Algebra Test

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Algebra Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following equations describes the statement given below?

'Quarter of a number added to 20 is 40.'

A
+ 20 = 40

B
+ 60 = 20

C
= 40 + 20

D
+ 40 = 20

Solution

Let the number be X.
So, + 20 = 40
Question 2
1 / -0

Sham is thinking of a number and multiplies the same number by 14. When the product is added to 15, it gives the value 141. What is the number that Sham is thinking of?

A
11

B
9

C
8

D
6

Solution

Let Sham be thinking of x.
According to the question:
14x + 15 = 141
14x = 141 - 15
14x = 126
x = = 9
Question 3
1 / -0

Which of the following equations describes the statement given below?

'Twice the height (h) of a wooden box is equal to 48 inches.'

A
3h = 48

B
2h = 48

C
2h = 84

D
48h = 2

Solution

Let the height of the wooden box be 'h'.
So, 2h = 48
Question 4
1 / -0

Soham's bucket can hold 105 litres of water, which is five times as much as Mohan's bucket can hold. How much can Mohan's bucket hold?

A
11 litres

B
16 litres

C
21 litres

D
27 litres

Solution

Let Mohan's bucket can hold x litres of water.
Capacity of Soham's bucket = 5x = 105
So, x =
So, Mohan's bucket can hold (x) = 21 litres of water.
Question 5
1 / -0

How to write the algebraic expression '2x - 3y' as a statement?

A
Twice of x is more than twice of y.

B
Thrice of x is less than twice of y.

C
Twice of x is less than thrice of y.

D
Twice of x is less than equal to thrice of y.

Solution

'2x - 3y' - Twice of x is less than thrice of y.
Question 6
1 / -0

Choose the correct option that justifies the statement given below:

''The perimeter of a square is four times its side 'a'.''

A
a x a x a x a

B
4 x 4 x 4 x 4

C
4 x a

D
4 + a

Solution

As we know, all the sides of a square are equal. So, the perimeter of a square is 4 x side.
Here, side = 'a'
So, the perimeter would be 4 x a.
Question 7
1 / -0

If 36 more than twice a number is 84, find the number.

A
21

B
24

C
28

D
33

Solution

Let the number be p.
So, 2p + 36 = 84
2p = 84 - 36
2p = 48
p =
p = 24
Question 8
1 / -0

Find the value of m in the equation given below:

21{ - 4} - 16 = 5

A
70

B
60

C
40

D
30

Solution

21{ - 4} - 16 = 5
21{} = 21
21m - 672 = 21 x 8
21m - 672 = 168
21m = 168 + 672
21m = 840
m =
m = 40
Question 9
1 / -0

A linear equation is one in which highest power of any variable in an equation must be less than or equal to

A
0

B
1

C
2

D
3

Solution

The highest power of variable in linear equation is 1.
Question 10
1 / -0

In an isosceles triangle, AB = BC. The length of side BC is x cm. The length of side AC is thrice the length of AB. What is the perimeter of the triangle?

A
2x

B
3x

C
4x

D
5x

Solution

Let the length of side AB be x cm.
Length of side BC = x cm
Length of side AC = 3x cm
Perimeter = x + x+ 3x = 5x
Question 11
1 / -0

The number of females in a company is 7 times the number of males. Which of the following cannot be the total number of employees in the company?

A
80

B
81

C
88

D
96

Solution

Let the number of males be x.
Number of females = 7x
If x + 7x = 81
8x = 81
x =
And we know that the number of employees can't be in fraction.
Question 12
1 / -0

The algebraic expression of the statement 'The reciprocal of the difference between the product of x and y, and the product of a and b' is

A
xy - ab

B

C

D

Solution

Product of x and y = xy
Product of a and b = ab

Difference between products = xy - ab

Reciprocal:
Question 13
1 / -0

The algebraic expression of the statement 'Twice of y is subtracted from y cubed' is

A
2y³ - y

B
2y - y³

C
y³ - 2y

D
2(y - y³)

Solution

Twice of y = 2y
y cubed = y³
According to the question:
y³ - 2y
Question 14
1 / -0

If x = , then xa equals

A

B

C

D

Solution

x =

As 'a' has been multiplied on LHS, the same will be multiplied on RHS as well.
So, xa =
Question 15
1 / -0

Which of the following equations has x = 7 as its solution?

A
2x - 14 = 0

B
x + 7 = 0

C
2x - 7 = 0

D
2x + 7 = 0

Solution

2x - 14 = 0
2x = 14
x =
x = 7
Question 16
1 / -0

The equations ______ and 3x - 6 = 0 have same solution.

A
x - 2 = 0

B
x + 2 = 0

C
2x - 2 = 0

D
2x + 2 = 0

Solution

Value of x in the given equation:
3x - 6 = 0
3x = 6
x = = 2

Same is the value of x - 2.
x - 2 = 0
x = 2

So, x - 2 = 0 is the correct answer.
Question 17
1 / -0

If , then the value of x is

A

B

C

D

Solution

x =
x =
Question 18
1 / -0

A ________is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

A
polynomial

B
linear equation

C
variable

D
substitution

Solution

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Question 19
1 / -0

Reema has Rs. 400. She gives Rs. to Rehana and Rs. to Nikki. She is left with . What is the approximate amount of money given to Nikki?

A
Rs. 102.05

B
Rs. 105.26

C
Rs. 108.62

D
Rs. 109.65

Solution

+ + = 400

=400

=>19Y= 8000
=> Y= 421.05

money given to Nikki=
=> = 105.26
Question 20
1 / -0

If a traveller travels x km in total and travels 3y km by car, 7z km on foot and the rest by bus, then which of the following represents the distance covered by bus?

A
x - y - z

B
x - 7y - 3z

C
x + 3y + 7z

D
x - 3y - 7z

Solution

According to the question:
The traveler travels x km in total, and travels 3y km by car, 7z km on foot and the rest by bus.
So, distance covered by bus =Total - Traveled by car - Traveled on foot
= x - 3y - 7z
Question 21
1 / -0

Gursimran weighs 76 kg. Balkaran weighs 'Z' kg less than him. What is their total weight?

A
152 + Z

B
76 + Z

C
152 - Z

D
76 - Z

Solution

Gursimran's weight = 76 kg
Balkaran's weight = (76 - Z) kg
Total weight = 76 + (76 - Z)
= 152 - Z
Question 22
1 / -0

Lovepreet has some packets of chocolates containing 25 chocolates each. Out of them, he gives 9 packets to Konark.
Which of the following expressions shows the number of chocolates left with Lovepreet?
Y = Number of packets of chocolates

A
25Y = 220

B
25Y x 9 = 225

C
25Y + 225

D
25Y - 225

Solution

Number of chocolates in a packet = 25
Number of chocolates in Y packets = 25Y
Number of chocolates left = 25Y - 25 x 9
= 25Y - 225
Question 23
1 / -0

A turtle covers 18 km more than one quarter of the distance covered by a rabbit. How much distance is covered by the turtle?

A

B

C

D
None of these

Solution

Suppose, distance covered by the rabbit = K
According to the question:
Question 24
1 / -0

Livie got 45 all types of sweets. The number of chocolates and candies with Livie are 8 less and 4 more than the number of toffees, respectively. If the number of toffees is 'R', then what sentence can be used to represent the total sweets with Livie?

A
45 = R - (R - 8 ) - (R + 4)

B
45 = R + (R - 8 ) + (R + 4)

C
45 = R - (R + 8 ) + (R + -4)

D
45 = R + (R + 8 ) - (R -4)

Solution

Number of toffees= R
Number of chocoaltes= R - 8
Number of candies= R + 4
Total number of sweets (45) = R + R - 8 + R + 4
= > 45 = R + (R - 8 ) + (R + 4) is the correct answer.

Question 25

1 / -0

Fill in the blanks.

(I) Something with a fixed value is called _____J_____.
(ii) 9 less than thrice of 'F' will be ____K_____.
(iii) A concept that shows correlation is called _____L_____.

J	K	L
a. ratio	3F + 9	constant
b. constant	3F - 9	ratio
c. ratio	3F - 9	constant
d. constant	3F + 9	ratio

a

b

c

d

Solution

(i) Something with a fixed value is called constant.
(ii) 9 less than thrice of 'F' will be 3F - 9.
(iii) A concept that shows correlation is called ratio.

Question 26
1 / -0

Which of the following equations will give an integer?

A
2p + 3 = 8

B
P + 9 = 12

C
3p - 2 = 5

D
4p = 15

Solution

(i) 2p + 3 = 8
=> p =
(ii) p + 9 = 12
=> p = 3

(iii) 3p - 2 = 5
=> p =
(iv) 4p = 15
=> p =
So, only option (2) gives a whole number or a positive integer.

Question 27

1 / -0

State true (T) or false (F).

(J) Comparative relation between things or magnitudes as to size, quantity, number, etc is called ratio.
(K) Z = 21 is the solution of equation 75 - Z = 54.
(L) Something with a fixed value is called variable.

J	K	L
a. F	F	F
b. T	T	F
c. T	F	T
d. F	T	T

a

b

c

d

Solution

J) Comparative relation between things or magnitudes as to size, quantity, number, etc is called ratio.
(K) Z= 21 is the solution of equation 75 - Z = 54.
=> Putting value;
75 - 21= 54
(L) Something with a fixed value is not called variable; it is called constant.

Question 28

1 / -0

Match the following:

A	B
(i)The value of 'y' is 21 more than four times the value of x.	(a) K + 9
(ii) Emma has Rs. G, which she distributes among her 4 friends fairly. The amount of money with each friend is ______.	(b) y = 21 + 4x
(iii) Neha has 'K' chocolates. Her sister gives her 9 more. How many chocolates does she have now?	(c)

(i) - (c), (ii) - (b), (iii) - (a)

(i) - (c), (ii) - (a), (iii) - (b)

(i) - (a), (ii) - (b), (iii) - (c)

(i) - (b), (ii) - (c), (iii) - (a)

Solution

(i) The value of 'y' is 21 more than four times the value of x.
=> y = 21 + 4x
(ii) Emma has Rs. G, which she distributes among her 4 friends fairly. The amount of money with each friend is .
(iii) Neha has 'K' chocolates. Her sister givesher 9 more. How many chocolates does she have now?
=> K + 9

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Algebra Test - 10

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Algebra Test - 10

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SHARING IS CARING

Question 1

+ 20 = 40

+ 60 = 20

= 40 + 20

+ 40 = 20

Solution

Question 2

11

9

8

6

Solution

Question 3

3h = 48

2h = 48

2h = 84

48h = 2

Solution

Question 4

11 litres

16 litres

21 litres

27 litres

Solution

Question 5

Twice of x is more than twice of y.

Thrice of x is less than twice of y.

Twice of x is less than thrice of y.

Twice of x is less than equal to thrice of y.

Solution

Question 6

a x a x a x a

4 x 4 x 4 x 4

4 x a

4 + a

Solution

Question 7

21

24

28

33

Solution

Question 8

70

60

40

30

Solution

Question 9

0

1

2

3

Solution

Question 10

2x

3x

4x

5x

Solution

Question 11

80

81

88

96

Solution

Question 12

xy - ab

Solution

Question 13

2y3 - y

2y - y3

2y³ - y

2y - y³

y³ - 2y

2(y - y³)