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

Question

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

Question: Self Made
OA after 24 hours

(A) 2/27

(B) 4/27

(C) 5/27

(D) 8/27

(E) 15/27

Question: Self Made

chetan2u · Answer

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

Abhishek009 · Answer

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

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)

inventgm · Answer

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!

Kurtosis · Answer

Thanks  inventgm . I have corrected the question to ensure better understanding.

bumpbot · Answer

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

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

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