Nowadays, with cut-throat competition, scoring well in competitive exams like **GMAT****, SAT exam, SSC CGL**, etc has become difficult. And with a number of sections evaluating a candidate’s knowledge on various parameters, it has become essential to practice all the topics in-depth in order to smoothly sail through the admission process of **top universities in the world**. Just like scores of other exams, the quantitative section of GMAT is highly important and the trickiest of all. Out of all the topics, Algebra questions also form an integral component of this section. So, if you are preparing for GMAT, then here are some of the questions for you to practice.

## Basic Algebra Identities

- (a + b)
^{2}= a^{2}+ b^{2}+ 2ab - (a – b)
^{2}= a^{2}+ b^{2}– 2ab - a
^{2}– b^{2}= (a + b)(a – b) - a
^{2}+ b^{2}= (a + b)^{2}– 2ab = (a – b)^{2}+ 2ab - a
^{3}+ b^{3}= (a + b)(a^{2}– ab + b^{2}) - a
^{3}– b^{3}= (a – b)(a^{2}+ ab + b^{2}) - (a + b)
^{3}= a^{3}+ 3ab(a + b) + b^{3} - (a – b)
^{3}= a^{3}– 3ab(a – b) – b^{3}

## Algebra Questions for Class 6

Students will be introduced to an algebra subject in class 6. You will learn how to represent unknown values in terms of variables in this section. Only if we know the value of the unknown variable can we solve the given expression. Let us look at some questions.

Give expressions for the following cases.

(a) 71 added to m

(b) 99 subtracted from m

(c) n multiplied by 8

(d) p divided by 10

**Question 2**

Which out of the following are expressions with both variables and numbers only?

(a) p−9p−9

(b) (11×20)−8x(11×20)−8x

(c) 5(21−7)+7×2+p5(21−7)+7×2+p

(d) 11

(e) 11x−111x−1 (f) 5+4+3+2+15+4+3+2+1

(g) (7×8)−(8×7)−45+11x(7×8)−(8×7)−45+11x

(i) 2z−112z−11

**Question 3**

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

(i) Subtraction of z from y.

(ii) One-half of the sum of numbers a and b.

(iii) The number y multiplied by itself.

(iv) One-Eight of the product of numbers x and y.

(v) Numbers p, q and r both squared and added.

(vi) Number 5 is added to three times the product of numbers m and n.

(vii) Product of numbers y and z subtracted from 10.

(viii)Sum of numbers x and y subtracted from their product.

**Question 4**: Six less than a number equals to two. What is the number?

Solution:

Let the number be ‘x’.

According to condition, we have x – 6 = 2

By inspections, we have 8 – 6 = 2

∴ x = 8

Thus, the required number is 8.

**Question 5**: Write an algebraic expression for the following expressions:

(a) The sum of a number x and 4 is doubled.

(b) One-fourth of a number x is added to one-third of the same number.

Solution:

(a) The required expression is 2 x (x + 4)

(b) The required expression is 14x + 13x

**Apart from the Algebra questions, here are some** **Time and Work Tricks** **for GMAT!**

## Algebra Problems for Class 7

Q. Group the like terms together from the following expressions:

-8x^{2}y, 3x, 4y, −32x , 2x^{2}y, -y

Solution:

Group of like terms are:

(i) -8x^{2}y, 2x^{2}y

(ii) 3x, −32x

(iii) 4y, -y

Q. Identify the pairs of like and unlike terms:

(i) −32x, y

(ii) -x, 3x

(iii) −12y2x, 32xy^{2}

(iv) 1000, -2

Solution:

(i) −32x, y → Unlike Terms

(ii) -x, 3x → Like Terms

(iii) −12y2x, 32xy^{2} → Like Terms

(iv) 1000, -2 → Like Terms

Q. Classify the following into monomials, binomial and trinomials.

(i) -6

(ii) -5 + x

(iii) 32x – y

(iv) 6x^{2} + 5x – 3

(v) z^{2} + 2

Solution:

(i) -6 is monomial

(ii) -5 + x is binomial

(iii) 32x – y is binomial

(iv) 6x^{2} + 5x – 3 is trinomial

(v) z^{2} + z is binomial

**Now that you have practiced some Algebra questions, check out Sequence and Series questions for GMAT!**

## Algebra Word Problems

### How Do We Solve Algebraic Word Problems?

Solving algebraic word problems necessitates combining our capacity to create and solve equations.

To solve an algebraic word problem, do the following:

- Define a variable.
- Write an equation with the variable.
- Solve the equation.

Use the variable to calculate the solution if it is not the answer to the word problem.

It’s critical that we remember how we define our variables. The complexity of what a variable signifies and the complexity of the equation is frequently trade-offs.

### Practice Questions

- A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost?
- Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give?
- There are 12 packets of chips in a big pack. I buy big packs of crisps. How many packets of chips have I bought?
- Think of a number. Double the number. Subtract 6 from the result and divide the answer by 2. The quotient will be 20. What is the number?

## Algebra Questions: Worksheet

- a, b, c are positive numbers. If
**b^2+ c^2= 117**, then what will be the value of**a^2 + c^2**?

- There are 22 students in a dance class. All the students either have a sibling or a pet. If 14 students have a pet and 18 students have siblings. How many students have both a sibling and a pet?

- At a ration shop, whole wheat bread costs Rs. 2.50 per pound on a minimum purchase of 20 pounds. If Rohit paid Rs. 80 for some whole wheat bread, how many pounds did Rohit by extra?

- Rohan’s teacher asked him to divide a number by 6 and then add 12 to the quotient. But by mistake, Rohan first added 12 and then divided the number by 6. The answer he got was 112. Find out the correct answer.

- Mr. Kapoor had to pay off a debt of Rs. 3600. He decides to pay it in 40 instalments which are in the Arithmetic Progression. He suddenly dies after paying the 30th instalment and leaves behind 1/3rd of the debt unpaid. What is the value of the 8th instalment?

**And you have finally completed all the Algebra questions! Now have a look Mean Median Mode questions to boost your preparation. **

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