How many balls are in the bag? The bag contains only three types of coloured balls. I. The ratio of blue balls to red balls is 4:5. The number of white balls is one more than the number of red balls. II. The number of ways of selecting 2 red balls from the bag is 10.

Only statement II is sufficient
Both statements together are necessary to answer
Both statements together are not sufficient to answer
Only statement I is sufficient

Correct answer: Both statements together are necessary to answer

Solution

From statement II, \(\binom{r}{2}=10\), so \(r=5\). Using statement I, blue:red = 4:5, hence blue = 4 and white = 6. Therefore total balls = 4 + 5 + 6 = 15. Neither statement alone is sufficient, but together they are sufficient.

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