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At a fruit store, apples are sold for $4 per pound and oranges are sol

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At a fruit store, apples are sold for $4 per pound and oranges are sol  [#permalink]

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New post 26 Jun 2018, 01:28
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Question Stats:

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[GMAT math practice question]

At a fruit store, apples are sold for $4 per pound and oranges are sold for $6 per pound. Is the total weight of apples sold greater than the total weight of oranges sold?

1) The average (arithmetic mean) price of fruit sold is less than $5.
2) The total weight of fruit sold is 10 pounds.

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At a fruit store, apples are sold for $4 per pound and oranges are sol  [#permalink]

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New post 26 Jun 2018, 01:42
here we have :

Apples = $4/pound
Oranges = $6/pound

Looking at option 1 :
The average price of fruits can be $5 only when both fruits are sold at equal quantities.
Let that quantity be x

Average cost = 6*x + 4*x / 2x = 10x/2x =$5
Now if the weight of oranges increases average cost will go over $5.
If the weight of apples increases the average cost will come down from $5.

{ Example : Av = 6*5+4*5/10 = $5 ; Av1 = 6*6+4*5/11 = $5.09 ; Av2 = 6*5+4*6/11 = $4.9 ;
You can see how the variation is. }

Thus we can safely conclude from this statement that weight of Apples sold > weight of Oranges.

Option A is SUFFICIENT.

Option B :

If total weight is 10 , there is no restriction on the weight of oranges or apples as there is not total amount or any other condition involved here.
I can buy 4 pounds of apples 6 pounds of Oranges or vice versa or any other quantity as well.

This option is INSUFFICIENT.

Thus the answer is : A
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Re: At a fruit store, apples are sold for $4 per pound and oranges are sol  [#permalink]

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New post 26 Jun 2018, 05:21
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MathRevolution wrote:
[GMAT math practice question]

At a fruit store, apples are sold for $4 per pound and oranges are sold for $6 per pound. Is the total weight of apples sold greater than the total weight of oranges sold?

1) The average (arithmetic mean) price of fruit sold is less than $5.
2) The total weight of fruit sold is 10 pounds.


Statement 1:
The average price-per-pound for the MIXTURE of apples and oranges (less than $5) is closer to the price-per-pound for apples ($4) than to the price-per-pound for oranges ($6).
Implication:
Weight-wise, the mixture must be composed mostly of apples.
Thus, the answer to the question stem is YES.
SUFFICIENT.

Statement 2:
If the mixture is composed of 9 pounds of apples and 1 pound of oranges, the answer to the question stem is YES.
If the mixture is composed of 1 pound of apples and 9 pounds of oranges, the answer to the question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.


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Re: At a fruit store, apples are sold for $4 per pound and oranges are sol  [#permalink]

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New post 28 Jun 2018, 02:30
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Let x and y be the weights of apples and oranges sold, respectively.
The question asks if \(x > y\).

Condition 1)
The average price of fruit sold is given by \(\frac{(4x + 6y)}{(x + y)}\). Now,
\(\frac{( 4x + 6y )}{( x + y )} < 5\)
\(=> 4x + 6y < 5(x+y)=5x+5y\)
\(=> 6y - 5y < 5x – 4x\)
\(=> y < x\)
and the answer is ‘yes’.
Thus, condition 1) is sufficient.

Condition 2)
Condition 2) tells us that \(x + y = 10\), but we cannot determine whether \(x >y\).
Condition 2) is not sufficient.

Therefore, A is the answer.

Answer: A
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Re: At a fruit store, apples are sold for $4 per pound and oranges are sol &nbs [#permalink] 28 Jun 2018, 02:30
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