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The number consists of two digits. If the digits interchange places and the new number is added to the original number. The resulting number will be divisible by______.

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Important Questions on Number Systems

HARD

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

3

chairs and

2

tables cost

R s . 700

and

5

chairs and

3

tables cost

R s . 1100

. What is the cost of

1

chair and

2

tables?

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

Find the value of

x

after solving the following equation.

0.12 \times (5 x - 4) = 0.5 x + 0.8

HARD

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The sum of the digits of a two-digit number is

10

. When the digits are reversed, the number decreases by

54

. Find the changed number:

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

x, y, z

are three integers such that

x + y = 8

y + z = 13

and

z + x = 17

, then the value of

\frac{x^{2}}{y z}

is:

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

A zoo has few number of penguins and polar bears. The total number of heads of both of them is

60

and total number of their feet is

160

. How many polar bears are there in the zoo.

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

4

5^{t h s}

of an estate is worth Rs. 16800, then the value of

3

7^{t h s}

of the estate is

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

Find the value/values of x for the given equation.

$2^{(2 x + 3)} - 17 = 9 (2^{x} - 2)$

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The graph of the equation

3 x + y - 5 = 0 and 2 x - y - 5 = 0

intersect at the point

P (α, β)

. What is the value of

(3 α + β)

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The population of Patna city is $96000$ , the decreasing rate of population is $800$ per year. Population of Patliputra is $68000$ , the increasing rate of population is $1200$ per year. In how many years will the population of both places be equal?

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

Find the number of solutions of a pair of linear equation

4 x - 9 y + 13 = 0

and

2 x + 3 y - 13 = 0

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The graph of the equation

5 x - 2 y + 1 = 0

and

4 y - 3 x + 5 = 0,

intersect at the point

P (α, β)

. What is the value of

(2 α - 3 β)

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

P and Q are two examination halls. If

10

examinees are sent from P into Q, the number of examinees becomes equal in both the halls. If

20

examinees are transferred from Q into P, the number of examinees becomes double in P in comparison with Q. What is the number of examinees in each P and Q separately ?

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The point of the intersection of the graph of the equations

3 x - 5 y = 19

and

3 y - 7 x + 1 = 0

P (α, β)

. What is the value of

(3 α - β)

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

A number exceeds its

\frac{1}{9}

64

. What is the number?

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

The graph of the equations

2 x + 3 y = 11

and

x - 2 y + 12 = 0

intersects at

P (x_{1}, y_{1})

and the graph of the equation

x - 2 y + 12 = 0

intersects the

x -

axis at

Q (x_{2}, y_{2})

. What is the value of

(x_{1} - x_{2} + y_{1} + y_{2})

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

For what value of $p,$ the following pair of linear equations in two variables will have infinitely many solutions?

$p x + 3 y - (p - 3) = 0 12 x + p y - p = 0$

EASY

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

X and Y

together have

₹ 1300

. If

₹ 10

less than three-fifth of the amount

X

is equal to half of the amount

Y

, then how much does

X

have?

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

How many solutions will a pair of linear equations have, if the equations are

4 x + 5 y - 6 = 0

and

16 x + 20 y + 20 = 0

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

x

and

y

are positive integers and

\frac{3 x}{y} = 4,

then find the minimum value of

(3 x + 4 y)

MEDIUM

Numerical and Mental Ability>Arithmetic>Number Systems>Basics of Number Systems

A number of two digits is equal to '

k

' times to the sum of these digits. If the places of these digits are mutually exchanged. the newly formed number is equal to the sum of these digits multiplied by which one of the following options ?

The number consists of two digits. If the digits interchange places and the new number is added to the original number. The resulting number will be divisible by______.

Important Questions on Number Systems

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