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02 Apr 2016, 19:49
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:47) correct
28%
(01:54)
wrong
based on 250
sessions
History
Date
Time
Result
Not Attempted Yet
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
Question: Self Made
(A) 2/27
(B) 4/27
(C) 5/27
(D) 8/27
(E) 15/27
Question: Self Made
02 Apr 2016, 20:19
Kudos
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Vyshak
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
03 Apr 2016, 06:22
Kudos
Bookmarks
Vyshak
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:
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)
