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Q 8. At a certain food stand, the price of each apple is

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Q 8. At a certain food stand, the price of each apple is  [#permalink]

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New post 10 Oct 2005, 11:45
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Q 8.
At a certain food stand, the price of each apple is ¢ 40 and the price of each orange is ¢60. Mary selects a total of 10 apples and oranges from the food stand, and the average (arithmetic mean) price of the 10 pieces of fruit is ¢ 56. How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is ¢ 52?
A. 1
B. 2
C. 3
D. 4
E. 5
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New post 10 Oct 2005, 11:56
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e. 5

let x be number of apples, y be number of oranges.

(40x+60y)/x+y = 56

or 40x+60y=560

or 4x+6y=56

we also know that x+y = 10

solving simultaneously for x & y, we get x = 2, y = 8

now, (2*40+y*60)/2+y = 52

or 80+60y=104+52y

= y=3

now subtracting the previous value of y from the new value, 8-3 = 5

so she must replace 5 oranges

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New post 10 Oct 2005, 12:09
The answer is B.

x + y = 10

40x + 60y/ x+y = 52

40x + 60y = 520

400 - 40y + 60y = 520

20 y = 120

y = 6

to get average 56, y = 56 (pls refer to chets post)

Hence 8 - 6 = 2.

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New post 10 Oct 2005, 12:14
sudhagar wrote:
The answer is B.

x + y = 10

40x + 60y/ x+y = 52

40x + 60y = 520

400 - 40y + 60y = 520

20 y = 120

y = 6

to get average 56, y = 56 (pls refer to chets post)

Hence 8 - 6 = 2.


when she returns oranges, x+y will no longer be equal to 10.

x will remain 2, and y will be the new number of oranges.

If she returns 5 oranges, she will have 3 oranges and 2 apples. To check accuracy, you can cross check by checking the average price of 3 oranges and 2 apples, which should equal 52 cents.

((2*40)+(3*60))/2+3 = (80+180)/5 = 260/5 = 52.

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New post 10 Oct 2005, 12:28
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E.
let x be the number of Oranges removed.
The difference in average will amount to the removed oranges value.

60 * x = 10 * 56 - [(10 - x) * 52]
or 8x = 40 or

x = 5

trick is to correctly put right side of the expression.
for example, it is wrong, here, to put:
60 * x = 4 * 10 or
60 * x = 4 * (10 - x)

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New post 10 Oct 2005, 12:52
Oops ... My mistake :-(

Thanks for clarifying Chets.

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New post 10 Oct 2005, 15:30
This one is really good I too forgot that I cannot divide by 10, my first answer was 2

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New post 11 Oct 2005, 04:08
Whats the OA ? I think it is B.2

The equation is 40X +60 (10-X)=560; whihc gives value of x=2;y=8
Now substituting, 520 instead of 560, we get x=4 adn y= 6, therefore to reduce the avearge she will have to put back 2 oranges. Therefore B ?

Smart one though !!

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New post 11 Oct 2005, 04:38
You cannot substitute 560 by 520 as you dont know the total number of items. The changed total number of items will be less than 10 - so the sum is 52(2+y)

E is the answer.
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New post 13 Oct 2005, 13:43
OA is E.
Thanks rahulraao
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Re: Q 8. At a certain food stand, the price of each apple is  [#permalink]

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Re: Q 8. At a certain food stand, the price of each apple is  [#permalink]

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New post 11 Sep 2017, 12:46
Hello from the GMAT Club BumpBot!

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Re: Q 8. At a certain food stand, the price of each apple is   [#permalink] 11 Sep 2017, 12:46
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