Mathematics · Quantitative Aptitude

Algebra and Arithmetic

406 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

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

Unsigned integer quantities are

  1. greater than ordinary integer quantities

  2. greater than ordinary integer quantities and can be negative

  3. lesser than ordinary integer quantities and cannot be negative

  4. greater than ordinary integer quantity and cannot be negative
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Unsigned integers use all bits for magnitude (no sign bit), giving them a larger positive range than signed integers of the same bit width. They cannot represent negative values, unlike signed integers.

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.

Multiple choice

The H.C.F of (x3 + x2 + x + 1) and (x4 - 1) is

  1. (x2 - 1) (x2 + 1)

  2. (x + 1) (x2 + 1)

  3. (x + 1 ) (x2 - 1)

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x3 + x2 + x + 1 = (x2 + 1) (x + 1) and x4 - 1 = (x - 1) (x + 1) (x2 + 1) H.C.F. = (x + 1) (x2 + 1)