Examples on Digits and Numbers

We will learn how to solve different types of examples on digits and numbers.

1. The sum of a 2-digit number & the number formed by interchanging the digits of the original (2-digit number) number is divisible by

(a) 11

(b) 9

(c) 5

(d) 3

Solution:

(10a + b) + (10b + a) = 11(a + b)

Therefore, 11(a + b) must be divisible by 11.

Answer: (a)

Note: Any two-digit number and the number obtained by interchanging its digit:

⟹ Their sum is divisible by 11.

⟹ Their difference is divisible by 9.


2. The product of two positive integers is 24. The greatest number is 1 ½ times the smaller number. The difference of the numbers is

(a) 6

(b) 4

(c) 2

(d) 1

Solution:

Ratio of greater to smaller number = 3/2 = 3 : 2

Therefore, 3x × 2x = 24

or, 6x\(^{2}\) = 24

or, x\(^{2}\) 4

or, x = 2

Therefore, the required difference = (3x - 2x) = 2

Answer: (c)

 

3. Find the sum of all 4-digit numbers which are formed by the digits 1, 2, 3 and 4 only once?

 (a) 66666

(b) 66662

(c) 66661

(d) 66660

Solution:

The required sum = 6666 × (1 + 2 + 3 + 4) = 66660

Answer: (d)

Note: Sum of all four digit numbers by using four difference digits (other than zero) = 6666 × Sum of digits


4. The number of digits in (125\(^{10}\) × 8\(^{9}\)) is:

(a) 19

(b) 28

(c) 29

(d) 30

Solution:

(125\(^{10}\) × 8\(^{9}\))

= 125(125 × 8)\(^{9}\)

= 125 × (1000)\(^{9}\)

= 125 × (10^3)\(^{9}\)

= 125 × (10)\(^{27}\)

Therefore, the required number of digits = 3 + 27 = 30

Answer: (d)

 

5. There are three consecutive positive integers. The difference of the squares of the extreme integers is 88. What is the average of three integers?

(a) 11

(b) 22

(c) 44

(d) None of these

Solution:

Of three consecutive positive integers, the difference of squares of two extreme integers = 88

Therefore, the average of three numbers = 88 ÷ 4 = 22

Answer: (b)

Note: If a, b and c are three consecutive integers, then average of the three numbers b =(c\(^{2}\) - a\(^{2}\)) ÷ 4.





Math Employment Test Samples 

From Examples on Digits and Numbers 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.



Share this page: What’s this?

Recent Articles

  1. Fundamental Geometrical Concepts | Point | Line | Properties of Lines

    Apr 18, 24 02:58 AM

    Point P
    The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.

    Read More

  2. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Apr 18, 24 02:15 AM

    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

  3. Simple Closed Curves | Types of Closed Curves | Collection of Curves

    Apr 18, 24 01:36 AM

    Closed Curves Examples
    In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

    Read More

  4. Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

    Apr 18, 24 12:31 AM

    Tangrams
    Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

    Read More

  5. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Apr 17, 24 01:32 PM

    Duration of Time
    We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

    Read More