Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 16 Playing with Numbers Questions Solution. In this chapter, there are total 50 math problems. We have given each questions solution step by step.
Edudel Class 8 Mental Maths Chapter 16 Playing with Numbers:
1.) Find the least possible missing digit of the number 13_64, if it is divisible by 3.
ANSWER:
We know, Divisibility test of 3.
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
We add all numbers.
1 + 3 + x + 6 + 4 = 14 + x
15 is nearest number divisible by 3.
x = 15 – 14
x = 1
The least possible missing digit of the number 13_64, if it is divisible by 3 is 1.
2.) Find the remainder when number 4191 is divided by 5.
ANSWER:
We know, Divisibility test of 5.
If the One’s digit of a number is 0 or 5, the number is divisible by 5.
Here, 4191 the last digit is greater than 1.
The remainder when number 4191 is divided by 5 is 1.
3.) Find the missing digit of the number 453_892, so that the number is divisible by 11.
ANSWER:
We know, Divisibility test of 11.
If the difference between the sum of digits of a number at its odd places and the even places is either ‘0’ or divisible by ‘11’, the number is divisible by 11
We 1st add odd places number = 2 + 8 + 3 + 4 = 17
We add even places number =9 + x + 5 = 14 + x
Difference = 17 – (14+x)
X = 3
The missing digit of the number 453_892, so that the number is divisible by 11 is 3.
4.) Find the greatest two digit number which when divided 11 gives remainder 2.
ANSWER:
We have to find the greatest two digit number which when divided 11 gives remainder 2.
When we divide 90 by 11 we get, 88 divisible by 8 and remainder is 2.
The greatest two digit number which when divided 11 gives remainder 2 is 90.
5.) If 7_1 is a multiple of 9, find the missing digit.
ANSWER:
We know, Divisibility test of 9.
If sum of digits of a number is divisible by 9 then the number is divisible by 9.
We add numbers.
7 + x + 1 = 8 + x
We know 9 is divisible by 9
X = 9 – 8
X = 1
The missing digit is 1.
6.) If 14_ is a multiple of 6, find the least possible missing digit.
ANSWER:
We know, Divisibility test of 6.
If the number is divisible by 2 and 3 both then the number is divisible by 6.
For divisibility of 2 the number is even.
For divisibility of 3, sum of digits of a number is divisible by 3 then the number is divisible by 3.
We first add numbers.
1 + 4 + x = 5 + x
X is even number and divisible by 3.
We put x = 4
9 is divisible by 3.
The least possible missing digit is 4. And number is 144.
7.) Find the quotient when the sum of 81 and 18 is divided by 9.
ANSWER:
We have to find quotient when the sum of 81 and 18 is divided by 9
First we add 81 + 18 = 99
99 / 9 = 11
The quotient is 11.
8.) Find the quotient when the difference of 184 and 55 is divided by 3.
ANSWER:
We have to find the quotient when the difference of 184 and 55 is divided by 3
First we find the difference of 184 and 55 = 184 – 55 = 129
129 / 2 = 43
The quotient is 43.
9.) If 58_ is a multiple of 11, find the missing digit.
ANSWER:
We know, Divisibility test of 11.
If the difference between the sum of digits of a number at its odd places and the even places is either ‘0’ or divisible by ‘11’, the number is divisible by 11
We add odd places number = x + 5
We add even places number = 8
We find difference = 8 – (x + 5) = 0
X = 3
The missing digit is 3.
10.) Find the smallest 3 digit number which is divisible by both 2 and 3.
ANSWER:
We know,
If the number is divisible by 2 and 3 both then the number is divisible by 6.
We have to find the smallest 3 digit number.
The smallest 3 digit number is 102.
102 is even number hence divisible by 2
Sum of 1 + 0 + 2 = 3 divisible by 3.
The smallest 3 digit number which is divisible by both 2 and 3 is 102.
11.) Find the greatest 4 digit number which is divisible by both 5 and 10.
ANSWER:
We know,
If the One’s digit of a number is 0, the number is divisible by 5 and 10.
We have to find the greatest 4 digit number which is divisible by both 5 and 10.
The greatest 4 digit number which is divisible by both 5 and 10 is 9990.
12.) Find the smallest 3 digit number which is divisible by 5.
ANSWER:
We know,
If the One’s digit of a number is 0 or 5, the number is divisible by 5.
We have to find the smallest 3 digit number which is divisible by 5
The smallest 3 digit number which is divisible by 5 is 100.
- What is the greatest 3 digit number which is divisible by 2?
ANSWER:
We know,
If the One’s digit of a number is 0,2,4,6, or 8, the number is divisible by 2.
We have to find the greatest 3 digit number which is divisible by 2
The greatest 3 digit number which is divisible by 2 is 998.
- )What is the greatest 4 digit number which is divisible by 9?
ANSWER:
We know,
If sum of digits of a number is divisible by 9 then the number is divisible by 9.
We have to find the greatest 4 digit number which is divisible by 9
The greatest 4 digit number which is divisible by 9 is 9999.
15.) Find the smallest 5 digit number divisible by 3.
ANSWER:
We know,
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
We have to find the smallest 5 digit number divisible by 3
The smallest 5 digit number divisible by 3 is 10002
16.) What least number should be added to 2184 so that it becomes divisible by 10?
ANSWER:
Let least number be added is x.
2184 + x = divisible by 10
We know,
If the One’s digit of a number is 0, the number is divisible by 10.
We put x = 6
2184 + 6 = divisible by 10
Least number be added is 6.
17.) Which least number should be subtracted from 43787, so that it becomes divisible by 5?
ANSWER:
Let least number be subtracted is x.
43787 – x = divisible by 5
We know,
If the One’s digit of a number is 0 or 5, the number is divisible by 5.
We put x = 2
43787 – 2 = divisible by 5
43785 = divisible by 5
Least number be subtracted is 2.
18.) What least number should be added to 27841, so that the number is divisible by 3?
ANSWER:
Let least number be added is x.
27841 + x = divisible by 3
We know,
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
2 + 7 + 8 + 4 + 1 + x = divisible by 3
22 + x = divisible by 3
We put x = 2
24 is divisible by 3.
Least number be added is 2.
19.) What least number should be subtracted from 4673, so that the number is divisible by 9?
ANSWER:
Let least number be subtracted is x.
4673 – x = divisible by 9
We know,
If sum of digits of a number is divisible by 9 then the number is divisible by 9.
4 + 6 + 7 + 3 – x = divisible by 9
20 – x = divisible by 9
We put x = 2
18 which is divisible by 9
Least number be subtracted is 2.
20.) Find the 3-digit greatest number which leaves a remainder 7 when divided by 9.
ANSWER:
Here we have to find the 3-digit greatest number which leaves a remainder 7 when divided by 9.
The greatest 3-digit greatest number divided by 9 is 999.
But we require remainder 7.
999 – 9 + 7 = 997
The 3-digit greatest number which leaves a remainder 7 when divided by 9 is 997.
21.) What least number should be added to 74862, so that the number is divisible by 3 and 4 both?
ANSWER:
Let least number be added is x.
74862 + x = divisible by 3
We know,
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
If the number formed by Ten’s and One’s digit is divisible by 4, the entire number is divisible by 4.
7 + 4 + 8 + 6 + 2 + x = divisible by 3 and 4
27 + x = divisible by 3 and 4
We put x = 6
33 is divisible by 3.
62 + 6 = 68 divisible by 4.
Least number be added is 6.
22.) By which least number 600 be multiplied to get a perfect square number?
ANSWER:
Let least number is x.
600x = perfect square number
We put x = 6
600 x 6 = 3600 which is perfect square number
6 is least number 600 be multiplied to get a perfect square number.
23.) Find the least number which when divided by 3, 9 and 12 leaves a remainder 2 in each case.
ANSWER:
We have to find the least number which when divided by 3, 9 and 12 leaves a remainder 2 in each case.
We take LCM of 3, 9 and 12.
The LCM of 3, 9 and 12 is 36.
A remainder 2 in each case we get.
36 + 2 = 38
The least number which when divided by 3, 9 and 12 leaves a remainder 2 in each case is 38.
24.) Find the smallest number by which 80 must be multiplied to make it a perfect cube.
ANSWER:
The smallest number is x.
80x = perfect cube.
We put x = 100
80 x 100 = 8000 which is perfect cube.
The smallest number is 100.
- If 63_ is divisible by 15, find the least possible missing digit.
ANSWER:
63_ is divisible by 15.
Let x is missing digit.
We know,
15 = 3 x 5
The number is divisible by 3 and 5.
We know,
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
If the One’s digit of a number is 0 or 5, the number is divisible by 5.
6 + 3 + x = divisible by 3 and 5.
9 + x = divisible by 3 and 5.
We put x = 0
9 is divisible by 3.
0 is One’s digit of a number, the number is divisible by 5.
The missing digit is 0.
26.) How many halves are there in 28(1/2)?
ANSWER:
We have to find How many halves are there in 28(1/2).
We write 28(1/2) as (28 x 2) + 1 / 2
28(1/2) = 57 / 2
There are 57 halves are there in 28(1/2).
27.) Find the least possible missing digit if 81972_6 is divisible by 8.
ANSWER:
81972_6 is divisible by 8.
Let x is missing digit.
We know,
If the number formed by hundred’s, ten’s and one’s digit is divisible by 8, then the number is divisible by 8.
81972_6 = last 3 digits divisible by 8, then the number is divisible by 8.
2×6 / 8
We put x = 1
216 is divisible by 8.
The missing digit is 1.
28.) Find the number of times a 5 m long rope needs to be cut for dividing it into 20 pieces.
ANSWER:
Cut for dividing it into 20 pieces we do 19 times process.
29.) You are participating in a race. You overtake the third runner, at what position are you?
ANSWER:
When we overtake the third runner then we are at third position.
- Subtract the smallest 2-digit negative integer from the largest 2-digit negative integer.
ANSWER:
We know,
The smallest 2-digit negative integer = -99
The largest 2-digit negative integer. = -10
Subtraction of the smallest 2-digit negative integer from the largest 2-digit negative integer. = -10 – (-99)
Subtraction of the smallest 2-digit negative integer from the largest 2-digit negative integer. = 89
31.) Find the remainder when 10084237825 is divided by 4.
ANSWER:
We have to find the remainder when 10084237825 is divided by 4
We know,
If the number formed by Ten’s and One’s digit is divisible by 4, the entire number is divisible by 4.
The last 2 digit are 10084237825 is 25.
25 / 4 = 6 and remainder 1.
The remainder when 10084237825 is divided by 4 is 1.
32.) If 62_5 is a multiple of 3, find the least possible missing digit.
ANSWER:
62_5 is a multiple of 3
Let missing digit is x.
We know,
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
6 + 2 + x + 5 = multiple of 3
13 + x = multiple of 3
We put x = 2
15 is multiple of 3
Missing digit is 2.
33.) Find the value of x so that 14×32 is a multiple of 11.
ANSWER:
14×32 is a multiple of 11.
We know,
If the difference between the sum of digits of a number at its odd places and the even places is either ‘0’ or divisible by ‘11’, the number is divisible by 11.
Sum of odd places digit = 2 + x + 1 = 3 + x
Sum of even places digit = 3 + 4 = 7
Difference = 7 – (3 + x) = 0
X = 4
Missing digit is 4.
34.) Find the values of y so that 32y4 is a multiple of 4.
ANSWER:
32y4 is a multiple of 4.
We know,
If the number formed by Ten’s and One’s digit is divisible by 4, the entire number is divisible by 4.
Last 2 digit is a multiple of 4.
y4is a multiple of 4.
We put y = 0, 2,4,6,8
2, 24,44,64,84 is multiple of 4.
The values of y are 0, 2,4,6,8
35.) Find the values of x so that 73×56 is divisible by 6.
ANSWER:
73×56 is divisible by 6.
We know,
If the number is divisible by 2 and 3 both then the number is divisible by 6.
73×56 is divisible by 2 because it is even number.
7 + 3 + x + 5 + 6 = 21 + x
We put x = 0,3,6,9
All values are divisible by 3.
The values of x are 0,3,6,9
36.) For what values of z, the number z536 is divisible by 11?
ANSWER:
z536 is divisible by 11
We know,
If the difference between the sum of digits of a number at its odd places and the even places is either ‘0’ or divisible by ‘11’, the number is divisible by 11.
Sum of odd places digit = 6 + 5 = 11
Sum of even places digit = 3 + z
Difference = 11 – (3 + z) = 0
Z = 8
Value of z is 8.
37.) Find the smallest number with 4 different digits which is divisible by 11.
ANSWER:
We have to find the smallest number with 4 different digits which is divisible by 11.
The smallest number with 4 different digits which is divisible by 11 is 1023.
38.) For 5AAA82, which least possible missing digit will make it divisible by 9?
ANSWER:
5AAA82 is divisible by 9.
We have to find least possible missing digit will make it divisible by 9
We know,
If sum of digits of a number is divisible by 9 then the number is divisible by 9.
5 + A + A + A + 8 + 2 = 15 + 3A
We put A = 1
18 is divisible by 9.
Least possible missing digit is 1.
39.) What should be added to 189573 to make it divisible by both 2 and 3?
ANSWER:
Let x is the number added to 189573
189573 + x = divisible by both 2 and 3
1 + 8 + 9 + 5 + 7 + 3 = 33 + x = divisible by both 2 and 3
We put x = 3
33 + 3 = 36 divisible by 3 and the number is even.
3 is the number added to 189573
40.) Find the smallest value of x, so that 92×5 is divisible by 5.
ANSWER:
92×5 is divisible by 5
We know,
If the One’s digit of a number is 0 or 5, the number is divisible by 5
92×5 the One’s digit of a number is 5, the number is divisible by 5
We put x = 0
9205 is divisible by 5
The smallest value of x is 0.
41.) For what value of x the number 92x5x6 is divisible by 9?
ANSWER:
92x5x6 is divisible by 9
We know,
If sum of digits of a number is divisible by 9 then the number is divisible by 9.
9 + 2 + x + 5 + x + 6 = 22 + 2x
We put x = 7
22 + 2 x 7 = 36 is divisible by 9.
Value of x is 7.
42.) If on dividing N by 5 we get a remainder 2, what might be the greatest one’s digit of N?
ANSWER:
Given,
On dividing N by 5 we get a remainder 2
N / 5 = remainder 2
Greatest one’s digit of N = 5 + 2
Greatest one’s digit of N = 7
43.) If 8237AA is a number divisible by 3 and ‘A’ is a digit, what are the possible values of ‘A’?
ANSWER:
8237AA is a number divisible by 3
We know,
If sum of digits of a number is divisible by 3 then the number is divisible by 3.
8 + 2 + 3 + 7 + 2A = 20 + 2A
We put, A = 2, 5, 8
24, 30, 36 are divisible by 3.
The possible values of ‘A are 2, 5, 8.
44.) What smallest number should be added to 789153 so that it becomes divisible by both 4 and 3?
ANSWER:
Let, smallest number should be added is x.
789153 + x = divisible by both 4 and 3
7 + 8 + 9 + 1 + 5 + 3+ x = divisible by both 4 and 3
33 + x = divisible by both 4 and 3
We put x = 3
36 divisible by both 4 and 3
Smallest number should be added is 3.
For the following questions, find X, Y and/or Z according to the question:
X Y
+1 X
——-
Y 7
——-
ANSWER:
We put,
X = 3 and y = 4
3 4
+1 3
——-
4 7
——-
46.)
Z Y 6
× Z
———
182Z
———
ANSWER:
We put,
Z= 4 and y = 5
4 5 6
× 4
———
1824
———
47.
12 X
+6XY
———
X 0 9
———
ANSWER:
We put,
X = 8 and y = 1
128
+ 681
——–
809
———
48.)
5 8 X
+3 Y1
——–
Z 0 9
——–
ANSWER:
We put,
X = 8, y = 2 and Z = 9
588
+321
——–
909
——–
49.)
2 Y
× Y
——-
12 Y
——-
ANSWER:
We put,
y = 5
25
×5
——-
125
——-
50.)
5 3 X
+2 Y 5
———
Z 0 7
———
ANSWER:
We put,
X = 2, y = 7 and Z = 8
532
+275
———
807
———
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