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# A retailer sells products that belong to different categories, A to F,

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Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1685
Location: India
A retailer sells products that belong to different categories, A to F,  [#permalink]

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02 Apr 2016, 19:49
1
5
00:00

Difficulty:

35% (medium)

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 at-least 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

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Joined: 02 Aug 2009
Posts: 7971
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

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02 Apr 2016, 20:19
3
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 at-least 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

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 = 28-1 =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 = 5/27

C
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Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

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03 Apr 2016, 06:22
1
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 at-least 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

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. at-least 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

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Joined: 22 Nov 2015
Posts: 3
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

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04 Apr 2016, 21:05
1
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 at-least 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

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
Joined: 13 Apr 2015
Posts: 1685
Location: India
Re: A retailer sells products that belong to different categories, A to F,  [#permalink]

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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 at-least 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

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,  [#permalink]

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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,   [#permalink] 02 Sep 2018, 05:51
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