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Each month a retailer sells 100 identical items. On each it

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Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 02 Aug 2014, 13:11
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Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

A. 191
B. 213
C. 221
D. 223
E. 226


N.B. Does this question clarifies that 5% discount is on selling Price or cost Price?

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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 02 Aug 2014, 15:56
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honchos wrote:
N.B. Does this question clarifies that 5% discount is on selling Price or cost Price?


A seller could give a discount from a selling price.

Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

A. 191
B. 213
C. 221
D. 223
E. 226

Since $20 constitutes 10% of the item's price to the retailer, then the cost of the item is $200 and the selling price is $220.

Current profit = $20*100 = $2000.
Profit from one item after the discount = $20 - 0.05*$220 = $9.

To get the same profit of $2000, the retailer has to sell at least $2000/9 = 222.something, so 223 items.

Answer: D.
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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 02 Aug 2014, 22:10
The retailer's profit is $20, which is 10% of the cost to the retailer. Original profit is $20 * 100 = $2000

So the cost price is $200, profit is $20 and selling price is $220. A 5 % discount on $220 is $11.
So his profit is reduced by $11 for every item sold. $20 - $11 = $9.

if new profit per item is $9, to get $2000 profit, the no. of goods that need to be sold is $2000/9 ~ 223
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Re: Each month a retailer sells 100 identical items. On each item he makes  [#permalink]

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New post 13 Jan 2015, 18:26
23a2012 wrote:
Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

A. 191
B. 213
C. 221
D. 223
E. 226


Bunuel I need your help

I tried to understand Bunuel answer why you devided the profile on 9?

what is the wrong in this answer 220 price after dis=209 and how many items we need to sell to make the same profile after pay the cost
209&M-20000=2000
M = 22000/209
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Re: Each month a retailer sells 100 identical items. On each item he makes  [#permalink]

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New post 13 Jan 2015, 21:28
Hi 23a2012,

The last part of the question is worded in an "awkward" way, but I assume it's meant to ask "how many discounted items would the retailer need to sell to generate the same total profit as before?"

For this question, we'll need the following formula:

Sell Price = Cost + Profit

We're told that the profit on 1 item is $20 and that this represents 10% of the cost:

Sell Price = Cost + $20
Sell Price = $200 + $20

Thus, the Sell Price is $220 for each item. Selling all 100 items gives the retailer...

100($20) = $2,000 of profit

If the retailer offers a 5% discount on the sell price, then the equation changes...

5%(220) = $11 discount

$209 = $200 + $9

Now, the retailer makes a profit of just $9 per item sold.

To earn $2,000 in profit, the retailer must sell....

$9(X) = $2,000
X = 2,000/9

X = 222.222222 items

You'll notice that this is not among the answer choices.... 221 and 223 are.

Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.

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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 13 Jan 2015, 21:36
Hi 23a2012,

It looks like you also posted your responses in a "new" thread. Here is my response to your post from that other thread:
-----------------------

The last part of the question is worded in an "awkward" way, but I assume it's meant to ask "how many discounted items would the retailer need to sell to generate the same total profit as before?"

For this question, we'll need the following formula:

Sell Price = Cost + Profit

We're told that the profit on 1 item is $20 and that this represents 10% of the cost:

Sell Price = Cost + $20
Sell Price = $200 + $20

Thus, the Sell Price is $220 for each item. Selling all 100 items gives the retailer...

100($20) = $2,000 of profit

If the retailer offers a 5% discount on the sell price, then the equation changes...

5%(220) = $11 discount

$209 = $200 + $9

Now, the retailer makes a profit of just $9 per item sold.

To earn $2,000 in profit, the retailer must sell....

$9(X) = $2,000
X = 2,000/9

X = 222.222222 items

You'll notice that this is not among the answer choices.... 221 and 223 are.

Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Re: Each month a retailer sells 100 identical items. On each item he makes  [#permalink]

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New post 13 Jan 2015, 23:49
23a2012 wrote:
Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

A. 191
B. 213
C. 221
D. 223
E. 226



"Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer."

Profit of $20 is 10% of cost price to retailer. So cost price of retailer is $200. He sells it for $220. Overall profit he makes is $20*100 = $2000

"If the retailer contemplates giving a 5% discount on the items he sells"

If he gives 5% off on $220, he will sell the items for 220*(95/100) = $209

He makes only $9 per item so to make $2000, he needs to sell 2000/9 = 222.22 = 223 items

Answer (D)
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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 14 Jan 2015, 06:53
VeritasPrepKarishma wrote:
23a2012 wrote:
Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

A. 191
B. 213
C. 221
D. 223
E. 226



"Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer."

Profit of $20 is 10% of cost price to retailer. So cost price of retailer is $200. He sells it for $220. Overall profit he makes is $20*100 = $2000

"If the retailer contemplates giving a 5% discount on the items he sells"

If he gives 5% off on $220, he will sell the items for 220*(95/100) = $209

He makes only $9 per item so to make $2000, he needs to sell 2000/9 = 222.22 = 223 items

Answer (D)

Thank you for your answer I see my mistake I should do as follow
209*m-200*m=2000
9m=2000
m=2000/9 =222.22 : :
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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 14 Jan 2015, 06:54
EMPOWERgmatRichC wrote:
Hi 23a2012,

It looks like you also posted your responses in a "new" thread. Here is my response to your post from that other thread:
-----------------------

The last part of the question is worded in an "awkward" way, but I assume it's meant to ask "how many discounted items would the retailer need to sell to generate the same total profit as before?"

For this question, we'll need the following formula:

Sell Price = Cost + Profit

We're told that the profit on 1 item is $20 and that this represents 10% of the cost:

Sell Price = Cost + $20
Sell Price = $200 + $20

Thus, the Sell Price is $220 for each item. Selling all 100 items gives the retailer...

100($20) = $2,000 of profit

If the retailer offers a 5% discount on the sell price, then the equation changes...

5%(220) = $11 discount

$209 = $200 + $9

Now, the retailer makes a profit of just $9 per item sold.

To earn $2,000 in profit, the retailer must sell....

$9(X) = $2,000
X = 2,000/9

X = 222.222222 items

You'll notice that this is not among the answer choices.... 221 and 223 are.

Selling 221 items would get us 9(221) = $1989 which is NOT enough money. To get back to AT LEAST $2,000, we need to sell 223 items.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Thank you for your answer I see my mistake I should do as follow
209*m-200*m=2000
9m=2000
m=2000/9 =222.22
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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 21 Jul 2016, 06:14
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Bunuel and others:
Request your help in understanding the meaning of "what is the least number of items he will have to sell each month to justify the policy of the discount?".
My interpretation is (220*95%)*x= 220*100. Basically we are trying to sell more items to break even after discounting the price of product.
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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 21 Jul 2016, 10:56
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Hi JarvisR,

In my prior post in this thread, I noted the 'awkward' wording of the prompt, but the 'intent' of the prompt is to ask how many discounted items would need to be sold to generate the SAME profit. If you were to take your calculation through to the end, what answer would you choose?

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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 29 Jan 2018, 10:41
honchos wrote:
Each month a retailer sells 100 identical items. On each item he makes a profit of $20 that constitutes 10% of the item's price to the retailer. If the retailer contemplates giving a 5% discount on the items he sells, what is the least number of items he will have to sell each month to justify the policy of the discount?

A. 191
B. 213
C. 221
D. 223
E. 226


Since he sells 100 items and each item has a profit of $20, he makes a total profit of 100 x 20 = 2000 dollars a month. Furthermore, Since $20 constitutes 10% of the item’s price to the retailer, the cost of each item when the retailer purchases it is 20/0.1 = 200 dollars and thus the price of each item when he sells it = 200 + 20 = 220 dollars.

Now he plans to discount the selling price by 5%; thus, each item would be sold for 220 x 0.95 = 209 dollars.

We can let n = the total number of items he has to sell now to still make the $2000 monthly profit.

R - C = P

209n - 200n = 2000

9n = 2000

n = 222.22

Since n has to be an integer, he has to sell at least 223 items. (Note: Selling 222 items will be just short of making the $2000 profit, but selling 223 items will do.)

Answer: D
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Re: Each month a retailer sells 100 identical items. On each it  [#permalink]

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New post 24 Apr 2019, 08:08
Hi friends,

I have approached the above problem the following way.

I have equated the revenues i.e. 220*100 = 209*n
n = (220*100)/209.

Can someone please tell mw what's wrong with my approach?

Thanks,
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Re: Each month a retailer sells 100 identical items. On each it   [#permalink] 24 Apr 2019, 08:08
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