A man observe some children playing ’cycle game’ in front of his house every Sunday. He observes that children come in groups and after every 15 minutes, one child from each group leaves their group and form a new group. When same number of groups with same size occurred again , ‘cycle’ has occurred. For example, let initially 3 children in a single group, regrouping 2, 1 and again regrouping 2,1 means cycle occurred. The following table gives the data of seven Sundays as
Sundays........Initial number of groups..........Number of children.........Final number of groups
Sunday 1.................... --- .........................................15 ..........................................---
Sunday 2 .................... 2 ......................................... --- .......................................... 6
Sunday 3 .................... --- ......................................... --- ....................................... 7
Sunday 4 .................... --- .........................................4 ..........................................---
Sunday 5 .................... 2 .........................................10 .......................................... 4
Sunday 6 .................... 5 .........................................18 ..........................................---
Sunday 7 .................... 2 ......................................... --- .......................................... ---
On the basis of the above data, answers the following Questions.
1. How many of the given Sundays, cycle does not occur?
(1) 1 (2) 2 (3) 4 (4) It occurs all the 7 Sundays
2. How many children were there on 3rd Sunday?
(1) 25 (2) 22 (3) 36 (4) 28
3. If six children comes at 9:00 am on 7th Sunday, at what time it is known that
Cycle has occurred first time?
(1) 9:45 am (2) 10:00am (3) 10:15am (4) 10:30am
4. The minimum time to know that ‘cycle’ has occurred first time on 5th Sunday?
(1) 45 minutes (2) 1 hr 15 minutes
(3) 1 hr (4) 2 hr 15 minutes
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