CAT 2022 Question Paper | Quant Slot 1

CAT Questions

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 2 : The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

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Video Explanation

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Explanatory Answer

Since each child gets an even number of non-zero balloons, let us assume that they get 2a, 2b, 2c, 2d number of balloons respectively where a, b, c, d are natural numbers.
There are 20 balloons to be distributed.
Therefore, 2a + 2b + 2c + 2d = 20
a + b + c + d = 10
The question basically transpires to be, “In how many ways can 4 natural numbers add up to 10?”

The answer is \(\frac{9}{3}\) ways.
\(\frac{9}{3}=\frac{9 * 8 * 7}{3 * 2 * 1}=84\) ways.
If you are not familiar with why the answer is \(\frac{9}{3}\), head over here and here.

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The question is " The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is "

Hence, the answer is '84'

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