Question 6 - Figure it out - Page 110, 111 - Chapter 5 Class 6 - Prime Time (Ganita Prakash)

Transcript

Question 6 Anshu and his friends play the ‘idli-vada’ game with two numbers, which are both smaller than 10. The first time anybody says ‘idlivada’ is after the number 50. What could the two numbers be which are assigned ‘idli’ and ‘vada’? Idli-vada game looks like Since both numbers are smaller than 10, possible numbers could be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 And, the first time someone says ‘idli-vada’ is after 50, that means that common multiple of the two numbers is greater than 50 So, we take larger numbers and check Taking 8 and 9 Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,… Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,…. Common multiple is 72 ∴ We say ‘idli-vada’ at 72, which is greater than 50 Thus, required numbers to play Idli-vada game can be 8 and 9 Let’s take some other numbers to check also Taking 7 and 9 Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, …. Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90,…. Common multiple is 63 ∴ We say ‘idli-vada’ at 63, which is greater than 50 Thus, required numbers to play Idli-vada game can be 7 and 9 Taking 7 and 8 Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, …. Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,… Common multiple is 56 ∴ We say ‘idli-vada’ at 56, which is greater than 50 Thus, required numbers to play Idli-vada game can be 7 and 8 Thus, the required numbers could be 8 and 9 7 and 9 7 and 8