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This mock test of Olympiad Test : Algebra - 2 for Class 6 helps you for every Class 6 entrance exam.
This contains 20 Multiple Choice Questions for Class 6 Olympiad Test : Algebra - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

What is the value of x? 3(x + 6) + 2 (x + 3) = 64

Solution:

3(x + 6) + 2(x + ) = 64

⇒ 3x + 18 + 2x + 6 =64

⇒ 5x + 24 = 64

⇒ 5x = 64 - 24

⇒ 5x = 40

QUESTION: 2

What is the value of P if 3(2 – 5P) – 2 (1 – 6P) = 1?

Solution:

Here, 3(2 – 5p) –2 (1 – 6p) = 1

⇒ 6 - 15p - 2 + 12p =1

⇒ 4 - 3p = 1 ⇒ 3p = 4 -1

QUESTION: 3

If 8 is subtracted from three times a number the result is 13. What is number?

Solution:

Let the number be x.

∴ 3x - 8 = 13 ⇒ 3x = 13 + 8

⇒ 3x = 21

QUESTION: 4

The sum of three consecutive natural numbers is 114. Which is the greatest number?

Solution:

Let the number are x, x + 1, x+ 2.

∴ x + x 1 + x + 2 = 114

⇒ 3x +3 = 114 ⇒ 3x = 114 - 3

Greatest number = 37 + 2 = 39

QUESTION: 5

The length of a rectangular field is 5m more than its breadth. If the perimeter of the field is 74 m what is its length?

Solution:

Let the breadth be x m.

Length = (x + 5)

Perimeter of rectangle = 74

⇒ 2(x + 5 + x) = 74

⇒ 2x + 5 = 37 ⇒ 2x = 37 - 5

⇒ 2x = 32

Length = 16 + 5 = 21m

QUESTION: 6

If 9 is added to twice of a certain number, the result is 57, what is that number?

Solution:

Let the number be x.

2x + 9 = 57 ⇒ 2x = 57– 9 = 48

x = 24

QUESTION: 7

If 7 is subtracted from a number, we get 37, then what is that number?

Solution:

Let the number be x.

∴ x - 7 = 37 ⇒ x = 37 + 7 = 44

QUESTION: 8

A man is thrice as old as his daughter. 5 years ago the man was four times as old as his daughter, what is the age of the daughter?

Solution:

Let the age of daughter be x years.

∴ Man's age = 3x.

and 5 years ago, daughter's age = x-5

∴ Man's age = 3x —5

⇒ 3x —5= 4x —20 = 4x —3x = — 5 + 20

⇒ x =15 years

QUESTION: 9

Karan’s father is thrice as old as Karan. After 14 years his age will be twice that of his son. What is the age of Karan?

Solution:

Let the age of karan be x years.

Father’s age = 3x years

After 14 years,

3x +14 = 2(x –14)

⇒ 3x + 14 = 2x + 28

⇒ x = 28 - 14

⇒ x = 14 years

QUESTION: 10

The sum of three consecutive even numbers is 78. Which number is smallest among them?

Solution:

Let the three consecutive even numbers are

x, x + 2, x + 4.

∴ x + x + 2 + x + 4 =78

⇒ 3x = 78 - 6

⇒ 3x = 72

QUESTION: 11

Five times the price of a radio is Rs 170 more than three times its price. What is the price of the radio?

Solution:

Let the price of the ratio be Rs x.

5x =170 + 3x

⇒ 2x =170

QUESTION: 12

The length of a rectangular park is thrice its breadth. If the perimeter of the park is 168m, what is its breadth?

Solution:

Let the breadth be x m

Length = 3xm

Perimeter of rectangular park = 168

QUESTION: 13

Kiran multiplies a certain number by 17 and adds 4 to the product, she gets 225. What is that number?

Solution:

Let the number be x.

∴ x × 17 + 4 = 225

⇒ 17x = 225 - 4

⇒ 17x = 221

QUESTION: 14

What is the sum of the expressions 3a – 2b + 5c, 2a + 5b – 7c and –a – b + c?

Solution:

Required result

= 3a –2b + 5c + 2a +5b –7c – a – b + c

= 4a + 2b – c

QUESTION: 15

What is the co-efficient of x^{3} in 4y^{2}zx^{3}?

Solution:

QUESTION: 16

What is the value of 2a – [3b –{a – (2c – 3b) + 4c – 3 (a – b – 2c)}]

Solution:

Required result

= 2a–[3b–{a – (2c + 3b) + 4c –3a + 3b + 6c}]

= 2a –[3b–{–2a +6b +8c}]

= 2a –[3b +2a – 6b – 8c]

= 2a –[2a–3b–8c] = 2a –2a + 3b +8c

= 3b + 8c

QUESTION: 17

What is the value of xy – [yz – zx –{yx – (3y – xz) – (xy – zy)}]?

Solution:

xy – [ yz – zx – {yx – (3y – xz) – (xy – zy)}]

= xy – [ yz – zx – {yx – 3y + xz– xy + zy}]

= xy – [ yz – zx – yx + 3y – xz + xy – zy]

= xy + 2xz –3y

QUESTION: 18

What is the value of x?

Solution:

QUESTION: 19

If a number is tripled and the result is increased by 7, we get 70, then what is the number?

Solution:

Let the number be x.

∴ 3 × x + 7 = 70

⇒ 3x = 70 - 7

⇒ 3x = 63

QUESTION: 20

A wire of length 86cm is bent in the form of a rectangle such that its length is 7 cm more than its breadth. What is its length ?

Solution:

Let the breadth be x.

∴ Length = x + 7

Perimeter of wire = 86

∴ Length = x + 7 = 18 + 7 = 25 cm

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