Algebra Test

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Algebra Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

Find the equation for the following statement:

Three-fourth of a number x added to 8 becomes 20.

A
= 8 + 20

B
+ 8 = 20

C
+ 20 = 8

D
- 20 = 8

Solution

Let the number be x.
So, + 8 = 20
Hence, option (2) is correct.
Question 2
1 / -0

When Reena divides a certain number by 5 and subtracts 12 from it, she gets 38. Find the number.

A
224

B
280

C
205

D
250

Solution

Let the number be x .
According to the question,
- 12 = 38
= 38 + 12
= 50
x = 50 x 5 = 250
Hence, option (4) is correct.
Question 3
1 / -0

Find the equation for the following statement:

Twice the length (L) of a platform is 256 metres.

A
2L + 256 = 0

B
2L = 256

C
2L = 526

D
2 + L = 256

Solution

Given: L is the length of the platform.
So, as per the information given in the given statement,
2L = 256
Hence, option (2) is correct.
Question 4
1 / -0

If three times of a number is 90, then the number is

A
15

B
180

C
30

D
- 30

Solution

Let the number be x.
According to the question, 3x = 90
So, x = 30
Hence, option (3) is correct.
Question 5
1 / -0

The algebraic expression (17 + p) can be written in statement as

A
17 added to p

B
p divided by 17

C
p multiplied by 17

D
17 subtracted from p

Solution

The given Algebraic Expression is (17 + p).
It can be written as 17 added to p.
Hence, option (1) is correct.
Question 6
1 / -0

Which equation justifies the given statement?

The perimeter of a rectangle is two times the sum of its length (l) and width (w).

A
2 (l + w)

B
2l + w

C
2l + 3w

D
2 (l x w)

Solution

Given: Length = l and width = w.

From the above figure, the perimeter of the rectangle can be calculated as = l + l + w + w
= 2l + 2w = 2(l + w)
Hence, option (1) is correct.
Question 7
1 / -0

Sixteen added to 2 times a number is 32. The number is

A
22

B
18

C
12

D
8

Solution

Let the number be x.
According to the question,
2x + 16 = 32
2x = 32 - 16 = 16
2x = 16
x = = 8
Hence, option (4) is correct.
Question 8
1 / -0

The value of y in the equation 12 ( - 3 ) + 7 = 10 is

A
9

B
17

C
13

D
20

Solution

We have, 12 ( - 3 ) + 7 = 10
12 ( ) = 10 - 7
3 ( y - 12 ) = 3
y - 12 =
y - 12 = 1
y = 1 + 12 = 13
Hence, option (3) is correct.
Question 9
1 / -0

To get the value of 'x', the number to be multiplied on both sides of the equation = is

A
8

B
15

C
12

D
10

Solution

We have , =
8 × = 8 ×
x = 10
So, to get the value of 'x' we had to multiply both sides of the equation by 8.
Hence, option (1) is correct.
Question 10
1 / -0

Find the value of x in the equation given below.

3x + 1 = 2.

A

B

C

D

Solution

We have , 3 x + 1 = 2
x + =
x = -
x = = = 1
x = =
Hence, option (2) is correct.
Question 11
1 / -0

What is the highest power of a variable in a quadratic equation?

A
Zero

B
One

C
Two

D
Three

Solution

The basic form of a quadratic equation is
The highest power of a variable in a quadratic equation is two, because the degree of an equation in one variable is the exponent of the highest power to which the variable is raised in that equation.
Hence, option (3) is correct.
Question 12
1 / -0

The breadth of a rectangular brick is b cm and the length is 3 times its breadth. What is the perimeter of this brick?

A
8b cm

B
3b² cm

C
(8 + 3b) cm

D
(10 + b²) cm

Solution

We have, breadth = b cm
So, length = 3b cm
We know that the perimeter of the rectangle is 2(Length + Breadth)
So, perimeter = 2 (3b + b) = 2 × 4b = 8b cm
Hence, option (1) is correct.
Question 13
1 / -0

The number of students in a school is 4 times the number of its staff. Which of the following cannot be the total number of people in the school?

(Given, total number of people = Total number of students + Total number of staff)

A
20

B
21

C
30

D
40

Solution

Let the number of staff be x.
Therefore, number of students = 4x
If x + 4x = 21
5x = 21
x = = 4.2
As we are talking about number of people, it cannot be in decimals. So, 21 cannot be the total number of people.
Hence, option (2) is correct.
Question 14
1 / -0

The algebraic expression for the statement 'the number x is divided by p, added with the product of z and reciprocal of d' is

A

B

C
+

D
pd + zx

Solution

According to the information given in the question,
The number x is divided by p which means and
The product of z and reciprocal of d, is ( )
So, we get
+
Hence, option (3) is correct.
Question 15
1 / -0

The algebraic expression for the statement, twice of y is subtracted to z divided by itself, is

A
y - z

B
2y - 1

C
3y - z

D
2z - y

Solution

Twice of y can be written as 2y and z divided by itself can be written as
So, z divided by itself is subtracted from twice of y
2 (y) - z x () = 2y - 1
Hence, option (2) is correct.
Question 16
1 / -0

If y = z, then z + y =

A
2z - 2y

B
y + 2z

C
z - y

D
2z

Solution

Given: z = y ........ (1)
So, z + y = z + z = 2z
Hence, option (4) is correct.
Question 17
1 / -0

Which of the following equations has y = - 8 as solution?

A
3y + 2 = 0

B
y + 3 = 2

C
y + 8 = 0

D
2y + 3 = 8

Solution

Statement (1) Putting y = -8 in 3y + 2, we get 3 x -8 + 2 = -24 + 2 = -22 ≠ 0
Statement (2) Putting y = -8 in y + 3, we get -8 + 3 = -5 ≠ 2
Statement (3) Putting y = -8 in y + 8, we get -8 + 8 =0
Statement (4) Putting y = -8 in 2y + 3, we get 2 x -8 + 3 = -16 + 3 = -13 ≠ 8
Thus, the above conditions show that y = -8 is the solution of y + 8 = 0.
Hence, option (3) is correct.
Question 18
1 / -0

Which of the following equations has the same solution as the equation 3y - 6 = 0?

A
y - 2 = 0

B
3y + 6 = 0

C
y + 2 = 0

D
y + 3 = 0

Solution

The solution for the given equation 3y - 6 = 0 is y = 2.
Statement (1), y - 2 = 0, so y = 2
Statement (2), 3y + 6 = 0, so y = -2
Statement (3), y + 2 = 0, so y = -2
Statement (4), y + 3 = 0, so y = -3
So, we can say that only statement (1) has the same solution as the given equation.
Hence, option (1) is correct.
Question 19
1 / -0

Ify - 5 = 15, then the value of y is

A
30

B
40

C
50

D
80

Solution

We have, y - 5 = 15
y = 15 + 5
y = 20
y = = 30
Hence, option (1) is correct.
Question 20
1 / -0

The method of finding the values of variables in a cubic equation by trying out various values for the variable is called

A
error method

B
testing method

C
trial and error method

D
checking method

Solution

The basic form of a cubic equation is
The method of finding the values of variables in a cubic equation is called trial and error method.
Hence, option (3) is correct.
Question 21
1 / -0

If Karun has Rs. 900 with him and he gives Rs. to Tina, Rs. to Rahul and keeps Rs. with himself, then how much money is left with him?

A
Rs. 380

B
Rs. 310

C
Rs. 240

D
Rs. 200

Solution

Now According to the Question

+ + = 900 ............. (1)

As the denominators are different we are going to make them same

9x = 10800
x = 1200
Therefore,
Money left with Karun can be calculated as

= = 200
Karun is left with Rs. 200.
Hence, option (4) is correct.
Question 22
1 / -0

Arjun stated from his home and travelled 11x km by bike, then took an auto and covered 5y km and at the end he walked 3 km to reach his office. Find the total distance travelled by him.

A
[16x + 3] km

B
[11x - 5y + 3] km

C
[11x + 5y + 3] km

D
19x km

Solution

Travelled 11x km by bike
Travelled 5y km by auto and walked 3 km
So, total distance = [11x + 5y + 3] km
Hence, option (3) is correct.

Question 23
1 / -0

While playing cricket Kapil scored 11 runs less than Rahul who scored 2x. Find the runs scored by both.

A
2x - 11

B
4x - 11

C
6x + 5

D
11x - 2

Solution

Runs scored by Rahul = 2x
Kapil scored 11 runs less than Rahul
Therefore,
2x - 11
Total runs scored = 2x + 2x - 11 = 4x - 11
Hence, option (2) is correct.

Question 24
1 / -0

In a cricket match, a batsman scored most of his runs in boundaries.
X = Number of fours hit by him
Each four is 4 runs
If he scored 18 runs running, then which operation shows the number of runs scored by him?

A
2X + 4

B
4X + 18

C
14X + 8

D
22X

Solution

Number of fours hit by batsman = X
One four is equal to 4 runs
Therefore, X number of fours = 4 X runs
And he scored 18 runs running
Total number of runs = 4 X + 18
= 4X + 18
Hence, option (2) is correct.

Question 25
1 / -0

Anil went to the market with Rs. X and bought fruits with three-quarters of the money, then he bought vegetables worth Rs. 30. Find the total money spent by Anil.

A
- 20

B
+ 30

C
- 30

D
+ 30

Solution

Total amount of money Anil had = Rs. X.
He bought fruits with of X
Then he bought vegetable worth Rs. 30
So, total amount of money he spent = + 30
Hence, option (4) is correct.

Question 26
1 / -0

Arun went outside four times in the last four days and covered a total of 50 km in four days. If the distance he covered on first day was x km, on the second day it was 2 km more than the first day and on third day it was 4 km more than the first day but on the fourth day he covered 3 km less than that on first day. Which of the following expressions can be used to find how much distance he covered on first day?

A
x + (x + 2) + (x + 4) - 3 = 50 km

B
x + (x + 2) + (x + 4) + (x - 3) = 50 km

C
x + (x + 2) + (x + 4) + 3 = 50 km

D
x + (x + 2) - (x + 4) + 3 = 50 km

Solution

Total distance covered = 50 km
Distance covered on first day = x km
Distance covered on second day = (x + 2 )km
Distance covered on third day = (x + 4 )km
Distance covered on fourth day = (x - 3 )km
Therefore
x + (x + 2) + (x + 4) + (x - 3) = 50 km
Hence Option (2) is correct option.

Question 27
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Fill in the blanks.

(i) 14 less than 4 times the number x can be written in algebraic form as ___P___.
(ii) In the above algebraic equation, x is a ____Q___
(iii) 13 more than double of x can be written as ____R______

Options P Q R

A 14x + 4 constant 2x = 13

B 4x + 14 constant 13x + 2

C 4x - 14 variable 2x + 13

D 4x + 14 constant 2x +13

A
B

B
D

C
C

D
A

Solution

(i) 14 less than 4 times x = 4x - 14
(ii) Variable as the value of x can change
(iii) 13 more than double of x = 2x + 13
Hence, option (3) is correct.

Question 28
1 / -0

Which of the following equations has a solution in integers?

A
2x - 1 = 23

B
5x + 1 = 35

C
6x + 12 = 58

D
7x - 4 = 21

Solution

(i) 2x - 1 = 23

Add 1 to both sides 2x - 1 + 1 = 23 + 1
2x = 24
x = = 12 which is an integers
(ii) 5x + 1 = 35

Subtract 1 from both sides
5x + 1 - 1 = 35 - 1
5x = 34
x = not an integer

(iii) 6x + 12 = 58

Subtract 12 from sides
6x + 12 - 12 = 58 - 12
6x = 46
x = not an integer

(iv) 7x - 4 = 21

Add 4 both sides
7x - 4 + 4 = 21 + 4
7x = 25
x = not an integer
Hence, option (1) is correct.

Question 29
1 / -0

State T for true and F for false.

(P) x = 1 is the solution of this equation 3x + 8 = 44
(Q) A Variable is a symbol for a number we don't know yet
(R) x is 8 more than twice of y can be written as x = 8y + 7

Options P Q R

A F T F

B T F T

C F F F

D T T F

A
A

B
B

C
C

D
D

Solution

(P) 3x + 8 = 44
Now, L.H.S of equation will be
3x + 8 = 3(1) + 8 = 3 + 8 = 11
R.H.S of equation = 44
Since 11 is not equal to 44, x = 1 is not a solution for this equation.

(Q) A variable is a symbol for a number we don't know yet is True.

(R) x is 8 more than twice of y can be written as x = 2y + 8
Hence, option (1) is correct.

Question 30
1 / -0

Match the following:

Column 1 Column 2

(a) The total age of three family members is 34. The age of first and second member is x and 2x respectively. The age of third member is (i)

(b) Aman had x candies, he gave 4 to his younger sister and half the number of candies that he gave to his younger sister, he gave to his brother. How many are left with him? (ii) 34 - 3x

(c) Ranjan had x number of mangoes, he gave all of that to his four brothers. How many each brother got? (iii) x - 6

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

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

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

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

Solution

Let the age of third member in statement (a) be p.
According to statement (a)
x + 2x + p = 34
p = 34 -3x

Let the number of candies Aman left with be p.
According to statement (b)
4 + 2 + p = x
p = x - 6

(c) four brother
total mangoes = x
Each brother's share =
Hence, Option (1) is correct.

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Re-Attempt Solution Weekly Quiz Competition

Options	P	Q	R
A	14x + 4	constant	2x = 13
B	4x + 14	constant	13x + 2
C	4x - 14	variable	2x + 13
D	4x + 14	constant	2x +13

Column 1	Column 2
(a) The total age of three family members is 34. The age of first and second member is x and 2x respectively. The age of third member is	(i)
(b) Aman had x candies, he gave 4 to his younger sister and half the number of candies that he gave to his younger sister, he gave to his brother. How many are left with him?	(ii) 34 - 3x
(c) Ranjan had x number of mangoes, he gave all of that to his four brothers. How many each brother got?	(iii) x - 6

Algebra Test - 11

Result

Algebra Test - 11

Score

-

Rank

-

SHARING IS CARING

Question 1

= 8 + 20

+ 8 = 20

+ 20 = 8

- 20 = 8

Solution

Question 2

224

280

205

250

Solution

Question 3

2L + 256 = 0

2L = 256

2L = 526

2 + L = 256

Solution

Question 4

15

180

30

- 30

Solution

Question 5

17 added to p

p divided by 17

p multiplied by 17

17 subtracted from p

Solution

Question 6

2 (l + w)

2l + w

2l + 3w

2 (l x w)

Solution

Question 7

22

18

12

8

Solution

Question 8

9

17

13

20

Solution

Question 9

8

15

12

10

Solution

Question 10

Solution

Question 11

Zero

One

Two

Three

Solution

Question 12

8b cm

3b² cm

(8 + 3b) cm

(10 + b²) cm

Solution

Question 13

20

21

30