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Math Expert V
Joined: 02 Sep 2009
Posts: 55272
M16-29  [#permalink]

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Question Stats: 44% (02:17) correct 56% (03:08) wrong based on 68 sessions

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 _________________ Math Expert V Joined: 02 Sep 2009 Posts: 55272 Re M16-29 [#permalink] ### Show Tags 2 1 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 $$=220 (1 - 0.05) =220 -11 =209$$. 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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1
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 Senior Manager  Status: Verbal Forum Moderator Joined: 17 Apr 2013 Posts: 468 Location: India GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49 GPA: 3.3 Re: M16-29 [#permalink] ### Show Tags 3 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. _________________ Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html Senior Manager  Joined: 31 Mar 2016 Posts: 376 Location: India Concentration: Operations, Finance GMAT 1: 670 Q48 V34 GPA: 3.8 WE: Operations (Commercial Banking) Re: M16-29 [#permalink] ### Show Tags I think this is a high-quality question and I agree with explanation. Intern  Joined: 07 Feb 2010 Posts: 2 Re: M16-29 [#permalink] ### Show Tags 1 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. Intern  B Joined: 09 Sep 2015 Posts: 20 Re: M16-29 [#permalink] ### Show Tags 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. Intern  B Joined: 22 Jan 2017 Posts: 33 Re: M16-29 [#permalink] ### Show Tags 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. Manager  B Joined: 27 Apr 2011 Posts: 52 Location: India GMAT Date: 06-13-2017 Re: M16-29 [#permalink] ### Show Tags Ambiguous Wording of the question.. please rectify ASAP. _________________ Hope it's clear. _________________ Please +1 KUDO if my post helps. Thank you. Manager  B Joined: 23 Jan 2017 Posts: 70 Re: M16-29 [#permalink] ### Show Tags Language not clear ... "justify the policy of the discount"? The question doesn't express what was the policy of the discount. I just made a guess that the question is trying to ask what is the least number of items he will have to sell so that his monthly profits doesn't decrease. This is not a 700 level question. It is just that the language is making it difficult to comprehend the question. Director  V Joined: 12 Feb 2015 Posts: 840 Re: M16-29 [#permalink] ### Show Tags 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. I agree the question per se is very easy but the ambiguity in wording leaves it open for interpretation & then its like you are gambling rather than solving GMAT quant. _________________ "Please hit +1 Kudos if you like this post" _________________ Manish "Only I can change my life. No one can do it for me" Manager  G Joined: 01 Aug 2017 Posts: 189 Location: India Concentration: General Management, Leadership GMAT 1: 500 Q47 V15 GPA: 3.4 WE: Information Technology (Computer Software) Re: M16-29 [#permalink] ### Show Tags 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 $$=20 * 100 =2000$$.
$20 constitutes 10% of the item's price to the retailer. It implies 20 = 10/100 * retail price of the item The retail price of one item = $$\frac{(20*100)}{10}= 200$$. The selling price of one item $$=200 + \text{ (profit on each item) }=220$$. Discount is 5%. There fore New Selling price is 95% of$220
After Discount, new selling price of one item $$=220 * 0.95 =209$$.
The new profit on each item $$=209 -200 =9$$.

Let the no of items retailer would sell at discounted price be $$x$$.

The new net monthly profit $$= x *9$$

The question is what must be $$x$$ so that the new net monthly profit would exceed or equal the current net monthly profit.
$$x *9 >= 2000$$
$$x >= 2000/9$$.
$$x>= 222.222$$
Because $$x$$ is number of item, hence it must be an integer. Nearest value $$x$$ is 223.

Answer: D
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Manager  G
Joined: 22 Jun 2017
Posts: 178
Location: Argentina
Schools: HBS, Stanford, Wharton
GMAT 1: 630 Q43 V34 Re: M16-29  [#permalink]

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I think this is a high-quality question and I agree with explanation. I would modify this question as for me it wasn't so clear what "justify the policy of the discount" means. Is it to cover the cost? or to have the same profits?
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Manager  G
Joined: 22 Jun 2017
Posts: 178
Location: Argentina
Schools: HBS, Stanford, Wharton
GMAT 1: 630 Q43 V34 Re: M16-29  [#permalink]

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I think this is a high-quality question and I don't agree with the explanation. The solution says:
The selling price of one item with the discount =$220(1−0.05)=$200−$11=$209=$220(1−0.05)=$200−$11=$209.

BUT, 200-11 is not 209.. 220-11 is 209.
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Intern  B
Joined: 13 Sep 2018
Posts: 14
M16-29  [#permalink]

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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 $$=220 (1 - 0.05) =220 -11 =209$$. 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 Bunuel can you kindly explain how you calculated the current selling price of$220 am having a hard time wrapping my head around how you came up with the answer and also what does justify the discount policy mean.
Manager  B
Joined: 18 Jul 2018
Posts: 51
Location: United Arab Emirates
M16-29  [#permalink]

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bridgetnamugga 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 $$=220 (1 - 0.05) =220 -11 =209$$. 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 Bunuel can you kindly explain how you calculated the current selling price of$220 am having a hard time wrapping my head around how you came up with the answer and also what does justify the discount policy mean.

Hi bridgetnamugga

Its mentioned in the question stem that "On each item he makes a profit of \$20"
This implies that S.P = 220
HOW?

We calculated earlier, C.P = 200
Hence,
Profit = S.P - C.P
20 = S.P - 200
220 = S.P

Now, Question is asking for "what is the least number of items he will have to sell each month to justify the policy of the discount?"

The retailer plans on a discount policy of 5% on the items he sells.
So, 220*0.05 = 11
220 - 11 = 209
SP after discount = 209

NEW PROFIT = 209 - 200 = 9

Since, CURRENT MONTHLY PROFIT = 20 * 100 = 2000
MONTHLY PROFIT AFTER DISCOUNT = 9*x (where x is the # of items required to sell to justify discount policy)

In order to "justify discount policy" the profit earned with discount policy should be more than the current profit earned

OR
what must be x so that the new net monthly profit is more than the current net monthly profit.

Hence,
9x > 2000
x > 2000/9
x > 222.22
# of items has to be an integer value so the closest next value is 223.

Hope this helps! M16-29   [#permalink] 05 Apr 2019, 10:30
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