Algebraic Expressions Quiz

A person invests a total of $5000 across two different schemes—one offering 6% annual interest and the other 10%. After one year, the combined interest earned is $400. What is the total amount invested across both schemes?

1. $4,000
2. $5,000
3. $4,500
4. $6,000

Answer: (b) $5,000

A shopkeeper buys an article for $x and sells it at $(x + 300). He has to pay a tax of 10% on the selling price. After paying the tax, his net profit is $200. Calculate the value of x.

1. $500
2. $600
3. $700
4. $800

Answer: (c) $700

The ratio of the present ages of A and B is 4:5. Five years ago, the ratio of their ages was 3:4. Additionally, the sum of twice A's age and three times B's age exceeds the sum of their current ages by 70 years. What is the age of B?

1. 12.5 years
2. 20 years
3. 17 years
4. 25 years

Answer: (d) 25 years

A large water tank has two inlet pipes and one outlet pipe. Pipe A can fill the tank in x hours, and Pipe B can fill it in x + 5 hours. An outlet pipe, Pipe C, can empty the entire tank in 2x hours. When all three pipes are opened together, they can fill the tank in exactly 12 hours. How long it would take for Pipe A and Pipe B alone to fill the tank together.

1. 7 hours
2. 8hours 20 minutes
3. 8 hours 34 minutes
4. 9 hours

Answer: (c) 8 hours 34 minutes

A number is such that the sum of twice the number and three times its reciprocal is equal to a number that is 2 more than the difference between 10 and the number itself. What is the algebraic expression of the above given statement?

1. 3x² - 12x + 3
2. x² - 7x + 3
3. 3x²-7x + 3
4. 2x² - 3x - 7

Answer: (a) 3x² - 12x + 3

A student starts with the expression 4x − 2y. She adds another algebraic expression to it and ends up with a result that contains only one variable, x, and is equal to twice the value of x. What expression must she have added?

1. 6x + 2y
2. 2y – 2x
3. –4y
4. 4y + 2x

Answer: (b) 2y – 2x

Factorise the following algebraic expressions. x²+x/6-1/6

1. (2x+1)(3x−1)/4
2. (2x-1)(3x−1)/6
3. (2x+1)(4x−1)/6
4. (2x+1)(3x−1)/6

Answer: (d) (2x+1)(3x−1)/6

A container has red and blue marbles. The number of red marbles is twice the number of blue marbles. Each red marble is labelled with a number equal to 4 times its position (e.g., 4, 8, 12...). The total of all numbers on the red marbles equals 40. How many blue marbles are there?

1. 3
2. 2
3. 5
4. 6

Answer: (b) 2

Let A(x) = (x + 1)², B(x) = (x - 2)², and define: P(x) = A(x) + B(x) + 2x - 3 What is the type of expression represented by P(x) after simplification?

1. Trinomial
2. Binomial
3. Polynomial with 4 terms
4. Polynomial with 3 terms but not a trinomial

Answer: (b) Binomial

Three roommates agree to share the rent in the ratio 3:4:5. The total rent is a three-digit amount between $300 and $400, and it is divisible by 3, 4, and 5. What is the difference between the highest and lowest individual rent shares of maximum valid rent?

1. $60
2. $50
3. $90
4. $55

Answer: (a) $60