Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64249

Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 06:59
Question Stats:
43% (02:02) correct 57% (02:38) wrong based on 248 sessions
HideShow timer Statistics
Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop? A. 200 B. 216 C. 220 D. 230 E. 260
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Senior Manager
Joined: 27 Aug 2014
Posts: 293
Location: Netherlands
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 07:23
IMO answe is E:
total number of items after 2 years = 2420 so, at this point i looked into the answer choices and checked if the total items can exceed 2420, given if 260 is the max, then min can be 26020*260/100 = 208. if 208 in all 9 shops then 208*9+260<2420, so 260 is possible max



Manager
Joined: 17 Apr 2018
Posts: 57

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 07:38
Total no of items after 2 years = 2000X(1.1)^2 = 2420
open 10 more shops. Total shops = 11
Condition >>no shop can have more than 20% items than any other shop
To find max items in one shop.
To max items in one shop. let other 10 shops has equal number of items.
let 100x be the items in 10 store and 120x items in the store with max items. 10(100x) + 120x = 2420 ==> 120x =~ 260
Hence, E is the Answer.



Manager
Joined: 05 Mar 2017
Posts: 205
Location: India
Concentration: General Management, Marketing
GPA: 3.6
WE: Marketing (Hospitality and Tourism)

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 07:38
Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop?
This is an easy question. A total number of items in the shop after 2 years is 2420. Now just in case, he has to divide equally then each shop will have 2420/11 = 220
But we are looking for the maximum increase he can do so that none of the shops have greater than 20% By now you should eliminate options A, B, C.
Take 230, which means that he is going 10 extra on 1 shop 10 pieces will be subtracted from each of the remaining stores.
If you take 260, which means that he is going for 40 extra. which means that 40/10 = 4 will be deducted equally for each of the remaining stores. So the maximum possible answer is 260.
A. 200 B. 216 C. 220 D. 230 E. 260
Hence the answer is E.



Intern
Joined: 10 Mar 2019
Posts: 23
Location: Russian Federation
GPA: 3.95

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 07:42
Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop?
After the first year  2000*1.1=2200 After the second year  2200*1.1=2420
Now, he opens 10 more shops and the total number of shops is 11. Let's make an equation 10x+1,2x=2420 11,2x=2420 x=216 but we need 1.2x =259.2
IMO E



CEO
Joined: 03 Jun 2019
Posts: 2911
Location: India
GMAT 1: 690 Q50 V34
WE: Engineering (Transportation)

Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
Updated on: 18 Jul 2019, 00:29
Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop? A. 200 B. 216 C. 220 D. 230 E. 260 Given: Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. Asked: What is the approximate maximum possible number of items in a shop? At present, the number of items in his shop = 2000 he plans to increase it by 10% every year. Next year, the number of items in his shop will be = 2000 * 1.1 = 2200 Second year, the number of items in his shop will be = 2200 * 1.1 = 2420 After 2 years, the number of shops he will have = 1 + 10 = 11 shops He distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. If all other shops have number of items = x => Total number of items in 10 shops = 10x Then the maximum number of items in 11th shop < 1.2x Total no of items in 11 shops approximately = 10x + 1.2x = 11.2x But total no of items in 11 shops = 2420 11.2x = 2420 x = 2420/11.2 1.2x = 2420/11.2*1.2 = 260 approx Maximum no of items a shop may have = 260 since no of items is a positive integer. IMO E
_________________
Kinshook Chaturvedi Email: kinshook.chaturvedi@gmail.com
Originally posted by Kinshook on 17 Jul 2019, 08:08.
Last edited by Kinshook on 18 Jul 2019, 00:29, edited 2 times in total.



Senior Manager
Joined: 13 Feb 2018
Posts: 432

Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 08:31
 let's calculate the number of items after two years: \(2000*1.1^2=2420\)  After two years sam will have 11 shops The average items in a shop will be 2420/11=220 items (instantly dismiss A, B and C as they are equal or less than the average and 20% difference will give us some room to go above the average) Let's test the values and begin with the maximum number 260 260 is 40 more than the average (220) We don't want to drop the lowest number, so we will distribute those 40 items burden evenly on the remaining 10 shops (40/10=4) so each shop can have 2204=216 items (216*10+260=2420 we are not missing anything) Now we have got one shop with 260 items and the rest ten shops with 216 items. Do we maintain 20% restriction? ({260216}/216)*100~20.3% As we could approximate, lets round to the nearest integer to get 20%, Fits IMO ANS: E



DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1853
Location: India

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
17 Jul 2019, 12:10
Total number of items Sam has in the shop= 2000*1.1*1.1=2420
Since we want to maximize the number of products in one shop and total items of no shop are greater than 20% of the total items of any other shop, we need to divide equal number of items in 10 shops and 11th shop has 20% more items than any other shop.
10*x+1.2x=2420 1.2x= (2420*1.2)/11.2 1.2x= 260(approximately)
the approximate maximum possible number of items in a shop= 260
IMO E



Senior Manager
Status: eternal student
Joined: 06 Mar 2018
Posts: 324
Location: Kazakhstan
Concentration: Technology, General Management
GPA: 3.87

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
18 Jul 2019, 02:05
Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop?
Current items in Sam's shop = 2000 1 year after = 2200 (2000+10%) 2 year after = 2420 (2200+10%) So now Sam has got 2420 items in 1 shop, he wants to open 10 more, 11 in total. And divide 2420 items among 11 shop, so that difference between items in the shop were not higher than 20 %. Let's imagine belos situation: Attachment:
shops.PNG [ 18.74 KiB  Viewed 452 times ]
Now let's calculate difference: 230  219 difference ~ 5% 240  218 difference ~ 9.2% 250  217 difference ~15% 260  216 difference ~ 20% Bingo! A. 200 B. 216 C. 220 D. 230E. 260 E is the answer.
_________________
My SC approach flowchartMy Verbal Flashcards(no one is ideal, please correct if you see any mistakes or gaps in my explanation, it will be helpful for both of us, thank you) ___________________ "Nothing in this life is to be feared, it is only to be understood" ~ Marie Curie



Math Expert
Joined: 02 Sep 2009
Posts: 64249

Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
Show Tags
19 Jul 2019, 01:44
Bunuel wrote: Sam owns a football accessory shop. At present, the number of items in his shop is 2000 and every year, he plans to increase it by 10% every year. After 2 years, he decides to open 10 more shops and distributes the total number of items he has in such a way that total items of no shop are greater than 20% of the total items of any other shop. What is the approximate maximum possible number of items in a shop? A. 200 B. 216 C. 220 D. 230 E. 260
OFFICIAL EXPLANATION FROM eGMAT: Given: Sam owns a football accessory shop. The number of items in his shop is 2000. Every year, he is increasing the number of items in his shop 10% After 2 years, he opens 10 more shops. He distributes the total number of items in all the shops in such a way that total items of no shop are greater than 20% of the total items of any other shop. To Find: Approximate maximum possible number of items in a shop. Approach & Working Out: After 2 years, number of items in the shop of Sam= 2000 * 1.1 * 1.1 = 2420 Now, Sam distributes these items among 1 old shop and 10 new shops. Let Minimum number of items in a shop is x. Then, maximum number of items in a shop can be = 1.2 x Let the number of shops having minimum number of items =a a × x + (11  a) × 1.2 x = 2420 Now, we want the maximum possible number of items in a shop, maximum possible number of shops should have minimum number of items. This will ensure at least one shop has maximum number of items. So, 11  a = 1 Thus, a = 10 Hence, 10x + 1.2x = 2420 11.2x = 2420 x = 2420/11.2 Hence, maximum possible number of items = 1.2 × 2420/11.2 = 259.28 ≈ 260. Therefore, the correct answer is option E.
_________________




Re: Sam owns a football accessory shop. At present, the number of items in
[#permalink]
19 Jul 2019, 01:44




