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 maths average arithmetic mean of ap introduction to averages means

If $a _{1}=0$ and $a _{1}, a _{2}, a _{3}, ...., a _{n}$ are real numbers such that $|a _{i}|=|a _{i-1}+1|$ for all $i$ then the Arithmetic mean of the numbers $a _{1}, a _{2}, ..., a _{n}$ has value $x$ where

  1. $x<-1$
  2. $x<-\dfrac{1}{2}$
  3. $x>-\dfrac{1}{2}$
  4. $x=-\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given |a_i| = |a_{i-1} + 1| with a_1 = 0, the sequence follows a pattern where a_i values alternate or grow. Calculating the first few terms: a_1=0, a_2=-1, a_3=0, a_4=-1. The mean of these terms will oscillate around -0.5, satisfying x > -0.5.

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

If a : b = 7 : 8 and b : c = 12 : 7 then find a : c in the simplest form is 3:2

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In the given ratios "b" is

the common term, and the values of b in both ratios are not equal.





To make them equal, find the L.C.M.

of values corresponding to b i.e., $ 8 $ and $ 12 $.





L.C.M. of $ 8  $ and $ 12 = 24 $





Therefore, an equivalent ratio of $ a:b $ such that $ b = 24 $ is $= 7 \times 3:8 \times 3 = 21:24 $





Similarly, an equivalent ratio of $ b:c$ is $ = 12 \times 2 :7 \times 2 = 24:14 $





Therefore,$ a: c = 21:14 $

Dividing by $ 7 $

$ a:c = 3:2 $

Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

Product of two integers with unlike signs is

  1. Negative

  2. 0

  3. Positive

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

Let us take two integers, one with positive sign and one with negative sign that is $+2$ and $-5$ then the product of these integers with different/unlike signs is:


$(+2)\times (-5)=-(2\times 5)=-10$ which is a negative integer.

Hence, product of two integers with unlike signs is always negative.

Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

Product of two integers with like signs is

  1. Negative

  2. Positive

  3. 0

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

Let us take two integers with positive signs that is $+2$ and $+5$ then the product of these integers with same/like signs is:


$(+2)\times (+5)=2\times 5=10$ which is also a positive integer.

Now, let us take two integers with negative signs that is $-2$ and $-5$ then the product of these integers with same/like signs is:

$(-2)\times (-5)=2\times 5=10$ which is also a positive integer.


Hence, product of two integers with like signs is always positive.

Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

If the dividend and divisor have like signs then the quotient will be_____.

  1. Positive

  2. Negative

  3. Zero

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

If the dividend and divisor have same  signs then the quotient will be positive.
For eg- $\displaystyle \frac{132}{12}=11$ and $\displaystyle \frac {-132}{-12}= 11$