Loading [MathJax]/jax/output/HTML-CSS/jax.js

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Divisibility Tests by 9 and 11

We will discuss here about the rules of divisibility tests by 9 and 11 with the help of different types of problems.

1. What least positive integral value must be given to * so that the number 7654*21 is divisible by 9?

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

Sum of known digits of 7654*21 is 25. The no. Just greater than 25 which is divisible by 9 is 27.

Now, 25 + (*) = 27

Therefore, * = 2

Answer: (b)

Note: Sum of digits when divisible by 9, then the no. is divisible by 9.


2. Which of the following numbers is exactly divisible by ninety-nine?

(a) 114345

(b) 3572404

(c) 135792

(d) 913464

Solution:

Co-prime factors of 99 are 9 and 11.

114345 is divisible by 99 because sum of digits is 18 and difference of (5 + 3 + 1) - (4 + 4 + 1) = 0

Therefore, required number is 114345.

Answer: (a)

Note: The difference of sums of the digits in odd and even places is zero or multiple of 11, then the no. is divisible by 11.


3. 491 + 492 + 493 + 494 is divisible by

(a) 17

(b) 13

(c) 11

(d) 3

Solution:

491 + 492 + 493 + 494

= 491(40 + 41 + 42 + 43)

= 491(1 + 4 + 16 + 64)

= 491 × 85

= 491 × 5 × 17, which is divisible by 17

Therefore, the required number is 17

Answer: (a)


4. The digits indicated by ⨂ in 3422213⨂⨂ so that this number is divisible by ninety-nine, are:

(a) 1, 9

(b) 3, 7

(c) 4, 6

(d) 5, 5

Solution:

Co-prime factors of 99 are 9 and 11. Sum of the digits of 3422213xy is (17 + x + y)

According to the given options,

x + y = 10

And, (3 + 2 + 2 + 3 + y) - (4 + 2 + 1 + x) = 11

Or, 10 + y - 7 - x = 11

Or, y - x = 8

Now, x + y = 10 and y - x = 8

Therefore, x = 1 and y =9

Thus, the required numbers are 1, 9

Answer: (a)

 

5. The number (1025 - 7) is divisible by

(a) 3

(b) 7

(c) 11

(d) 13

Solution:

The number (1025 - 7) is divisible by 3.

Answer: (a)

Note: (10n - 7) is always divisible by 3, for all values of n





Math Employment Test Samples

From Divisibility Tests by 9 and 11 to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More