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Published on: 30/07/2018
Based on the chapter Playing with Numbers, some of the important questions are prepared in this question paper.
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Questions + Answers key
Take MCQ Mathematics Test

1.
Write the following number in generalised form: 73
2.
Check the divisibility of the following numbers by 9: 616
3.
If the number 253z is divisible by 4, where z is the unit's digit, find all the possible values of z.
4.
What will be the unit's digit of N, if it is divisible by exactly?
5.
Check the divisibility of the following number by 9.
23457891
6.
Find the values of the letters in each of the following and give reasons for the steps involved.\(\begin{matrix} \quad \quad 2\quad A\quad B \\ +\quad A\quad B\quad 1 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad B\quad 1\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)
7.
If 48101 B 095 is divisible by 33, then find the value of B.
8.
In a 2-digit number, the di.9it in the one's place is three times the digit in the ten's place the sum of the digits is equal to 12. What is the number?
9.
Generalised form of a 3-digit number abc is
a+ b + c
100a+10b+c
100c+10b+a
100b+10a+c
10.
If abc is a 3-digit number, then the number abc- a - b - c is divisible b
9
90
10
11
11.
If the sum of digits of a number is divisible by three, then the number is always divisible by
2
3
6
9
12.
A 4-digit number aabb is divisible by 55. Then possible value(s) of b is/are
0 and 2
2 and 5
0 and 5
7
13.
If 5A x A = 399, then the value of A is
3
6
7
9
14.
The sum of a 2-digit number and the number obtained by reversing the digits is always divisible by ___________
15.
A 4-digit number abcd is divisible by 11, if d + b = _________ or _________
16.
1 x 34 is divisible by 9, if x = ___________
17.
If \(\begin{matrix} \quad \quad 2\quad B \\ +\quad A\quad B \\ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 8\quad A \\ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)and there is no carry over in addition, then A= ____________ and B=_________
18.
(6 x 1000 + 0 x 100 + 0 x 10 + 7) can be written in usual form as __________
19.
If AB x 4 = 192, then A + B = 7.
20.
If a number a is divisible by b, then it must be divisible by each factor of b.
21.
If 213x 27 is divisible by 9, then the value of x is 0.
22.
If AB + 7C = 102, where B \(\neq\) 0, C \(\neq\) 0, then A + B + C =14.
23.
A 3-digit number abc is divisible by 5 if c is an even number
24.
If 1481018095 is divisible by 33, find the value of B.
1.
A number is said to be in a generalised form, if it is expressed as the sum of the products of its digits with their respective place values as ab = a x 10 + b and abc = a x 100 + b x 10 + c.
73 = 10 x 7 + 3 [ \(\because\)ab = 10a + b ]
2.
The given number is 616.
Sum of digits = 6 +1+6 = 13
Now, 13 \(\div\) 9 = 1and remainder = 4
which is not divisible by 9.
Hence, 616 is not divisible by 9.
3.
1 or 5 or 9
4.
0 or 5
5.
No
6.
\(\begin{matrix} \quad \quad 2\quad A\quad B \\ +\quad A\quad B\quad 1 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad B\quad 1\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)
Here, we have two letters A and B whose values are to be found.
Studying the addition in the one's column, we have B + 1 which gives 8, therefore B must be 7.
Then, the puzzle becomes
\(\begin{matrix} \quad \quad 2\quad A\quad 7 \\ +\quad A\quad 7\quad 1 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 7\quad 1\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)
Studying the addition in ten's digit column. We have A + 7 which gives 1, i.e. a number whose unit's digit is 1.
So, A must be 4.
Then, the puzzle is solved as shown below:
\(\begin{matrix} \quad \quad 2\quad 4\quad 7 \\ +\quad 4\quad 7\quad 1 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 7\quad 1\quad 8 \\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \end{matrix}\)
Hence, A = 4 and B = 7.
7.
It is given that, 48101B095 is divisible by 33 = 3 x11.
Hence, it will be divisible by 3 and 11.
If 48101B095 is divisible by 3. Sum of digits
= 4 + 8 + 1 + 0 + 1 + B + 0 + 9 + 5 = 28 + B
(28 + B) is a multiple of 3.
If 481018095 is divisible by 11,
Sum of digits at odd places = 5 + 0 + 1 + 1+ 4 = 11
Sum of digits at even places = 9 + B + 0 + 8
= 17 + B
Difference = 17 + B -11 = 6 + B (6 + 8) is a multiple of 11.
Least value of 6 + B = 11
B=11-6=5
Since, (28 + B) is a multiple of 3.
Least possible value of 28 +B = 30
8 = 30 - 28 = 2
Which is impossible because we have obtained
B = 5.
Now, we take next value, 28 + B = 33
B = 33 -28 =5
Hence, B = 5 is the solution.
8.
39
9.
(b)
100a+10b+c
10.
(a)
9
11.
(b)
3
12.
(c)
0 and 5
13.
(c)
7
14.
( )
11
15.
( )
(a+c) or 12(a+c)
16.
( )
1
17.
( )
A = 6, B = 3
18.
( )
6007
19.
(b)
20.
(a)
21.
(b)
22.
(a)
23.
(b)
24.
148101 B095 is divisible by 33. So, it is divisible by 3 also because 33 is a multiple of 3.
Then, the sum of all digits
=1 + 4 + 8 + 1 + 0 + 1 + B + 0 + 9 + 5= 29 + B
Now, it is a multiple of 3
So, 29 + B is multiple of 3.
\(\Rightarrow\)29 + B = 0, 3, 9 ... , 33, 36, ... , 39, 42
\(\therefore\)B = 1 or 4 or 7
So, B = 4 and required number is 1481014095.
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