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M16-29

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M16-29 [#permalink]

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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
[Reveal] Spoiler: OA

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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
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Re: M16-29 [#permalink]

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New post 14 Jan 2015, 06:10
what is the least number of items he will have to sell each month to justify the policy of the discount? - KEYWORDS !!

POLICY - Current Profit = 20 * 100 = $ 2000 has to be maintained !!

As per solving stmnts,
Profit = 10% CP = 1/10 CP = 1/11 SP
{ Profit =1/n * CP = 1/(n+1) * SP } .... Formula

Hence Profit = 20, CP = 200 , SP = 220

Now, 5% discount on SP = 209. Hence Profit = 209 - 200 = $ 9

The least number of items he will have to sell each month to justify policy
9x > 2000 . x >222.22

or Backsolve
( 9 * What? will give atleast $ 2000)

Ans - D

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Re: M16-29 [#permalink]

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New post 02 Jul 2015, 01:45
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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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Re M16-29 [#permalink]

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New post 20 Aug 2016, 04:44
I think this is a high-quality question and I agree with explanation.

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Re: M16-29 [#permalink]

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There are two problems with the wording of this question. Firstly the reference should be to cost and not to 'price to the retailer' which is unclear and confusing. Secondly, the question does not specify that the discount is only applied to some of the products sold. Again unclear and confusing.

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M16-29 [#permalink]

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New post 29 Mar 2017, 21:17
honchos wrote:
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.



hi,
Item's price always refers to selling price.
above statement "$20 that constitutes 10% of the item's price to the retailer" can be written as -> 10% of Item Price=$20 => $200.
Now total Selling Price(SP) = $200+$20(profit on each item) = $220

hope this helps.

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Re: M16-29 [#permalink]

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New post 30 Sep 2017, 20:48
Yeah, the wording here is pretty ambiguous. Without going into anything else, there is no indication of what criteria are used to evaluate the suitability of the discount whatsoever. The question could very easily have been amended to ask, "what is the least number of items that the retailer must sell such that his net profit exceeds his current profit?" I think this is a good question, but that last line really need a bit more clarity.

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Re: M16-29 [#permalink]

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New post 04 Oct 2017, 10:19
Ambiguous Wording of the question.. please rectify ASAP.

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Re: M16-29   [#permalink] 04 Oct 2017, 10:19
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