Bunuel wrote:

Official Solution:

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

The current net monthly profit \(=$20 * 100 =$2000\). The item's price to the retailer = \(\frac{$20}{10}*100=$200\). The current selling price of one item \(=$200 + \text{ (profit on each item) }=$220\).

The selling price of one item with the discount \(=$220 (1 - 0.05) =$200 -$11 =$209\). The new profit on each item \(=$209 -$200 =$9\). The new net monthly profit \(= x *$9\) where \(x\) is the number of items the retailer will sell after the discount is announced. The question is what must be \(x\) so that the new net monthly profit would exceed the current net monthly profit. In other words, what is the least \(x\) such that \(9x \gt 2000\)? \(x\) must be larger than \(\frac{2000}{9} = 222.222..\). Because \(x\) has to be an integer, the least \(x\) is 223.

Answer: D

I belive language is slightly unclear -

$20 that constitutes 10% of the item's price to the retailer.

items price refers to Cost Price or selling price, normally Gmat prep question doesn't have that kind of ambiguity.

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