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# A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.

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Joined: 02 Sep 2009
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A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.  [#permalink]

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20 Mar 2018, 06:54
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Difficulty:

25% (medium)

Question Stats:

91% (01:08) correct 9% (01:53) wrong based on 28 sessions

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A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each. How many avocados did the grocer sell today?

(1) The number of avocados sold today is 20 more than twice the number of pineapples sold.
(2) Today the grocer received a total of \$155 from the sale of avocados and pineapples.

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Re: A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.  [#permalink]

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20 Mar 2018, 07:05
Bunuel wrote:
A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each. How many avocados did the grocer sell today?

(1) The number of avocados sold today is 20 more than twice the number of pineapples sold.
(2) Today the grocer received a total of \$155 from the sale of avocados and pineapples.

We'll use simple numbers to help show ourselves the logic.
This is an Alternative approach.

(1) Say 1 pineapple was sold. Then 2*1 + 20 = 22 avocados were sold.
Say 2 pineapples were sold. Then 2*2 + 20 = 24 avocados were sold.
Insufficient.

(2) Say the grocer sold as many pineapples as possible. That is, he sold 152/2 = 76 pineapples and 2 avocados.
Now, say we try to contradict this by having the grocer sell as many avocados as possible. Even without calculating, we can SEE that this gives a different solution.
Insufficient.

Combined:
So if the grocer sells p pineapples and a avocados (1) gives us a = 2p + 20 and (2) gives us 1.5a + 2p = 155.
Even without solving, we can see this is 2 distinct linear equations with 2 variables and therefore has one solution. (which happens to be p=25, a = 70)
Sufficient.

(C) is our answer.
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Re: A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.  [#permalink]

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20 Mar 2018, 07:06
Bunuel wrote:
A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each. How many avocados did the grocer sell today?

(1) The number of avocados sold today is 20 more than twice the number of pineapples sold.
(2) Today the grocer received a total of \$155 from the sale of avocados and pineapples.

St1 : A = 2P+20
2 variables, 1 eq...Insufficient.

St2 : 1.5A + 2.0P = 155.0
Again 2 variables, 1 equation => insufficient

Combining 1 & 2
We can solve for number of Avocados

Hence C
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Re: A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.  [#permalink]

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20 Mar 2018, 10:05
rkgstyle wrote:
Bunuel wrote:
A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each. How many avocados did the grocer sell today?

(1) The number of avocados sold today is 20 more than twice the number of pineapples sold.
(2) Today the grocer received a total of \$155 from the sale of avocados and pineapples.

St1 : A = 2P+20
2 variables, 1 eq...Insufficient.

St2 : 1.5A + 2.0P = 155.0
Again 2 variables, 1 equation => insufficient

Combining 1 & 2
We can solve for number of Avocados

Hence C

Also while using the variable method to solve such DS questions. It is advisable to see wether both the given equations are the same. Sometimes the statements are such the no new information is provided and in such cases the answer would be E.

Best,
Gladi
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Re: A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.  [#permalink]

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20 Mar 2018, 12:19
The mathematical solution has already been provided by other users. I will try to give an oral explanation and arrive at the answer through mental maths!-

1. Looking at statement (1)- we dont know the total money earned by the Shopkeeper, so we cannot determine the total number of Avocados sold- Not Sufficient
2. Looking at statement (2)- we can have many combinations that will satisfy the equation- Not Sufficient

Now combining, we know the total amount earned by the shopkeeper and also the constraint on the proportion of avocados and pineapples. So we will get the exact number of avocados only by combining the 2 statements
Re: A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.   [#permalink] 20 Mar 2018, 12:19
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# A grocer sells avocados for \$1.50 each and pineapples for \$2.00 each.

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