A retailer sells 100 identical items each month, earning a $20 profit

Question

A retailer sells 100 identical items each month, earning a $20 profit on each item. This profit constitutes 10% of the item's cost to the retailer. The retailer is considering offering a 5% discount on the items. What is the minimum number of items the retailer must sell each month to at least maintain the same level of monthly profit as without the discount?

A. 220 
 B. 221 
 C. 222 
 D. 223 
 E. 224

Bunuel · Accepted Answer

A retailer sells 100 identical items each month, earning a $20 profit on each item. This profit constitutes 10% of the item's cost to the retailer. The retailer is considering offering a 5% discount on the items. What is the minimum number of items the retailer must sell each month to at least maintain the same level of monthly profit as without the discount?

A. 220
B. 221
C. 222
D. 223
E. 224

To solve this problem, we start by calculating the current monthly profit, which is 20 dollars*100 = 2000 dollars.

Next, we need to find the cost of each item to the retailer. Since the profit of 20 dollars is 10% of the item's cost, the item's cost is 200 dollars. Therefore, the current selling price of one item is 200 dollars + 20 dollars = 220 dollars.

Now, we can determine the new selling price with the 5% discount. Which would be 220 - 5% of 220 = 209 dollars. This means that the new profit on each item is 209 dollars - 200 dollars = 9 dollars. Therefore, the new net monthly profit is  9x  dollars, where  x  is the number of items the retailer will sell after the discount is announced.

The problem asks us to find the minimum value of  x  that will result in a new net monthly profit of at least 2000 dollars. To solve this, we set up the inequality  9x ≥ 2000  and solve for  x . Dividing both sides by 9, we get  x ≥ \frac{2000}{9} , which is approximately 222.22. Since  x  has to be an integer, we round up to the smallest integer greater than or equal to 222.22, which is 223. Therefore, the retailer must sell at least 223 items each month to maintain a monthly profit of at least 2000 dollars.

Answer: D

23a2012 · Answer

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

EMPOWERgmatRichC · Answer

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.

Final Answer:  D

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

EMPOWERgmatRichC · Answer

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:  D

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

KarishmaB · Answer

"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)

JeffTargetTestPrep · Answer

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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A retailer sells 100 identical items each month, earning a $20 profit

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