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This contains 5 Multiple Choice Questions for UPSC Divisibility Test - MCQ Test (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Find the least of value of ‘x’ so that the number 73818x4 is divisible by 8

Solution:

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.

QUESTION: 2

Divisibility Rules Solved Problem 7.Find the least of value of ‘*’ so that the number 37*124 is divisible by 9 ?

Solution:

**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.

QUESTION: 3

Divisibility Rules Solved Problem 8.For a number to be divisible by 88 it should be:

Solution:

**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.

QUESTION: 4

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?

Solution:

**Answer : B**

**Explanation:**

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.

QUESTION: 5

What is the missing digit which makes the number 9724* exactly divisible by 6?

Solution:

**Answer : A**

**Explanation:**

Divisibility by 6 requires that the number be divisible by 2 as well as 3 , i.e, the following 2 conditions must be met

i) Unit digit be Zero or even

ii) Sum of digits be divisible by 3

The 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) also

Out of 2 and 5, only 2 is even.

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