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

The product of two negative integer is

  1. Positive integer

  2. A negative integer

  3. Either a positive integer or a negative integer

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

The product of two negative integers is always a positive integer (e.g., -2 * -3 = 6).

Multiple choice

Which of the following is true?

  1. (-8) + (-4) > (-8) - (-4)

  2. (-8) + (-4) < (-8) - (-4)

  3. (-8) + (-4) = (-8) - (-4)

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

Calculating both sides: (-8) + (-4) = -12, while (-8) - (-4) = -8 + 4 = -4. Since -12 is less than -4, the statement (-8) + (-4) < (-8) - (-4) is true.

Multiple choice

If A 1 + 1 B = B 0, then the value of A and B is

  1. A = 7 , B = 9

  2. A = 0 , B = 1

  3. A = 1 , B = 0

  4. A = 9 , B = 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(10A + 1) + (10 + B) = 10B + 0. Simplifying: 10A + B + 11 = 10B. 10A + 11 = 9B. Testing A=7: 70 + 11 = 81, so 9B = 81, B = 9. This matches.

Multiple choice

Find the correct mathematical statement

  1. ( x + 2 ) 2 = x2+4

  2. ( a2+b2)=( a + b )2

  3. 2/3x +2 = 2/3x +2

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

Option C is an identity (2/3x + 2 = 2/3x + 2). Option A is incorrect because (x+2)^2 = x^2 + 4x + 4. Option B is incorrect because a^2 + b^2 is not (a+b)^2.

Multiple choice

The value of ( a + b)2+(a -b)2 is

  1. 2a2b2

  2. 2a2 + b2

  3. 2( a2+b2)

  4. 4ab
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Expand both squares: (a^2 + 2ab + b^2) + (a^2 - 2ab + b^2). The 2ab and -2ab cancel out, leaving 2a^2 + 2b^2, which is 2(a^2 + b^2).

Multiple choice comparison of irrational numbers surds and law of surds rational and irrational numbers exponents maths

$if\,A\, = \sqrt 7  - \sqrt 6 \,and\,B = \,\sqrt 6  - \sqrt {5,} \,then\,$

  1. $A > B$
  2. $A = B$
  3. $A < B\,$
  4. $A \geqslant B$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given numbers are $A=\sqrt{7}-\sqrt{6}$ and $B=\sqrt{6}- \sqrt{5}$
Let $x =\sqrt{5}$ and $y= \sqrt{7}$ then by
$A.M$ and $G.M$
$\dfrac{x+y}{2} \le \sqrt{\dfrac{x^{2}+y^{2}}{2}}$
$\Rightarrow \dfrac{\sqrt{5}+ \sqrt{7}}{2} \le \sqrt{6}$
$\Rightarrow \sqrt{5}+ \sqrt{7} \le 2 \sqrt{6}$
$\Rightarrow \sqrt{7}- \sqrt{6} \le \sqrt{6} - \sqrt{5}$