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14 Sep 2016, 19:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
50% (01:16) correct
50%
(02:35)
wrong
based on 4
sessions
History
Date
Time
Result
Not Attempted Yet
Three variables X,Y,Z have a sum of 30. All three are Non-Negative integers. If any 2 variables don't have the same value and exactly one variable has value less than or equal to 3, find the number of possible solutions.
(A) 84
(B) 252
(C) 98
(D) 126
(E) 294
(A) 84
(B) 252
(C) 98
(D) 126
(E) 294
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Senthil1981
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14 Sep 2016, 21:20
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rudra316
It's easy to think in terms of Balls and Boxes. Let X,Y and Z be three boxes and these are the rules for filling the boxes,
1) only one box should always have 3 or less balls
2) None of the boxes should have same number of balls
3) the sum of balls in all three boxes should be equal to 30
So Let's start with X being less than or equal to 3 and this can have 4 different ways, X=0,1,2,3 and Y and Z can range based on that.
so if X = 0 , Y and Z can range from 4 to 26 = 22 ways
X = 1 , Y and Z can range from 4 to 25 = 22 ways
X = 2, Y and Z can range from 4 to 24 = 20 ways
X = 3, Y and Z can range from 4 to 23 = 20 ways
So 84 ways and X,Y,Z can take turns, so 84 * 3 = 252.
Answer is B
(This took around 5 mins, Looking for a short cut)
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Hi there,
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