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

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 366
Joined: Fri Jun 05, 2015 3:35 am
Thanked: 3 times
Followed by:2 members
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

OA: D

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Jan 24, 2018 7:00 pm
NandishSS,

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
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Mon Jan 29, 2018 9:48 am
NandishSS 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews