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# By selling 32 orange in a dollar, a man loses 40%. How many orange

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Manager
Joined: 04 Aug 2013
Posts: 94
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
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WE: Manufacturing and Production (Pharmaceuticals and Biotech)
By selling 32 orange in a dollar, a man loses 40%. How many orange  [#permalink]

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Updated on: 09 Jul 2016, 23:19
10
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:03) correct 34% (02:37) wrong based on 180 sessions

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By selling 32 orange in a dollar, a man loses 40%. How many orange must he sell in a dollar to gain 20% profit?

A. 16
B. 18
C. 20
D. 25
E. 28

Originally posted by anceer on 17 May 2015, 18:57.
Last edited by Bunuel on 09 Jul 2016, 23:19, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 3018
Re: By selling 32 orange in a dollar, a man loses 40%. How many orange  [#permalink]

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18 May 2015, 05:28
4
6
Hi anceer,

You can use the relation between Cost Price & Selling Price to get to your answer.

Given
We are given that a person sells 32 oranges for a dollar to make a loss of 40%. We are asked to find the number of oranges he must sell in a dollar to make a profit of 20%

Approach
We know that Selling Price = Cost Price *( 1 - Loss%) and Selling Price = Cost Price ( 1 + Profit%) Since we know the selling price and the loss%, we can find out the cost price.

Once we know the cost price and we know that the person needs to make a profit of 20%, we can find the selling price which would give us the number of oranges he needs to sell to make 20% profit.

Working Out
The person sells 32 oranges in 1 dollar. So, his SP for 1 orange = $$\frac{1}{32}$$. Since he has made a loss of 40%, we can write

SP = CP *(1 - 0.4) i.e. CP for one orange = $$\frac{1}{32* 0.6}$$

For the person to make 20% profit, he would need to have his SP = CP (1 + 0.2) = 1.2*CP. Since we know the CP of 1 orange, we can write

SP for one orange to make a profit of 20% = $$1.2 * \frac{1}{32*0.6}$$ = $$\frac{1}{16}$$ i.e. selling price of 1 orange to make a profit of 20% is $$\frac{1}{16}$$ dollars. So he needs to sell 16 oranges for a dollar to make a profit of 20%.

In such questions avoid calculating numbers at each point as the numbers taken together will cancel out to give the final answer.

Hope this helps

Regards
Harsh
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Re: By selling 32 orange in a dollar, a man loses 40%. How many orange  [#permalink]

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17 May 2015, 19:18
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3
This is a question that is much easier than it first appears. If you work with the percents directly, you can solve it very quickly. If the man sells 32 oranges for a dollar, he loses 40%. That means he is at 60% of his cost (100% - 40% = 60%). We are trying to figure out how many oranges he has to sell in order to make a 20% profit, or be at 120% (100% + 20% = 120%). 120% is double 60%, meaning that we simply cut the number of oranges in half to double our returns (from 60% to 120%), yielding 32/2 = 16 oranges, or answer choice A.

I hope this helps!
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Brandon
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Manager Joined: 04 Aug 2013 Posts: 94 Location: India Schools: McCombs '17 GMAT 1: 670 Q47 V35 GPA: 3 WE: Manufacturing and Production (Pharmaceuticals and Biotech) Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink] ### Show Tags 17 May 2015, 21:11 Thanks Brandon. It really helps but what if it ask for any other numbers such as 22% profit or any number else. Manager Joined: 28 Dec 2012 Posts: 99 Location: India Concentration: Strategy, Finance WE: Engineering (Energy and Utilities) Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink] ### Show Tags 18 May 2015, 10:39 1 1 anceer wrote: By selling 32 orange in a dollar, a man loses 40%. How many orange must he sell in a dollar to gain 20% profit? A.16 B.18 C.20 D.25 E.28 Solution: simply use new quantity = 32* (100-60)/(100+20) = 16 I have the same logic as that of Brandon. Very elegantly solved by him! _________________ Impossibility is a relative concept!! Veritas Prep GMAT Instructor Joined: 23 Oct 2013 Posts: 144 Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink] ### Show Tags 18 May 2015, 17:51 sagarsir wrote: anceer wrote: By selling 32 orange in a dollar, a man loses 40%. How many orange must he sell in a dollar to gain 20% profit? A.16 B.18 C.20 D.25 E.28 Solution: simply use new quantity = 32* (100-60)/(100+20) = 16 I have the same logic as that of Brandon. Very elegantly solved by him! I like Sagarsir's approach. Harsh' approach also works, but he accidentally made a mistake in his math. His formula works, but CP for one orange is 1/32 divided by .6 (not multiplied by .6). 1.2*1/32 divided by .6 will get to 1/16, as he says. But Like Sagarsir states, there are easier ways to solve this problem! _________________ Brandon Veritas Prep | GMAT Instructor If you found this post helpful, please give me kudos!!! Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: By selling 32 orange in a dollar, a man loses 40%. How many orange  [#permalink]

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18 May 2015, 23:15
VeritasPrepBrandon wrote:
sagarsir wrote:
anceer wrote:
By selling 32 orange in a dollar, a man loses 40%. How many orange must he sell in a dollar to gain 20% profit?

A.16
B.18
C.20
D.25
E.28

Solution: simply use new quantity = 32* (100-60)/(100+20) = 16

I have the same logic as that of Brandon. Very elegantly solved by him!

I like Sagarsir's approach. Harsh' approach also works, but he accidentally made a mistake in his math. His formula works, but CP for one orange is 1/32 divided by .6 (not multiplied by .6). 1.2*1/32 divided by .6 will get to 1/16, as he says. But Like Sagarsir states, there are easier ways to solve this problem!

Hi Brandon,

We are both saying the same thing . You are right to say that CP for one orange = $$\frac{SP}{0.6}$$. Since SP for one orange = $$\frac{1}{32}$$ that would give us CP = $$= \frac{1}{32} * \frac{1}{0.6}$$ which is what I have mentioned in my solution

Regards
Harsh
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Re: By selling 32 orange in a dollar, a man loses 40%. How many orange  [#permalink]

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20 Jul 2015, 09:48
Please let me know my approach is correct or wrong.

For 1 dollar i.e 100 cents , we are selling 32 oranges and getting a loss of 40%.
So in order to get no loss or no profit, I need to sell 32 oranges at 140 cents.
That means cost price of 32 oranges is 140 cents.

Now going by options, for example cost of price of 16 oranges is 70 cents, if I sell 16 oranges at 100 cents, I am likely to get 30% profit. That means if I sell 16 oranges, I mostly likes to get more than 20% profit. Likewise , I get the following profit percentages
for the following options
A) 16 oranges ~30% profit
B) 18 oranges ~22% profit
C) 20 oranges ~12% profit
D) 25 oranges ~9% loss
E) 28 oranges ~22% loss

This shows that option A i.e 16 orangs is sufficient to give us 20% profit.
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Re: By selling 32 orange in a dollar, a man loses 40%. How many orange  [#permalink]

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06 Nov 2015, 22:37
x - expenses

So, oranges per dollar for 20% profit or to make $120 = (60 x 32) / 120 = 16 VP Joined: 07 Dec 2014 Posts: 1232 Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink] ### Show Tags 10 Jul 2016, 11:26 let c=cost of oranges per dollar p=selling price of oranges per dollar x=# of oranges he needs to sell per dollar to make 20% profit p/32=.6c p/x=1.2c .6c*32=1.2c*x x=16 Intern Status: Current Student Joined: 27 Mar 2014 Posts: 26 Location: Bangladesh Concentration: Entrepreneurship, Finance Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink] ### Show Tags 24 Feb 2018, 07:17 ** The wording is somewhat ambiguous. If it were written as "32 oranges for a dollar", then the math would be easier.$1 is actually 60% or $$\frac{3}{5}$$ of total cost.
to calculate total cost, t: $$\frac{3}{5}*t=1 => t=\frac{5}{3}$$ { which is the actual cost}
With 20% profit, selling price should be 120% or $$\frac{6}{5}$$ of $$\frac{5}{3}$$. that is: selling price= $$\frac{5}{3}*\frac{6}{5} = 2$$
Then $2 dollar must be earned from 32 oranges. So, We need to sell 16 oranges for a dollar. Intern Joined: 18 Jun 2017 Posts: 23 Re: By selling 32 orange in a dollar, a man loses 40%. How many orange [#permalink] ### Show Tags 24 Feb 2018, 07:31$1 --> 32 oranges ---> Loss of 40 percent
Price per orange ---> $1/32 ---> Loss of 40 percent per orange Let x be the cost price per orange x - (40/100)x = 1/32 x= 5/(3*32) Now, he has to make a profit of 20 % New selling price per orange = x + (20/100)x = 6/5x Substitute x; Selling price per orange =$ 2/32 = $1/16 So, in$1 he can sell 16 oranges which is the answer.
Re: By selling 32 orange in a dollar, a man loses 40%. How many orange   [#permalink] 24 Feb 2018, 07:31
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