GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Nov 2019, 15:50 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # At a certain fruit stand, the price of each apple is 40 cents and the

Author Message
TAGS:

### Hide Tags

Intern  Joined: 16 Apr 2018
Posts: 1
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

Hi experts, i understand the above mentioned approach but could you please tell me why is the following approach wrong

Let 'x' be the number of Apples, 'y' be the number of Oranges so x+y=10
Since the average (i.e., price of fruits/ the the total number of fruits) is 56
(40x + 60y)/10 = 56
On solving x=2 and y =8

Now the question states that the adjusted average is 52
So (40x + 60y)/10 = 52
On solving x=4 and y=6

So if Mary picks up 8 Oranges the average is 56 but if she picks up 6 Oranges the average drops to 52
Clearly she has to drop 2 Oranges to acquire the desired average.
Intern  B
Joined: 28 Apr 2016
Posts: 43
Location: United States
GMAT 1: 780 Q51 V47 GPA: 3.9
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

AkhilRao wrote:
Hi experts, i understand the above mentioned approach but could you please tell me why is the following approach wrong

Let 'x' be the number of Apples, 'y' be the number of Oranges so x+y=10
Since the average (i.e., price of fruits/ the the total number of fruits) is 56
(40x + 60y)/10 = 56
On solving x=2 and y =8

Now the question states that the adjusted average is 52
So (40x + 60y)/10 = 52
On solving x=4 and y=6

So if Mary picks up 8 Oranges the average is 56 but if she picks up 6 Oranges the average drops to 52
Clearly she has to drop 2 Oranges to acquire the desired average.

Sure! Your approach would be correct if the question asked about how many oranges she would need to exchange for apples in order to have the average price be 52 cents. In that case, the number of fruits would remain 10, and 6 oranges/4 apples would give an average price of 52 cents.

However, the question asks how many oranges she must put back, so all she can do is reduce the number of oranges; she cannot increase the number of apples. So, the number of apples must remain 2, and we need to know how many oranges she will need to have in order for the average price to be 52 cents. This is 3 oranges, so she needs to put back 5 oranges to go from having 8 oranges/2 apples to having 3 oranges/2 apples.

Please let me know if you have more questions!
_________________
Online GMAT tutor with a 780 GMAT score. Harvard graduate.

GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4066
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

1
Top Contributor
1
Bunuel wrote:
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

Kudos for a correct solution.

It turns out that the cost per apple is irrelevant. Here's why:

The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents
So, (total value of all 10 pieces of fruit)/10 = 56 cents
This means, total value of all 10 pieces of fruit = 560 cents

How many oranges must Mary put back so that the average price of the pieces of fruit that she keeps is 52 cents?
Let x = the number of oranges to be removed.
Each orange costs 60 cents, so the value of the x oranges to be removed = 60x
This means 560 - 60x = the value of the REMAINING fruit
Also, if we remove x oranges, then 10 - x = the number of pieces of fruit REMAINING.

We want the REMAINING fruit to have an average value of 52 cents.
We can write: (value of REMAINING fruit)/(number of pieces of fruit REMAINING) = 52
Rewrite as: (560 - 60x)/(10 - x) = 52
Multiply both sides by (10-x) to get: 560 - 60x = 52(10 - x)
Expand right side to get: 560 - 60x = 520 - 52x
Add 60x to both sides: 560 = 520 + 8x
Subtract 520 from both sides: 40 = 8x
Solve: x = 5

Cheers,
Brent
_________________
Manager  B
Joined: 17 Jul 2016
Posts: 54
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

This can be done very quickly using weighted average principles.

since the average ends up being 52 cents.

40 60
52

(60-52) (52-40)

8/12=2/3. So the number of apples is 2x and the number of oranges is 3x. The sum has to be a multiple of 5. After some number of oranges were removed there must have been 5 left. Therefore, he must have removed 5 oranges.
VP  D
Joined: 14 Feb 2017
Posts: 1286
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26 GMAT 2: 550 Q43 V23 GMAT 3: 650 Q47 V33 GMAT 4: 650 Q44 V36 GMAT 5: 650 Q48 V31 GPA: 3
WE: Management Consulting (Consulting)
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

Here's an easy way to solve this:

Let A = apples, B = oranges

(40A + 60B)/10 = 56
(40A +60 (10-A))/10 = 56
40A + 600 - 60A = 560
-20A = -40
A = 2

Therefore, B = 8

So, how many of the 8 oranges do we need to remove to bring down the average?
let x = the number of oranges we need to remove
(40*(2apples) + 60 (8-x) )/10-x = 52
80+480 -60x = 520 - 52x
560 =520+8x
40= 8x
x = 5

(E)
_________________
Goal: Q49, V41

+1 Kudos if I have helped you
Intern  B
Joined: 18 Feb 2019
Posts: 5
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

v12345 wrote:
Bunuel wrote:
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

Kudos for a correct solution.

here price of apple = 40 cents and price of orange = 60 cents

average price = 56 cents

so, the apples and oranges are in ratio

apple : orange = 60 - 56 : 56 - 40
=> apple : orange = 4 : 16
=> apple : orange = 1 : 4

total no =10, therefore apples = 2 nos. and oranges = 8 nos.

now we have to make average price = 52 cents
so, the apples and oranges will be in ratio

apple : orange = 60 - 52 : 52 - 40
=> apple : orange = 8 : 12
=> apple : orange = 2 : 3

now we have apples = 2 nos. from above, therefore oranges must be 3 in number

oranges to be put back = 8 - 3 = 5 nos

kudos if you like the explanation

Why did you assume, in the second ratio, 2:3, that the total apples is 2 and oranges is 3? You are not given total, as in the first ratio (where total given is 10). Here, total is less than 10, but you don't know what.
Manager  B
Joined: 03 Aug 2017
Posts: 79
At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

Bunuel wrote:
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

Kudos for a correct solution.

Hello Bunuel,

I have a very basic doubt.. In one of the solutions

it is given

apple : orange = 60 - 56 : 56 - 40
=> apple : orange = 4 : 16
=> apple : orange = 1 : 4

I want to know how the ratio of Apple is 4 And Oranges 16? How did we arrive at this?

For your help i have pasted one of the answers below from where this is taken

" here price of apple = 40 cents and price of orange = 60 cents

average price = 56 cents

so, the apples and oranges are in ratio

apple : orange = 60 - 56 : 56 - 40
=> apple : orange = 4 : 16
=> apple : orange = 1 : 4

total no =10, therefore apples = 2 nos. and oranges = 8 nos.

now we have to make average price = 52 cents
so, the apples and oranges will be in ratio

apple : orange = 60 - 52 : 52 - 40
=> apple : orange = 8 : 12
=> apple : orange = 2 : 3

now we have apples = 2 nos. from above, therefore oranges must be 3 in number

oranges to be put back = 8 - 3 = 5 nos

Intern  B
Joined: 10 Jul 2018
Posts: 5
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

As is given in the quwstion
60x + 40y = 56*10
And x+y = 10
Thus x = 8 and y = 2
Now, 60p + 40*2 = 52 (p+2)
8p = 104 -80 thus p = 3
So the number of orange is to be reduced by 5 =(8-3)
OA: E

Posted from my mobile device
Intern  B
Joined: 26 May 2019
Posts: 19
Re: At a certain fruit stand, the price of each apple is 40 cents and the  [#permalink]

### Show Tags

There is a much simpler approach to this problem. We do not require any use of weighted averages or ratios or any other complex calculations. This sum can be solved within 10-25sec, after reading the question.

40a+60o = 560 (average of 10 fruits is 56)

a + o = 10

40a + 60(o-x) = 52(10-x) (Since the new average is 52)

We can see from the left side of the equation that the total price is a multiple of 10. This is possible only if 10-x = 10 or 5. 10 can be eliminated because we have to return some oranges.
There is only 1 value of x for which 52 will be a multiple of 10, which is 5.

Solved only with common sense. Re: At a certain fruit stand, the price of each apple is 40 cents and the   [#permalink] 17 Oct 2019, 03:09

Go to page   Previous    1   2   [ 29 posts ]

Display posts from previous: Sort by

# At a certain fruit stand, the price of each apple is 40 cents and the  