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All questions of Divisibility Rules for Bank Exams Exam
Find the least of value of ‘x’ so that the number 73818x4 is divisible by 8- a)1
- b)2
- c)3
- d)4
- e)6
Correct answer is option 'B'. Can you explain this answer?
Find the least of value of ‘x’ so that the number 73818x4 is divisible by 8
a)
1
b)
2
c)
3
d)
4
e)
6
|
Dhruba Chavan answered |
Answer : B
Explanation:A number is exactly divisible by 8, then the last 3 digits of the numbers must be divisible by 83
Here the last 3 digits are 8x4.
Put each value in given options in the place of x and check whether it is divisible by 8 or not .
Option b , 824 which is exactly divisible by 8.
So answer is option b.
If 522x is a three digit number with as a digit x . If the number is divisible by 6, What is the value of the digit x is?- a) 1
- b)2
- c)3
- d)4
- e)6
Correct answer is option 'E'. Can you explain this answer?
If 522x is a three digit number with as a digit x . If the number is divisible by 6, What is the value of the digit x is?
a)
1
b)
2
c)
3
d)
4
e)
6
|
Harshitha Choudhury answered |
If a number is divisible by 6 , it must be divisible by both 2 and 3
In 522x, To this number be divisible by 2, the value of x must be even . So it can be 2,4 or 6 from given options
552x is divisible by 3, If sum of its digits is a multiple of 3 .
5+5+2+x =12+x ,
If put x =2 , 12+2=14 not a multiple of 3
If put x =4 , 12+6=18 is a multiple of 3
If put x =6 , 12+2=14 not a multiple of 3
The value of x is 6.
In 522x, To this number be divisible by 2, the value of x must be even . So it can be 2,4 or 6 from given options
552x is divisible by 3, If sum of its digits is a multiple of 3 .
5+5+2+x =12+x ,
If put x =2 , 12+2=14 not a multiple of 3
If put x =4 , 12+6=18 is a multiple of 3
If put x =6 , 12+2=14 not a multiple of 3
The value of x is 6.
Divisibility Rules Solved Problem 8.For a number to be divisible by 88 it should be: - a)Divisible by 8.
- b)Divisible by 8 and 22.
- c)Divisible by 8 and 11.
- d)Divisible by 4,22
- e)can’t say
Correct answer is option 'C'. Can you explain this answer?
Divisibility Rules Solved Problem 8.For a number to be divisible by 88 it should be:
a)
Divisible by 8.
b)
Divisible by 8 and 22.
c)
Divisible by 8 and 11.
d)
Divisible by 4,22
e)
can’t say
|
Akanksha Bose answered |
Answer: C
Explanation:
For a number to be divisible by 88, the number must be divisible by 8 and 11.
Write 88 as product of two factors : 22 ,2
11 ,8
44,2
Of these pairs , 11 and 8 are co primes.
So the number must be divisible by 8 and 11.
So the number must be divisible by 8 and 11.
Divisibility Rules Solved Problem 7.Find the least of value of ‘*’ so that the number 37*124 is divisible by 9 ? - a)1
- b)10
- c)2
- d)3
- e)4
Correct answer is option 'A'. Can you explain this answer?
Divisibility Rules Solved Problem 7.Find the least of value of ‘*’ so that the number 37*124 is divisible by 9 ?
a)
1
b)
10
c)
2
d)
3
e)
4
|
Zara Khan answered |
Answer : A
Explanation:
if a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 3+7+*+1+2+4=17+*
Here the value of * must be 1 because the next multiple of 9 is 18.
What is the smallest number that should be added to 27452 to make it exactly divisible by 9? - a)1
- b)2
- c)7
- d)8
- e)9
Correct answer is option 'C'. Can you explain this answer?
What is the smallest number that should be added to 27452 to make it exactly divisible by 9?
a)
1
b)
2
c)
7
d)
8
e)
9
|
Rajesh Khatri answered |
If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 2+7+4+5+2=20, the next multiple of 9 is 27.
7 must be added to 27452 to make it divisible by 9.
What least whole number should be added to 532869 to make it divisible by 9? - a)2
- b)1
- c)3
- d)4
- e)5
Correct answer is option 'C'. Can you explain this answer?
What least whole number should be added to 532869 to make it divisible by 9?
a)
2
b)
1
c)
3
d)
4
e)
5
|
|
Rajesh Khatri answered |
If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 5+3+2+8+6+9=33, the next multiple of 9 is 36.
3 must be added to 532869 to make it divisible by 9.
What is the least value of x such that 7648x is divisible by 11?- a)3
- b)2
- c)1
- d)0
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
What is the least value of x such that 7648x is divisible by 11?
a)
3
b)
2
c)
1
d)
0
e)
None of these
|
Neha Joshi answered |
A number is divisible by 11 when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11
The given number is 7648x.
(Sum of digits at EVEN places) – (sum of digits at ODD places) = 0
⇒ (6 + 8 ) - ( X + 7 + 4 ) = 0
⇒ 14 - ( X + 11 ) = 0
Here the value of x must be 3
So, the least value of x is 3.
So, the least value of x is 3.
What is the missing digit which makes the number 9724* exactly divisible by 6?
- a)2
- b)4
- c)5
- d)6
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
What is the missing digit which makes the number 9724* exactly divisible by 6?
a)
2
b)
4
c)
5
d)
6
e)
None of these
|
Varun Kapoor answered |
Divisibility by 6 requires that the number be divisible by 2 as well as 3 , i.e, the following 2 conditions must be meti) Unit digit be Zero or evenii) Sum of digits be divisible by 3The given number is 9724*Sum of the digits =9 +7 +2 +4 +* =22+*The digit which on being added to 22 will give the sum divisible by 3 are 22+2 =24 and 22 +5=7.2 and 7 satisfy the condition ii.The blank space is at unit's place. So the missing digit must satisfy the condition(i) alsoOut of 2 and 5, only 2 is even.
If M183 is divisible by 11, find the value of the smallest natural number M ? - a)5
- b)6
- c)7
- d)9
- e)8
Correct answer is option 'C'. Can you explain this answer?
If M183 is divisible by 11, find the value of the smallest natural number M ?
a)
5
b)
6
c)
7
d)
9
e)
8
|
Malavika Datta answered |
To determine the value of the smallest natural number M, we need to find a number that is divisible by 11 and is the smallest among all possible values.
Let's analyze the divisibility rule for 11. If the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is divisible by 11, then the number itself is divisible by 11.
Let's represent the number M183 in terms of its digits: M = 1000a + 100b + 10c + 1d.
Using the divisibility rule for 11, we can write the equation:
(1d + 10c + 100b + 1000a) - (10c + 1d) = 99a + 99b = 11(9a + 9b).
From this equation, we can see that M183 will be divisible by 11 if and only if 9a + 9b is divisible by 11.
The smallest natural numbers for a and b that satisfy this condition are a = 1 and b = 2. This gives us M = 1000(1) + 100(2) + 10c + 1d = 1200 + 10c + 1d.
Now, we need to find the smallest values for c and d that make M divisible by 11.
Substituting a = 1 and b = 2 into the equation 9a + 9b = 11(9a + 9b), we get 9(1) + 9(2) = 9 + 18 = 27.
To make 27 divisible by 11, we need to find the smallest values for c and d that satisfy the equation 10c + 1d = 27.
The smallest values that satisfy this equation are c = 2 and d = 7. Substituting these values into M = 1200 + 10c + 1d, we get M = 1200 + 10(2) + 1(7) = 1200 + 20 + 7 = 1227.
Therefore, the smallest natural number M that is divisible by 11 is M = 1227.
Hence, the correct answer is option C) 7.
Let's analyze the divisibility rule for 11. If the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is divisible by 11, then the number itself is divisible by 11.
Let's represent the number M183 in terms of its digits: M = 1000a + 100b + 10c + 1d.
Using the divisibility rule for 11, we can write the equation:
(1d + 10c + 100b + 1000a) - (10c + 1d) = 99a + 99b = 11(9a + 9b).
From this equation, we can see that M183 will be divisible by 11 if and only if 9a + 9b is divisible by 11.
The smallest natural numbers for a and b that satisfy this condition are a = 1 and b = 2. This gives us M = 1000(1) + 100(2) + 10c + 1d = 1200 + 10c + 1d.
Now, we need to find the smallest values for c and d that make M divisible by 11.
Substituting a = 1 and b = 2 into the equation 9a + 9b = 11(9a + 9b), we get 9(1) + 9(2) = 9 + 18 = 27.
To make 27 divisible by 11, we need to find the smallest values for c and d that satisfy the equation 10c + 1d = 27.
The smallest values that satisfy this equation are c = 2 and d = 7. Substituting these values into M = 1200 + 10c + 1d, we get M = 1200 + 10(2) + 1(7) = 1200 + 20 + 7 = 1227.
Therefore, the smallest natural number M that is divisible by 11 is M = 1227.
Hence, the correct answer is option C) 7.
Divisibility Rules Solved Problem 9.What is the smallest number which must be added to 8261955 so as to obtain a sum which is divisible by 11?- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'B'. Can you explain this answer?
Divisibility Rules Solved Problem 9.What is the smallest number which must be added to 8261955 so as to obtain a sum which is divisible by 11?
a)
1
b)
2
c)
3
d)
4
e)
5
|
Aruna Singh answered |
For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 8261955, Difference =(8+6+9+5) -(2+1+5)=28-8=20.
The units digit is at odd place. So we add 2 to the number
=> 8261955 +2 = 8261957
Now , (8+6+9+7) -(2+1+5)=30-8=22 => 22 is a multiple of 11 and hence 8261957 is also divisible by 11.
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