Mathematics · Quantitative Aptitude

Algebra and Arithmetic

333 Questions

Algebra and arithmetic questions cover fundamental mathematical operations, inequalities, and binomial products. They assess core quantitative reasoning skills required for various aptitude tests. Solving these problems strengthens the understanding of number systems and algebraic identities.

Binomial productsLinear inequalitiesLeast common multipleQuadratic equationsInteger properties

Algebra and Arithmetic Questions

Multiple choice

Which of the following expressions is obtained on multiplying 39 with the difference of 20 and 6?

  1. 39 - (20 x 6)

  2. (39 x 20) - 6

  3. 39 x (6 - 20 )

  4. 39 x (20 - 6)

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since 20 > 6, the difference of 20 and 6 can be represented as (20 - 6). Accordingly, the multiplication of 39 with the difference of 20 and 6 can be represented as 39 x (20 - 6). Thus, the required expression is 39 x (20 - 6). The correct answer is option (4). 

Multiple choice

Which of the following statements is/are correct?

  1. Additive inverse of - 121/10 is greater than 10.

  2. Multiplicative inverse of 10/18 is less than 1.

  3. Sum of number and its additive inverse is 0.

  4. Product of a number and its multiplicative inverse is - 1.

  5. Both (1) and (3)

Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement (1) is correct, as additive inverse of - 121/10 is 121/10, which is greater than 10. Statement (2) is incorrect, as multiplicative inverse of 10/18 is 18/10, which is more than 1. Statement (3) is correct, as sum of a number and its additive inverse is 0. Statement (4) is incorrect, as product of a number and its multiplicative inverse is 1. Therefore, both (1) and (3) are correct.

Multiple choice

In Boolean algebra, x. 0 is equal to

  1. 0

  2. 1

  3. x

  4. y
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In Boolean algebra, the expression x · 0 (x AND 0) always equals 0. This is known as the null law or annihilator property - anything AND 0 is 0.

Multiple choice

If both ac and bc are integers, which of the following must also be an integer? I. a + c II. abc III. (a2 + b2) c2

  1. I only

  2. III only

  3. I, II and III

  4. II and III only

  5. I and III only
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Consistent with the given condition (a, b, c) can be 1/2, 1/3 and 6. So, I need not be true. Similarly, (a, b, c) can be (1/2, 1/2, 2). So, II need not be true. If ac and bc are both integers, then (ac)2 + (bc)2 must also be an integer. So, III must always be true. So, (3) is the answer.

Multiple choice

If k is a positive integer, which of the following must be an even integer?

  1. k2

  2. k(k - 1)

  3. k - 1

  4. 3k + 1

  5. 4k + 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since we have to test all the choices, Let us consider one odd value (1) for k. Then (1) = 1, (2) = 0 , (3) = 0, (4) = 4 and (5) = 7. Now let us consider one even value (2) for k. Then (1) = 4, (2) = 2, (3) = 1, (4) = 7 and (5) = 11.In both cases Choice (2) is even, is the answer.

Multiple choice

Matrices are often used to organize data for business and

  1. fortran language

  2. scientific applications

  3. binary coding

  4. none of these

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Matrices are widely used to organize data for business applications like financial modeling, inventory management, and scientific applications including physics simulations, statistical analysis, and engineering calculations. Their grid structure efficiently represents multi-dimensional data and transformations.

Multiple choice

If a and b are positive integers and (a-b)/3.5 = 4/7, then

  1. b < a

  2. b > a

  3. b = a

  4. b > = a

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given (a-b)/3.5 = 4/7 and a, b are positive integers. Cross-multiply: 7(a-b) = 4 × 3.5 = 14, so a - b = 2. Since a - b = 2 > 0, we have a > b, which means b < a. Option A is correct.

Multiple choice

Suppose a, b and c are integer variables assigned values 8, 3 and -5 respectively. In this case, the respective values of arithmetic expressions (a*c)%b and a*(c%b) are

  1. -1 & 16

  2. 1 & 16

  3. 1 & -16

  4. -1 & -16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For (a*c)%b: (8*-5) = -40, then -40%3 = -1 (C's modulo preserves the sign of the dividend). For a*(c%b): -5%3 = -2, then 8*(-2) = -16. The key is that modulo with negative numbers gives negative remainders in C.