A bag has 15 red, green and blue balls. Number of each balls is different in…
2018
A bag has 15 red, green and blue balls. Number of each balls is different in the bag. Difference between red ball and green ball is same as difference between green ball and blue ball. Probability of selecting one blue ball from the bag is greater than 0.2, then number of blue balls in the bag can be
(A) 3
(B) 4
(C) 5
(D) 7
(E) 9
- A.
Only B, C, D and E
- B.
Only B, D, E
- C.
All A, B, C, D and E
- D.
Only C, D, E
- E.
Only A, B, D, E
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Let the numbers of red, green, and blue balls be R, G, and B.
R + G + B = 15, and the equal-difference condition places the counts in an arithmetic progression, so the middle count is 5.
The blue count must be greater than 20% of 15, so B > 3.
Among the listed possible blue counts A=3, B=4, C=5, D=7, E=9, the valid values greater than 3 that can fit a positive distinct arithmetic progression are 4, 7, and 9.
Therefore only B, D, and E are possible.