It is currently 22 Jan 2018, 18:06

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43361
At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 02:19
Expert's post
63
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

51% (02:26) correct 49% (02:36) wrong based on 1258 sessions

### HideShow timer Statistics

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.
[Reveal] Spoiler: OA

_________________
SVP
Joined: 08 Jul 2010
Posts: 1920
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 03:15
14
KUDOS
Expert's post
6
This post was
BOOKMARKED
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.

Apple (A) = 40 cemts
Orange (B) = 60 cents
Average of 10 fruits = 56 cents
u.e. Total Price of 10 Fruits = 56*10 = 560 cents

i.e. 40A + 60 B = 560
and A + B = 10

i.e. 40A + 60 (10-A) = 560
i.e. -20A + 600 = 560
i.e. A = 2
i.e. B = 8

Average to be brought at = 52 cents
let oranges to be put back = C
i.e. Total Fruits = 10-C
where total Oranges left = 8-C
i.e. Total Price of New lot of fruits = 52*(10-C)

i.e. 40*2 + 60*(8-C) = 52*(10-C)
i.e. 80 + 480 - 60C = 520 - 52C
i.e. 8 C = 40
i.e. C = 5

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Status: Out of my Mind , will be back in 2 minutes
Joined: 27 Aug 2015
Posts: 13
Location: India
GMAT 1: 610 Q49 V25
WE: Other (Other)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 03:31
3
KUDOS
Ans E

Sum of Apples and Oranges is 10

A + O = 10

Apple cost 40 cent and Orange cost 60 cent and there mean is 56 , therefore

(40*A + 60*O)/10 = 56 , which gives us

4A + 6O = 56

Solving the above 2 equation we get , Apples = 2 , Oranges = 8.

Now as she has remove some oranges ( x ) such that the new mean of the remaining fruits become 52

note that the number of Apples remain the same , therefore new equation will become

( 2*40 + (8-x)60 ) / 10 -x = 52

As the remaining fruits will be 10 - x

On solving for x we will get our ans 5
Verbal Forum Moderator
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 1892
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 04:39
3
KUDOS
4
This post was
BOOKMARKED
Let number of Apples = A
number of oranges = B
A+B=10 --- 1
.56 =(.4A + .6 B)/10
=> 56 = 4A + 6B ----2
Solving 1 and 2, we get
A= 2
B= 8

Let the number of oranges put back = C
52*(10-c) = 40*2 + 60(8-C)
=> C= 5

Alternatively , we can use Scale method
Since average is .56 , distance of the average from price of apple =.56-.4=.16
and distance of the average from price of orange = .6 - .56 = .04
Ratio of distances is .16:.04 = 4:1

Therefore , number of apples and oranges will be in inverse proportion =1:4
Number of apples = 2
Number of oranges = 8

After removing a certain number of oranges C , the new average will be .52
Ratio of distances is .08:.12 = 2:3

Number of oranges will be 3
Therefore Mary must put 5 oranges back .

_________________

When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
+1 Kudos if you find this post helpful

Current Student
Joined: 10 Aug 2015
Posts: 54
Concentration: General Management, Entrepreneurship
GMAT 1: 730 Q48 V42
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 05:34
6
KUDOS
3
This post was
BOOKMARKED
Step 1: We start with the first average to find the total price of the apples and oranges.

Using the formula : Sum = Average * Number of terms
Sum = 56 * 10 = 560

Step 2: Set up the new average based on the first one.
x : number of oranges we need to take away.
We will have the previous sum (i.e. 560) minus the price of all oranges we will take away (i.e. 60x) and the number of elements will be 10 minus x.

So :
(560-60x) / (10-x) = 52
560 - 60x = (10-x) * 52
560 - 520 = -52x + 60x
40 = 8x
x=5

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7875
Location: Pune, India
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 20:37
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
Manager
Joined: 01 Mar 2015
Posts: 50
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

20 Oct 2015, 21:25
4
KUDOS
4
This post was
BOOKMARKED
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
Intern
Joined: 23 Oct 2015
Posts: 4
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

22 Mar 2016, 02:34
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

Hi!

I used the exact same way as you did in solving this question, but when reaching the last part 2:3 I interpereted it as 3/5 oranges and 2/5 apples? Seeing as we're still closer to 60 than 40. And then we should have 6 oranges and 4 apples? Please explain!
Intern
Joined: 23 Oct 2015
Posts: 4
At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

22 Mar 2016, 02:37
My bad, I see now that we were not supposed to replace them with any apples but just remove them from the total. Didn't read carefully enough
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2069
Location: United States (CA)
At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

04 May 2016, 08:50
3
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

Solution:

We can let the number of apples = x and the number of oranges = y. Using these variables we can create the following two equations:

1) x + y = 10

Using the formula average = sum/quantity, we have:

2) (40x + 60y)/10 = 56

Let’s first simplify equation 2:

40x + 60y = 560

4x + 6y = 56

2x + 3y = 28

Isolating for y in equation one gives us: y = 10 – x.

Since y = 10 – x, we can substitute 10 – x for y in the equation 2x + 3y = 28. This gives us:

2x + 3(10 – x) = 28

2x + 30 – 3x = 28

-x = -2

x = 2

Since x + y = 10, then y = 8.

We thus know that Mary originally selected 2 apples and 8 oranges.

We must determine the number of oranges that Mary must put back so that the average price of the pieces of fruit that she keeps is 52¢. We can let n = the number of oranges Mary must put back.

Let’s use a weighted average equation to determine the value of n.

[40(2) + 60(8-n)]/(10 – n) = 52

(80 + 480 - 60n)/(10 – n) = 52

560 – 60n = 520 – 52n

40 = 8n

5 = n

Thus, Mary must put back 5 oranges so that the average cost of the fruit she has kept would be 52 cents.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Last edited by ScottTargetTestPrep on 04 Sep 2016, 05:29, edited 1 time in total.
Director
Joined: 07 Dec 2014
Posts: 885
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

04 May 2016, 14:07
let a=#apples
r=#oranges
we know that .4a+.6r=(.56)(10)=5.6➡.4a=5.6-.6r
after mary returns x oranges, then
.4a+.6(r-x)=(.52)(10-x)
substituting for .4a,
5.6-.6r+.6r-.6x=5.2-.52x
.08x=.4
8x=40
x=5 oranges put back
Manager
Joined: 16 Mar 2016
Posts: 134
Location: France
GMAT 1: 660 Q47 V33
GPA: 3.25
At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

04 May 2016, 14:19
4
KUDOS
2
This post was
BOOKMARKED
A = number of apples
B = number of oranges

We have :

$$\frac{40A + 60 B}{10}$$ = 56

and $$\frac{40A + 60 (B - x)}{10 - x}$$ = 52

$$\frac{40A + 60 B - 60 x}{10 - x}$$ = 52

$$\frac{560 - 60 x}{10 - x}$$ = 52

560 - 60 x = 520 - 52 x

40 = 8 x

x = 5

Last edited by Alex75PAris on 18 May 2016, 09:02, edited 1 time in total.
Senior Manager
Joined: 09 Feb 2015
Posts: 382
Location: India
Concentration: Social Entrepreneurship, General Management
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
GPA: 2.8
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

14 May 2016, 10:28
Using Averages and Allegations

40 60
56
4 16

A:O =1: 4==>A=2 ,O=8(as total no of apples+ oranges =10)
now we know there are 2 Apples and 8 Oranges

Using Statistics

when Mean =52

52-40=12
12*2(bcos 2 apples)
60-52=8
x= no. of remaining oranges
24-(8*x)=0
==>x=3
Hence 5 oranges must be removed.
Current Student
Joined: 23 Mar 2016
Posts: 36
Schools: Tulane '18 (M)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

17 May 2016, 20:17
1
KUDOS
i did this one with a scale method

Apples : Price : Oranges
40 cents : 56 average : 60 cents
= 16 cents from average : average : 4 cents from average
= 1 apple for every 4 oranges
= 2 apples and 8 oranges = 10 fruits = 2*.4 + 8*.6 = 5.60 / 10 = .56

40 cents : 52 average : 60 cents
= 12 cents from average : average : 8 cents from average
= 2 apples for every 3 oranges

8 oranges - 3 oranges = 5 oranges must be put back

Hope this helps!
Manager
Joined: 23 Jan 2016
Posts: 220
Location: India
GPA: 3.2
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

18 Jun 2016, 00:43
Although I got this right, it took me 10 minutes to solve it. Can anyone help me with a strategy to tackle this type of question on GMAT? There is no way im going to solve this question on the exam.
Manager
Joined: 29 Nov 2011
Posts: 114
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

18 Jun 2016, 04:08
total amount = avg * number of items
old amount = 56 * 10 = 560

new amount will be 52 *10-x
10-x , you have same number of apples , only decrease in number of oranges
now new amount is equal to what
560 - 60 x = new amount
solve and x= 5
Senior Manager
Joined: 27 Mar 2016
Posts: 346
Location: United States (CO)
GMAT 1: 770 Q51 V44
GPA: 3.69
WE: Analyst (Consulting)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

19 Jun 2016, 01:14
4
KUDOS
The current total price is divisible by 10, and so is the price of each orange. The adjusted total price therefore will have to be divisible by 10, and at the same time divisible by 52. The only possible value for the adjusted total price is 260. Hence 300 cents' worth of oranges, or 5 oranges, will have to be removed.
Manager
Joined: 30 Dec 2015
Posts: 90
GPA: 3.92
WE: Engineering (Aerospace and Defense)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

09 Oct 2016, 19:13
3
KUDOS
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.

$$\frac{Wa}{Wo} = \frac{(60-56)}{(56-40}) = \frac{1}{4}$$
Apple = 2 & Orange = 8
New Avg
$$\frac{Wa}{Wo} = \frac{(60-52)}{(52-40)} = \frac{2}{3}$$
$$\frac{2}{Wo} = \frac{2}{3}$$
Orange = 3

Hence, Oranges have to reduce from 8 to 3 i.e. 5
_________________

If you analyze enough data, you can predict the future.....its calculating probability, nothing more!

Intern
Joined: 13 Dec 2015
Posts: 16
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

15 Oct 2016, 02:01
Not convinced mate... I am able to get to fractions 1/4 and 2/3.... but given the total number of items is 10, why would make the ratio of 1/4 to 2/8 and keep the ratio 2/3 as it is ?

If someone can breakdown this using the same formula that would be helpful.

colorblind 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.

$$\frac{Wa}{Wo} = \frac{(60-56)}{(56-40}) = \frac{1}{4}$$
Apple = 2 & Orange = 8
New Avg
$$\frac{Wa}{Wo} = \frac{(60-52)}{(52-40)} = \frac{2}{3}$$
$$\frac{2}{Wo} = \frac{2}{3}$$
Orange = 3

Hence, Oranges have to reduce from 8 to 3 i.e. 5
SVP
Joined: 08 Jul 2010
Posts: 1920
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: At a certain fruit stand, the price of each apple is 40 cents and the [#permalink]

### Show Tags

15 Oct 2016, 02:16
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
Dev1212 wrote:
Not convinced mate... I am able to get to fractions 1/4 and 2/3.... but given the total number of items is 10, why would make the ratio of 1/4 to 2/8 and keep the ratio 2/3 as it is ?

If someone can breakdown this using the same formula that would be helpful.

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.

Please find the solution as attached.

I hope this helps!!!
Attachments

File comment: www.GMATinsight.com

Ans.jpg [ 194.7 KiB | Viewed 12916 times ]

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Re: At a certain fruit stand, the price of each apple is 40 cents and the   [#permalink] 15 Oct 2016, 02:16

Go to page    1   2    Next  [ 35 posts ]

Display posts from previous: Sort by