Description

This mock test of Divisibility Test - Practice Test for UPSC helps you for every UPSC entrance exam.
This contains 5 Multiple Choice Questions for UPSC Divisibility Test - Practice Test (mcq) to study with solutions a complete question bank.
The solved questions answers in this Divisibility Test - Practice Test quiz give you a good mix of easy questions and tough questions. UPSC
students definitely take this Divisibility Test - Practice Test exercise for a better result in the exam. You can find other Divisibility Test - Practice Test extra questions,
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QUESTION: 1

What is the smallest number that should be added to 27452 to make it exactly divisible by 9?

Solution:

If we divide 27452 by 9 the remainder will be 2. Since the question asks for the number to added, we will find out the difference between next number divisible.

9-2= 7

We will add 7 to 27452 = 27459 which is divisible by 9.

QUESTION: 2

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?

Solution:

**The correct option is Option E.**

**Given, **

**522x is a three digit number but actually, it's a four digit number**

**522x is divisible by 6 if it's divisible by 2 and 3 both**

**522x would be divisible by 2**

**If 5 + 2 + 2 + x is divisible by 3**

**If 9 + x is divisible by 3**

**If x = 0, 3, 6 or 9**

**Taking intersection of 0, 2, 4, 6 or 8 and 0, 3, 6 or 9**

**x = 0 or 6**

**5220 and 5226is divisible by 6**

**If we take 522x is three digit number then 52y should be divisible by 6 where y = 2x**

**52y is divisible by 3**

**If 5 + 2 + y is divisible by 3 **

**If y = 2, 5, 8**

**Taking common y = 2 or 8**

** y = 2x **

**=> x = 1 or 4**

**522 and 528 are divisible by 6**

QUESTION: 3

What is the least value of x such that 7648x is divisible by 11?

Solution:

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.

QUESTION: 4

If M183 is divisible by 11, find the value of the smallest natural number M ?

Solution:

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 M183.

(Sum of digits at EVEN places) – (sum of digits at ODD places) = 0

(8 + M )- (3+1)= 0

(8 + M ) - 4 = 0

Here the value of M must be 7 .

QUESTION: 5

What least whole number should be added to 532869 to make it divisible by 9?

Solution:

Answer : C

Explanation: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.

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