These Class 8 Maths Extra Questions Chapter 16 Playing with Numbers will help students prepare well for the exams.
Class 8 Maths Chapter 16 Extra Questions Playing with Numbers
Playing with Numbers Class 8 Extra Questions
Question 1.
Find Q in the addition.
Solution:
There is just one letter Q whose value we have to find.
Study the addition in the ones column: from Q + 3, we get ‘1’ that is, a number whose ones digit is 1.
For this to happen, the digit Q should be 8. So the puzzle can be solve as shown below.
That is, Q = 8
Question 2.
Find A and B in the addition.
Solution:
This has two letters A and B whose values are to be found.
Study the addition in the ones column: the sum of three A’s is a number whose ones digit is A. Therefore, the sum of two A’s must be a number whose ones digit is 0.
This happens only for A = 0 and A = 5. If A = 0, then the sum is 0 + 0 + 0 = 0, which makes B = 0 too. We do not want this (as it makes A = B, and then the tens digit of BA too becomes 0), so we reject this possibility. So, A = 5.
Therefore, the puzzle is solved as shown below.
That is A = 5 and B = 1.
Question 3.
Find the digits A and B.
Solution:
This also has two letters A and B whose values are to be found.
Since the ones digit of 3 × A is A, it must,, be that A = 0 or A = 5.
Now look at B. If B = 1, then BA × B3 would at most be equal to 19 × 19; that is, it would at most be equal to 361. But the product here is 57A, which is mote than 500. So we cannot have B = 1.
If B = 3, then BA × B3 would be more than 30 × 30; that is, more than 900. But 57A is less than 600. So, B can not be equal to 3.
Putting these two facts together, we see that B = 2 only. So the multiplication is either 20 × 23, or 25 × 23.
The first possibility fails, since 20 × 23 = 460. But, the second one works out correctly, since 25 × 23 = 575.
So the answer is A = 5, B – 2.
Question 4.
Check the divisibility of 21436587 by 9.
Solution:
The sum of the digits of 21436587 is 2 + 1 + 4 + 3 + 6 + 5 + 8 + 7 = 36.
This number is divisible by 9
(for 36 ÷ 9 = 4). We conclude that 21436587 is divisible by 9.
We can double-check :
\(\frac{21436587}{9}\) = 2381843 (the division is exact).
Question 5.
Check the divisibility of 152875 by 9.
Solution:
The sum of the digits of 152875 is 1 + 5 + 2 + 8 + 7 + 5 = 28.
This number is not divisible by 9.
We conclude that 152875 is not divisible by 9.
Question 6.
If the three digit number 24x is divisible by 9, what is the value of x ?
Solution:
Since 24x is divisible by 9, sum of it’s digits, i.e., 2 + 4 + x should be divisible by 9, i.e., 6 + x should be divisible by 9. This is possible when 6 + x = 9 or 18, ….
But, since x is a digit, therefore, 6 + x = 9, i.e., x = 3.
Question 7.
Check the divisibility of 2146587 by 3.
Solution:
The sum of the digits of 2146587 is 2 + 1 + 4 + 6 + 5 + 8 + 7 = 33.
This number is divisible by 3 (for 33 ÷ 3 = 11).
We conclude that 2146587 is divisible by 3.
Question 8.
Check the divisibility of 15287 by 3.
Solution:
The sum of the digits of 15287 is 1 + 5 + 2 + 8 + 7 = 23.
This number is not divisible by 3. We conclude that 15287 too Is not divisible by 3.