Anshu and his friends play the ‘idli- vada’ game with two numbers, which are both smaller than 10. The first time

Anshu and his friends play the ‘idli- vada’ game with two numbers, which are both smaller than 10. The first time

Question 1.

Anshu and his friends play the ‘idli- vada’ game with two numbers, which are both smaller than 10. The first time anybody says ‘idli-vada’ is after the number 50. What could the two numbers be which are assigned ‘idli’ and ‘vada’? Class 6

Solution:

Numbers less than 10 are 1, 2, 3, 4, 5, 6, 7, 8 and 9. Some numbers coming after 50 are 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, ...

As the number represent ‘idli-vada’, we have to choose a common multiple of two numbers (1 to 9) from the above numbers.

Also, we know that 51 = 3 × 17, 52 = 4 × 13, 53 = 1 × 53, 54 = 6 × 9, 55 = 5 × 11, 56 = 7 × 8, 57 = 3 × 19, 58 = 2 × 29, 59 - 1 × 59, 60 = 5 × 12 = 6 × 10 and so on.

As the two numbers must be less than 10, so the possible pairs are 6 and 9; and 7 and 8.

Now, multiples of 6 are 6, 12, 18, 24, ... and that of 9 are 9, 18, 27, ...

So, from this phir of numbers, we get the first common multiple (idli-vada) as 18, which

is less than 50. Hence, this pair of numbers 6 and 9 is rejected.

Now, multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, ... and multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, ...

Here, first common multiple (idli-vada) is 56, which just comes after 50. Hence, the required pair of numbers is 7 and 8.

Question 2.

In the treasure hunting game, Grumpy has kept treasures on 28 and 70. What jump sizes will land on both the numbers? Class 6

Solution:

Factors of 28 are 1, 2, 4, 7, 14 and 28.

Factors of 70 are 1, 2, 5, 7, 10, 14, 35 and 70.

Their common factors are 1, 2, 7 and 14.

So, jump sizes 1, 2, 7 and 14 will land on both the numbers.