CAT 2021 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 13 : The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

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Given that the numbers 3 and 5 should be present in every subset and contain at least 3 numbers in it.

First, we need to find the subsets possible

{3, 5, 1, 2, 4, 6, 7, 8} except 3 and 5, remaining all numbers have two possible outcomes that either it is in the set or out of the set.

So, the number of possible subsets containing at least 3 numbers is 2^{6}-1 = 63

(In this 2^{6}, we have a possibility that nothing is present from {1, 2, 4, 6, 7, 8}. So, we should remove that possibility.)

From these 63, we need to remove the subsets which have {3, 5, 7, 8}

{3, 5, 7, 8, 1, 2, 4, 6} except 3, 5, 7, 8 remaining all numbers {1, 2, 4, 6} have two possible outcomes that either it is in the set or out of the set.

So, the number of sets possible is 2^{4} = 16

Therefore, the answer would be 63 - 16 = 47.

The question is **" The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is " **

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