CAT 2018 Quant Questions

Question:
In a tournament, there are 43 junior level and 51 senior level participants. Each pair of juniors play one match. Each pair of seniors play one match. There is no junior versus senior match. The number of girl versus girl matches in junior level is 153, while the number of boy versus boy matches in senior level is 276. The number of matches a boy plays against a girl is

Show Answer
Correct Answer: 1098
Among a group of n persons, number of matches played = n(n – 1)/2
Among the Junior participants, let the number of girls be n.
The number of matches played among girls
= n(n – 1)/2 = 153
=> n(n – 1) = 306 = 18 × 17 => n = 18
Number of boys = 43 – 18 = 25
The number of matches played between a boy and a girl = 25×18 = 450
Among the Senior level participants, let the number of boys be n.
The number of matches played between two boys
= n(n – 1)/2 = 276
=> n(n – 1) = 552 = 24 × 23 => n = 24
The number of girls = 51 – 24 = 27
The number of matches played between a boy and a girl = 27 × 24 = 648
Required answer = 450 + 648 = 1098

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