Question 9 - Figure it out - Page 63, 64 - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Transcript

Question 9 Children are playing ‘Fire in the Mountain’. When the number 6 was called out, no one got out. When the number 9 was called out, no one got out. But when the number 10 was called out, some people got out. How many children could have been playing initially? (a) 72 (b) 90 (c) 45 (d) 3 (e) 36 (f) None of theseLet’s look at the game ‘Fire in the Mountain’. The rules are: Whenever the leader calls out a number, People are supposed to arrange themselves in groups of that number. Whoever is not part of the announced group size, is out. 33 people, divided into groups of 5 Now, our question is When the number 6 was called out, no one got out. When the number 9 was called out, no one got out. But when the number 10 was called out, some people got out. Thus, the total students are divisible by 6 & 9, but not 10 We can check each option Option (a) – 72 Now, 72 is a multiple of 6 72 is a multiple of 9 And, 72 is not divisible by 10 Thus, 72 is possible Option (b) – 90 Now, 90 is a multiple of 6 90 is a multiple of 9 And, 90 is divisible by 10 Thus, 90 is not possible Option (c) – 45 Now, 45 is not a multiple of 6 Thus, 45 is not possible Option (d) – 3 Now, 3 is not a multiple of 6 Thus, 3 is not possible Option (e) – 36 Now, 36 is a multiple of 6 36 is a multiple of 9 And, 36 is not divisible by 10 Thus, 36 is possible Therefore, Number students could be 36 or 72