Olympiad Test: Algebra - Class 6 MCQ

In algebra, unknown quantities are represented by lower case letters.

Literals usually represent variables.

from the figure it is confirmed that we need 2 matchstick minium for a 'L' shape. so matchsticks will be multiple of 2. so, we need 2n matchsticks

Let the number be represented by x.

The statement "half of a number added to 10 is 15" can be translated into an equation:

x / 2 + 10 = 15

Here's the breakdown:

• "Half of a number" means dividing the number (x) by 2, which gives x / 2.
• "Added to 10" means adding 10 to x / 2.
• The phrase "is 15" represents an equality, so we set the expression equal to 15.

Thus, the final equation is:

x / 2 + 10 = 15

⇒ The length of room is l.

⇒ So, thrice the length means 3l.

∴ According to the statement given in question,

⇒ 3l = 340

6a = -144

a = -144/6

a = -24

6a = −30 ⇒ a = -30/6 = -5

6(2a-1)+8 = 14
12a-6+8 = 14
12a+2 = 14
12a = 12
a = 1

Let, Ramu's age be x years
∴ Ramu's father's age will be 3x years

Father's age is 45
∴3x = 45

⟹  x = 45/3 = 15

∴ Ramu's age is 15 years

Let the number be x
Then, x×6 + 12 = 84
⇒ 6x = 84−12 = 72
⇒x = 72/6 = 12
Hence required number is x = 12

Let the side of an equilateral triangular garden be x m.
So, 3x = 66 ⇒ x = 22m

From the figure,x^∘ + 3x^∘ = 180^∘ (straight angle) 
⇒ 4x^∘ =180^∘
⇒x^∘ = 45^∘
∴ 3x^∘ = 3×45^∘ = 135^∘

Let the breadth of the rectangle be b units. The length is twice its breadth. 

⇒ Its length = 2b units 

∴  Area = b × 2b sq units 

⇒2×b×b = 72 b × b=  72/2 ⇒b × b = 36 = 6 × 6

⇒ b = 6m

A regular hexagon has 6 equal sides. Hence perimeter = 6s units.

2n - 1 is 1 subtracted from the product of 2 and n.

Let the number of 50 paise coins be x. 
⇒ 25 paise coins = 5x
Given that total coins = 120 
⇒ x + 5x = 120 
⇒ 6x = 120 
⇒ x = 120/6 = 20 
∴ 50 paise coins = 20
⇒ Amount = 20×50 p = Rs. 10
Value of 25 paise coins = 25p × 5 × 20
= 25p × 100 = Rs. 25
Total amount Rs. (25 + 10) = Rs. 35