Mathematics · Quantitative Aptitude

Number Operations and Properties

896 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

The value of $555 \displaystyle \times   193 - 555 \displaystyle \times  93$ is

  1. $555,931$
  2. $1,210,321$
  3. $53,912$
  4. $55,500$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving the given expression,
$555$  $\displaystyle \times  $ $193 - 555$ $\displaystyle \times  $ $93$
$= 555 \displaystyle \times    (193 - 93)$
$= 555 \displaystyle \times   100 = 55500$

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

What will be the sign of the product if we together multiply $199$ negative integers and $10$ positive integers?

  1. Negative

  2. Positive

  3. Can't say

  4. Data is insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Multiplication of $2$ negative integer result into positive integer.

 
If we multiply $199$ negative integer, then the result will be negative integer

Now if we multiply $10$ positive numbers with $199$ negative integers 

we will get a negative integer because multiplication of negative and positive 
integer will always result in negative integer.

Hence option A is correct.

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

$(-12) \times (+21) =$

  1. $-2412$
  2. $-242$
  3. $-252$
  4. $+252$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
We know that the product of two integers with unlike signs is always negative.

We are given the two unlike integers, one with positive sign and one with negative sign that is $-12$ and $+21$ then the product of these integers is:

$(-12)\times (+21)=-(12\times 21)=-252$ which is a negative integer.

Hence, $(-12)\times (+21)=-252$.
Multiple choice maths multiplication and division of integers division of integers and its properties multiplying and dividing integers multiplication of integers

One integer is greater than the other by $+4$. If one number is $-16$ then the other is_____.

  1. $+12$
  2. $0$
  3. $-1$
  4. $-12$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two integers be $x$ and $y$. One of the integer is given, that is $-16$. So let $y=-16$


Also, it is given that one integer is greater than the other by $+4$. Therefore, we have:

$x-y=+4\ \Rightarrow x-(-16)=4\ \Rightarrow x+16=4\ \Rightarrow x=4-16\ \Rightarrow x=-12$

Hence, the other integer is $-12$.

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 is $-48$. If one of the integers is $-6$ then the other is

  1. $+1$
  2. $+288$
  3. $0$
  4. $+8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the other integer be $x$. One of the integer is given that is $-6$.


Also, it is given that the product of the two integers is $-48$. Therefore, we have:

$x\times (-6)=-48\ \Rightarrow -6x=-48\ \Rightarrow 6x=48\ \Rightarrow x=\dfrac { 48 }{ 6 } \ \Rightarrow x=8$

Hence, the other integer is $+8$.

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.