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Marshall & McDonough Moderator
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A retailer sells products that belong to different categories, A to F,
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02 Apr 2016, 19:49
Question Stats:
72% (01:49) correct 28% (01:52) wrong based on 168 sessions
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A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If atleast 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product sold last week belonged to Category D? (A) 2/27 (B) 4/27 (C) 5/27 (D) 8/27 (E) 15/27 Question: Self Made
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Re: A retailer sells products that belong to different categories, A to F,
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02 Apr 2016, 20:19
Vyshak wrote: A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If atleast 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?
(A) 2/27
(B) 4/27
(C) 5/27
(D) 8/27
(E) 15/27
Question: Self Made OA after 24 hours Hi, there are 6 distinct categories..Since each category has to have atleast 2 products.. let A have 2 and each thereafter has ONE more than previous.. so A,B,C,D,E, and F will have minimum 2+3+4+5+6+7 = 7*8/2 1 = 281 =27.. therefore ONLY possiblity of products in each due to restriction of TOTAL as 27 is 2,3,4,5,6,7 so D will have 5 products.. Probability = 5/27C
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Re: A retailer sells products that belong to different categories, A to F,
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03 Apr 2016, 06:22
Vyshak wrote: A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If atleast 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?
(A) 2/27
(B) 4/27
(C) 5/27
(D) 8/27
(E) 15/27
Question: Self Made OA after 24 hours Since there are 2 products in any category , we can write as under  A = 2n B = 2n+1 C = 2n+2 D = 2n+3 E = 2n+4 F = 2n+5 Given Quote: 1. a total of 27 products were sold last week 2. atleast 2 products are sold in any category So the minimum value of n must have to be 1 ( To satisfy condition 2 above) Further while solving the problem, the possible number of products sold can be as follows A = 2*1 => 2 B = 2*1+1 => 3 C = 2*1+2 => 4 D = 2*1+3 => 5 E = 2*1+4 => 6 F = 2*1+5 => 7 Thus we find D has minimum 5 products ( Satisfying conditions 1 and 2 above) So the required probability is 5/27 Answer is (C)
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Re: A retailer sells products that belong to different categories, A to F,
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04 Apr 2016, 21:05
Vyshak wrote: A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If atleast 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?
(A) 2/27
(B) 4/27
(C) 5/27
(D) 8/27
(E) 15/27
Question: Self Made OA after 24 hours Going by the options I marked this answer as C = 5/27 solving in the same manner as explained by others. But I find a glitch here. Question says  "What is the probability that a product was sold from Category D last week"?  means whether a product was sold or not from category D last week. In all the outcomes a product was definitely sold from category D. By arranging the figures I can certainly say that a product was sold, for sure, from category D. Doesn't that makes the probability as 1? If the question were  "If a product was bought by me then what is the probability that it belonged to category D?" then I believe that answer C would be the correct option. Can anybody help me here understand whether my thinking is correct or not? Thanks!



Marshall & McDonough Moderator
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Re: A retailer sells products that belong to different categories, A to F,
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04 Apr 2016, 23:49
inventgm wrote: Vyshak wrote: A retailer sells products that belong to different categories, A to F, in alphabetical order. The number of products sold in each category is distinct and in ascending order. If atleast 2 products are sold in any category and a total of 27 products were sold last week, what is the probability that a product from category D was sold last week?
(A) 2/27
(B) 4/27
(C) 5/27
(D) 8/27
(E) 15/27
Question: Self Made OA after 24 hours Going by the options I marked this answer as C = 5/27 solving in the same manner as explained by others. But I find a glitch here. Question says  "What is the probability that a product was sold from Category D last week"?  means whether a product was sold or not from category D last week. In all the outcomes a product was definitely sold from category D. By arranging the figures I can certainly say that a product was sold, for sure, from category D. Doesn't that makes the probability as 1? If the question were  "If a product was bought by me then what is the probability that it belonged to category D?" then I believe that answer C would be the correct option. Can anybody help me here understand whether my thinking is correct or not? Thanks! Thanks inventgm. I have corrected the question to ensure better understanding.



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Re: A retailer sells products that belong to different categories, A to F,
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02 Sep 2018, 05:51
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Re: A retailer sells products that belong to different categories, A to F,
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