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

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by Max@Math Revolution » Tue Jun 26, 2018 1:17 am

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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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Source: — Data Sufficiency |
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by GMATGuruNY » Tue Jun 26, 2018 5:17 am
Max@Math Revolution 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.

The correct answer is A.
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by Max@Math Revolution » Thu Jun 28, 2018 12:45 am
=>

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 (4x + 6y)/(x + y). Now,
( 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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