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A bowl contains a total of 18 fruit: a apples, o oranges, and p pears

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A bowl contains a total of 18 fruit: a apples, o oranges, and p pears  [#permalink]

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New post 01 Feb 2017, 10:43
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A bowl contains a total of 18 fruit: a apples, o oranges, and p pears. If each fruit in the bowl is one of these types, how many apples are in the bowl?

(1) There are three times as many apples as oranges and two times as many oranges as there are pears in the bowl.
(2) There are 4 oranges in the bowl.

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Re: A bowl contains a total of 18 fruit: a apples, o oranges, and p pears  [#permalink]

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New post 02 Feb 2017, 10:26
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Bunuel wrote:
A bowl contains a total of 18 fruit: a apples, o oranges, and p pears. If each fruit in the bowl is one of these types, how many apples are in the bowl?

(1) There are three times as many apples as oranges and two times as many oranges as there are pears in the bowl.
(2) There are 4 oranges in the bowl.


Target question: How many apples are in the bowl?

Given: There are 18 pieces of fruit, and there are a apples, o oranges, and p pears
So, we can write: a + o + p = 18

Statement 1: There are three times as many apples as oranges and two times as many oranges as there are pears in the bowl
"There are three times as many apples as oranges": a = 3o

"...there are two times as many oranges as there are pears":
o = 2p

Now take a = 3o, and replace o with 2p to get: a = 3(2p) = 6p

Since all 3 variables can be expressed in terms of p, we can take a + o + p = 18 and REPLACE a and o to get...
6p + 2p + p = 18
Simplify: 9p = 18
So, p = 2

If there are 2 pears, then there are 4 oranges, and there are 12 apples.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There are 4 oranges in the bowl
In other words, o = 4
Take a + o + p = 18 and replace o with 4 to get: a + 4 + p = 18
Simplify: a + p = 14
There's no way to determine the value of a (the number of apples).
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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Re: A bowl contains a total of 18 fruit: a apples, o oranges, and p pears  [#permalink]

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New post 03 Feb 2017, 05:51
Bunuel wrote:
A bowl contains a total of 18 fruit: a apples, o oranges, and p pears. If each fruit in the bowl is one of these types, how many apples are in the bowl?

(1) There are three times as many apples as oranges and two times as many oranges as there are pears in the bowl.
(2) There are 4 oranges in the bowl.



Statement 1 gives the ratio of a:o:p :: 6:2:1
Maximum fruit is the bowl is 18 , got by multiplying the ratio by 2 .
a = 12
Sufficient


Statement 1 says 4 oranges . Clearly not sufficient .

Answer is A .
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Re: A bowl contains a total of 18 fruit: a apples, o oranges, and p pears  [#permalink]

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New post 01 Sep 2018, 08:16
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Re: A bowl contains a total of 18 fruit: a apples, o oranges, and p pears &nbs [#permalink] 01 Sep 2018, 08:16
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