8th CBSE Mathematics Unit 4 Playing with Numbers Important Question Paper | QB365

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8th CBSE Mathematics Unit 4 Playing with Numbers Important Question Paper

Published on: 30/07/2019

Playing with Numbers

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Std: 8th Standard CBSE - Mathematics

chapter: - Model Question paper

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Questions:

Generic 2

5 x 2 = 10

Without division state, whether the given number is divisible by 2 or not. 2248

If the number 253z is divisible by 4, where z is the unit's digit, find all the possible values of z.

Check the divisibility of the following number by 3. 108

Check the divisibility of the following number by 2. 98

Write the following in the usual form: 10 x 5 + 6

Generic 5

3 x 5 = 15

Is it possible to have a right circular cylinder to have volume numerically equal to its curved surface area? If yes state when.

Find the values of A, B, and C, if \(\begin{matrix} \quad \quad 4\ 5\ A \\ -\quad C\ B\ 7 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \ \quad2\ 8\ 4 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Write a 2-digit number ab and the number obtained by reversing its digits, i.e. ba. Find their sum. Let the sum be a 3-digit number dad
i.e. ab + ba = dad
(10a + b) + (10b + a) = dad
11(a+ b) = dad
The sum a + b cannot exceed 18 (why?).
Is dad a multiple of 11?
Is dad less than 198?
Write all the 3-digit numbers which are multiples of 11 up to 198. Find the values of a and d.

Generic 3

3 x 3 = 9

If 27x is a multiple of 3 and x is a digit then find the value of x.

10.

If 1y3y6 is divisible by 11, then find the value of y.

11.

Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad 4\quad A \\ +\quad 9\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad C\quad B\quad 3 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)

Match the following

5 x 1 = 5

12.

If D is a digit and the number21 D5 is divisible by 9, then the value of D is

13.

If N \(\div\) 2 leaves a remainder 1, then one's digit of N is

14.

The number divisible by 6

15.

The usual form of 9000 + 30 + 6

16.

The generalised form of 347

Fill up / 1 Marks

5 x 1 = 5

17.

The difference of a 2-digit number and the number obtained by reversing its digits is always divisible by _________

18.

A 4-digit number abcd is divisible by 11, if d + b = _________ or _________

19.

If A x 3 =1A ,then A = __________

20.

The sum of a 2-digit number and the number obtained by reversing the digits is always divisible by ___________

21.

3134673 is divisible by 3 and __________

True or False

5 x 1 = 5

22.

A 3-digit number abc is divisible by 5 if c is an even number

(a)

True

(b)

False

23.

If AB + 7C = 102, where B \(\neq\) 0, C \(\neq\) 0, then A + B + C =14.

(a)

False

(b)

True

24.

If 213x 27 is divisible by 9, then the value of x is 0.

(a)

True

(b)

False

25.

A 3-digit number abc is divisible by 6. If c is an even number, then a + b + c is a multiple of 3.

(a)

False

(b)

True

26.

If a number a is divisible by b, then it must be divisible by each factor of b.

(a)

False

(b)

True

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Answers Key:

Generic 2

5 x 2 = 10

The given number is 2248. Unit's digit of the given number is an even number. Hence, this number is divisible by 2.

1 or 5 or 9

The given number is 108.
Sum of digits of 108 = 1+0 +8 = 9
Now, on dividing this sum by 3, we get
9 \(\div\) 3 = 3 and remainder = 0
which is divisible by 3.
Hence, 108 is divisible by 3.

98
This number is divisible by 2 because the digit at unit's place is 8, which is an even number.

10 x 5 + 6 = 50 + 6 = 56

Generic 5

3 x 5 = 15

Let the radius of the base and height of the right circular cylinder be r units and h units respectively.
Then,
Volume of the cylinder = πr²h cubic units
Curved surface area of the cylinder = 2πrh square units
If volume = curved surface area, then πr²h = 2πrh ⇒ r = 2
Hence, it is possible only when radius of the base is 2 units.

A = 1, B = 6 and C = 1

Let the 2-digit number be ab and the number obtained by reversing the digits is ba.
Let the sum be a 3-digit number dad.
\(\therefore\) ab + ba = dad
\(\Rightarrow\) 10a + b + 10b + a = dad
\(\Rightarrow\) 11a + 11b = dad
\(\Rightarrow\) 11(a+b) = dad
The sum a + b cannot exceed 18 because the greatest 2-digit number is 99 and 9 + 9 = 18
Since, 11(a + b) = dad, so dad is the multiple of 11
Also, 99 + 99 = 198
So, dad is less than 198.
All the 3-digit numbers which are multiples of 11 upto 198 are 110, 121, 132, 143, 154, 165, 176, 187 and 198.
Clearly, dad = 121
Hence, a = 2 and d = 1

Generic 3

3 x 3 = 9

Sum of the digits of 27x
= 2 + 7 + x = 9 + x
Since, 27x is a multiple of 3,
∴ (9 + x) is divisible by 3.
⇒ 9 + x must be equal to 9 or 12 or 15
When 9 + x = 9 ⇒ x = 0
When 9 + x = 12 ⇒ x = 3
When 9 + x = 15 ⇒ x = 6
When 9 + x = 18 ⇒ x = 9
When 9 + x = 21 ⇒ x = 12, which is not possible. [∵ x is a digit]
∴ x can equal to 0, 3, 6 or 9.

10.

y = 5

11.

\(\begin{matrix}\quad 4\quad A \\ +\quad 9\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad C\quad B\quad 3 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)
Here, we have three letters A, B, and C whose values are to be found.
Studying the addition in the one's column, we have A + 8 and we get 3 from this, i.e. a number whose one's digit is 3, for this A has to be 5.
\(\because\) A + 8 = 5 + 8 = 13
Now, for sum in ten's column, we have
1 + 4 + 9 = CB \(\Rightarrow\) 14 = CB
Here, B = 4 and C = 1
Therefore, the puzzle is solved as shown below:
\(\begin{matrix}\quad \quad 4\quad 5 \\ +\quad 9\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 14\quad 3 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)
Hence, A = 5, B = 4 and C = 1