Mathematics · Quantitative Aptitude

Number Operations and Properties

974 Questions

Improve your quantitative aptitude with these number operations and properties questions. The topics range from basic subtraction and division to highest common factor and roman numerals. Regular practice of these fundamentals builds speed for exams.

Basic arithmetic operationsHCF and number propertiesRoman numeral calculationsNumber series evaluation

Number Operations and Properties Questions

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

Without actual multiplication, then value of $687 \times 687 - 313 \times 313$

  1. $3,50,004$
  2. $3,74,000$
  3. $5,74,000$
  4. $2,74,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$687\times687-313\times313$


$=(687)^2-(313)^2$

Using identity $(a+b)(a-b)=a²-b²$

$= (687+313)(687-313)$

$=1000\times374$

$= 3,74,000$

$\therefore \text{option B is correct}.$

Multiple choice maths arithmetic progressions complete the a.p series with given information properties of an ap problems on ap

If we divide $20$ into four parts which are in A.P  such that product of the first and the fourth is to the product of the second and the third is the same as $2$:$3$ then the smallest part is 

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the four parts be $a-3d,\,a-d,\,a+d$ and $a+3d$

Hence, $(a-3d)+(a-d)+(a+d)+(a+3d)=20$
$\Rightarrow$  $4a=20$
$\therefore$  $a=5$

It is also given that, 
$(a-3d)(a+3d):(a-d)(a+d)=2:3$

$\Rightarrow$  $(a^2-9d^2):(a^2-d^2)=2:3$

$\Rightarrow$  $\dfrac{a^2-9d^2}{a^2-d^2}=\dfrac{2}{3}$

$\Rightarrow$  $3(a^2-9d^2)=2(a^2-d^2)$
$\Rightarrow$  $3a^2-27d^2=2a^2-2d^2$
$\Rightarrow$  $3a^2-2a^2=27d^2-2d^2$
$\Rightarrow$  $a^2=25d^2$
$\Rightarrow$  $(5)^2=25d^2$                        [ Substituting value of $a$ ]
$\Rightarrow$  $25=25d^2$
$\Rightarrow$  $d^2=1$
$\therefore$  $d=\pm 1$

Case $I:$ When $d=1$
$\Rightarrow$  $a-3d=5-3=2$
$\Rightarrow$  $a-d=5-1=4$
$\Rightarrow$  $a+d=5+1=6$
$\Rightarrow$  $a+3d=5+3=8$

$\therefore$  The four numbers are $2,4,6$ and $8$

Case $II:$ When $d=-1$
$\Rightarrow$  $a-3d=5+3=8$
$\Rightarrow$  $a-d=5+1=6$
$\Rightarrow$  $a+d=-5-1=4$
$\Rightarrow$  $a+3d=5-3=2$

$\therefore$  The four numbers are $8,6,4$ and $2$

$\therefore$  In both cases we can see the smallest value is $2$

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

Which of the following is not in the form of G.P.?

  1. $2 + 6 + 18 + 54 +...$
  2. $3 + 12 + 48 + 192 +....$
  3. $1 + 4 + 7 + 10 +....$
  4. $1 + 3 + 9 + 27 +....$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In option A, the common ratio is $3$.
In option B, the common ratio is $4$.
In option D, the common ratio is $3$.
$1 + 4 + 7 + 10 +...$. is not a G.P., since the sequence is in the form of A.P.

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

The first three of four given numbers are in G.P. and last three are in A.P. whose common difference is $6$. If the first and last numbers are same, then first will be?

  1. $2$
  2. $4$
  3. $6$
  4. $8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Last $3$ of the $4$ numbers are in AP.


Let they are, $a-d, a, a+d$. Also the first number is same as $4th, a+d$.

Therefore the $4$ numbers are $a+d, a-d, a, a+d$

The first $3$ of these are in G.P.


$\therefore (a-d)^2=a(a+d)$ But $d=6$

$\therefore (a-6)^2=a(a+6)$

$\therefore a^2-2a+36=0$

Solving the above quadratic equation, we get,

$a=2$

Therefore the series is:

$8,-4,2,8$


Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

When a number $x$ is subtracted from each of the numbers $8, 16$, and $40$, the resulting three numbers form a geometric progression. Find the value of $x$.

  1. $3$
  2. $4$
  3. $6$
  4. $12$
  5. $18$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that ${(16-x)}^{2}=(8-x)(40-x)$
$\Rightarrow 256-32x+{x}^{2} = 320-48x+{x}^{2}$
$\Rightarrow 16x = 64$ 

$\Rightarrow x = 4$

Multiple choice maths geometric sequences introduction to geometric progression understanding geometric progressions introduction to geometric progressions

Which of the following is not a G.P.?

  1. $2, 4, 6, 8....$
  2. $5, 25, 125, 625....$
  3. $1.5, 3.0, 6.0, 12.0....$
  4. $8, 16, 24, 32, ....$
Reveal answer Fill a bubble to check yourself
A,D Correct answer
Explanation

In series $2,4,6,8,....$ difference is same i.e. $2$

In $8,16,24,32,......$ difference again is same $8$
$\therefore$ both the series (a) and (b) are in AP as the difference between their consecutive terms is the same.

Multiple choice

What is the value of $$M_5$$?

  1. 5

  2. 10

  3. 15

  4. 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The value of $$M_5$$ is 15.

Multiple choice

In the multiplication of two numbers, if one of the numbers is zero, what is the product?

  1. The other number

  2. Zero

  3. The product of the digits of the other number

  4. The sum of the two numbers
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When multiplying two numbers, if one of the numbers is zero, the product is always zero. This is because multiplying any number by zero results in zero.

Multiple choice

What is the value of $S(3, 2)$?

  1. 3

  2. 4

  3. 6

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(3, 2)$ represents the number of ways to partition a set of 3 elements into 2 nonempty subsets. There are 3 ways to do this: {1, 2} and {3}, {1, 3} and {2}, and {2, 3} and {1}. Therefore, $S(3, 2) = 3$.

Multiple choice

What is the value of $S(4, 3)$?

  1. 6

  2. 8

  3. 16

  4. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(4, 3)$ represents the number of ways to partition a set of 4 elements into 3 nonempty subsets. There are 6 ways to do this: {1, 2, 3} and {4}, {1, 2, 4} and {3}, {1, 3, 4} and {2}, {2, 3, 4} and {1}, {1, 2} and {3, 4}, and {1, 3} and {2, 4}. Therefore, $S(4, 3) = 6$.

Multiple choice

What is the value of $S(5, 4)$?

  1. 10

  2. 15

  3. 20

  4. 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$S(5, 4)$ represents the number of ways to partition a set of 5 elements into 4 nonempty subsets. There are 15 ways to do this. Therefore, $S(5, 4) = 15$.

Multiple choice

What is the value of $S(6, 5)$?

  1. 20

  2. 30

  3. 40

  4. 50
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(6, 5)$ represents the number of ways to partition a set of 6 elements into 5 nonempty subsets. There are 20 ways to do this. Therefore, $S(6, 5) = 20$.

Multiple choice

What is the value of $S(7, 6)$?

  1. 35

  2. 45

  3. 55

  4. 65
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$S(7, 6)$ represents the number of ways to partition a set of 7 elements into 6 nonempty subsets. There are 35 ways to do this. Therefore, $S(7, 6) = 35$.