Question: At a certain fruit stand, the price of each apple is 40 cents and the price of each orange is 60 cents. Mary selects a total of 10 apples and oranges from the fruit stand, and the average (arithmetic mean) price of the 10 pieces of fruit is 56 cents. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Solutions and Explanation

Approach Solution : 1

Here, an orange costs 60 cents and an apple costs 40 cents.
The average cost is 56 cents.
The ratio between the apples and oranges is thus
Orange : apple = 56-40 : 60-56
Orange: apple = 4: 16

Therefore, Orange:apple = 1:4
10 is the total, so 2 are apples and 8 are oranges.
The average price must now be 52 cents.
Apples and oranges will therefore be in proportion,
Orange: apple = 52-40 : 60-52
Orange: apple = 8: 12
Orange: apple = 8: 12 range : apple = 2:3
Since there are 2 apples from the previous calculation, oranges must be 3 in total.

Number of oranges to be returned are 8 - 3 = 5

Correct Answer: (E)

Approach Solution : 2

Consider x as the number of apples and y as the number of oranges.

Orange is 60 cents while apple is 40 cents.

10 apples and oranges are chosen.

Average (Mean in Arithmetic) = Sum/Total

=> Average (Mean in Arithmetic) 56 = (40x+60y)/10
=> 40x + 60y = 560. Let this be (1)

Consider 'p' as oranges that should be reinserted. Then,

Average = Sum/Total

=> Average52 = [40x+(y−p) 60] / (10−p)
=> 40x + 60y - 60p = 520 - 52p. Let this be (2)

Subtract (1) and (2)
=> 60 p = 40 + 52p
=> 8p = 40
=> p = 5

Correct Answer: (E)

Approach Solution : 3

Let us go for a simple approach

The average cost of the fruit pieces she keeps is 52 cents.
Each fruit piece costs either 40 or 60 cents, so the total price has to be a multiple of 10.
Only if the quantity of fruit is an integer with a value that ends in 5 or 0, the total cost be a multiple of 10 given an average price of 52.
Mary must put 5 pieces of fruit back because the original quantity was 10. This will result in a new quantity that is either 5 or 0. (The number 5 is chosen from the options as it is the only number from the options that fits the basic requirements)
10-5 = 5

Correct Answer: (E)

“At a certain fruit stand, the price of each apple is 40 cents” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

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