of a?

_____

Statement 1

This tells us 26 of the apples in the basket are sweet.

Remember, a + b + c = 30

Of these, only a and c are sweet, so a + c = 26

b is therefore = 4

We also know from the original info that a + b = 10

a is therefore = 6.

Sufficient!

_______

Statement 2

We're told there are 4 red apples that are not sweet in the basket.

Basically, this directly tells us b = 4

Again, we can use what we know from the original info in that a + b = 10

a is therefore = 6

Sufficient!

_______

(D) is your answer.

Fiona picks 30 apples and puts them in her basket. The apples have

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