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Set Theory - Quant/Math - CAT 2009
Question 4 the day:
September 03, 2003
The question for the day is from the topic of Set Theory.
- Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?
| (1) |
36 days |
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(2) |
14 days |
| (3) |
29 days |
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(4) |
Cannot be determined. |
Correct Answer - (3)
Solution:
Let the number of days that they holidayed be equal to T.
Then, they practiced Yoga on (T – 24) mornings.
They played tennis on (T – 12) evenings.
As they did not do both the activities together on any single day,
Yoga U Tennis = No of days practiced Yoga + No. of days played tennis
=> 22 = T – 24 + T – 12
=> 22 + 24 +12 = 2T
=> 58 = 2T
=> T = 29.
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