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 logarithm and its uses basic mathematical concepts physics

The antilog of $(4.8779)$ will be 

  1. $7500$
  2. $750$
  3. $75500$
  4. $750000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The number before decimal point is $4,$ so decimal point will be after $5$ digits.

Value of $0.8779$ from antilog table $=7534+16=7550$
Now place a decimal point after $5$ digits of the number from left we get, $75500$
Antilog $4.8779=75500$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find G.C.D of: $8(x^4-16)$ and $12(x^3-8)$

  1. $4(x-2)$
  2. $3(x^3-8)$
  3. $2(x^2-4)$

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

$p(x) =8(x^4-16)$
   $= 4\times 2 [(x^2)^2 - 4^2] $
   $ = 4\times 2 (x^2 - 4) (x^2 + 4) $
   $ = 4\times 2  (x+2)(x-2) (x^2 +4) $
and
 $q(x) = 12(x^3-8)$
       $=4\times 3 (x^3 - 2^3) $
         $=4\times 3 (x - 2)(x^2 + 2x + 4) $
$\therefore $ G.C.D of $p(x)$ and $q(x) = 4(x-2) $
Option A is correct.

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

What is the greatest common factor of $45,135$ and $270$?

  1. $5$
  2. $9$
  3. $15$
  4. $25$
  5. $45$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The factors of the given numbers are :
$45  = 1,3,5,9,15$ and $45$
$135 = 1,3,5,9,15,45$ and $135$
$270 = 1,3,5,9,15,45,90,135$ and $270$
The common factors in each of the above numbers are $3,3$ and $5$.
Hence, the GCF is $3\times 3\times 5$ = 45
and as $45$ is also a factor of both $135$ and $270$.
The GCF of $45, 135$ and $270$ is $45$.
The correct answer is Option E, the number $45$.

Ans: E

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

How many different positive integers are factors of both $28$ and $42$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. More than $4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$4$ positive integers are factors of $28$ and $42$ both.
For example,
$1,4, 7, 6$ and $28$ itself is a factor of $28$.
$1,4, 7, 6$ and $42$ itself is factor of $42$.

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The G.C.D. of two whole numbers is $5$ and their L.C.M. is $60$. If one of the numbers is $20$, then the other number would be

  1. $23$
  2. $13$
  3. $16$
  4. $15$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If we are given two numbers $N _1$ and $N _2$ and their $G.C.D$ and $L.C.M.$.

then by property of numbers $N _1$$\times$$N _2=G.C.D$ $\times$ $L.C.M.$

Here Given:
$N _1=20$
$G.C.D.=5$
and $L.C.M=60$
Let, $N _2=x$

then from  above relation
$20$$\times$$x=5$$\times$$60$

$=>x=\dfrac{300}{20}$

$=>x=15$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

The solution of: $8\mod x\equiv 6\mod 14$ is,

  1. ${8, 6}$
  2. ${6, 14}$
  3. ${6, 13}$
  4. ${8, 14}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Solution:-
$8x \equiv 6 \left( mod \ 14 \right)$

$\because \; gcd \left( 8, 14 \right) = 2 \text{ divides } 6$

To find solutions, we first solve

$8x − 14y = 6$

By trial and error method, we find a solution

$\left( x, y \right) = \left( 6, 3 \right)$

This means that $x \equiv 6 \left( mod \ 14 \right)$ is a solution

To the congruence $8x \equiv 6 \left( mod \ 14  \right)$

$\therefore$ Incongruent solutions are,

$x = 6 +\left ( k \times \dfrac{14}{2} \right );  k = 0, 1$

$\therefore \; x = 6, 13$

Hence option $C$ is the answer.
Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

What is the least number by which $825$ must be multiplied in order to produce a multiple of $715 ?$

  1. $13$
  2. $15$
  3. $11$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$825=3\times5\times5\times 11$

$715=5\times11\times13$
In the factor of both numbers, $13$ is not common. 
Hence, the least number by which $825$ must be multiplied in order to produce a multiple of $715=13.$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find the G.C.F of $2541$ and $3102$ in the scale of seven.

  1. $87$
  2. $54$
  3. $33$
  4. $85$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Prime factors of $2541$ are $3, 7, 11, 11$. Prime factorization of $3102$ in exponential form is

$2541=3^1\times 7^1\times 11^2$


Prime factors of $3102$ are $2, 3, 11, 47$. Prime factorization of $3102$ in exponential form is

$3102=2^1\times 3^1\times 11^1\times 47^1$

We found the factors and prime factorization of $2541$ and $3102$. The biggest common factor number is the $GCF$ number.


So, the greatest common factor $2541$ and $3102$ is $3\times 11=33$.

Hence, this is the answer.

Multiple choice maths gst (goods and service tax) more about gst commission, brokerage and vat taxation, calculation of income tax

In the format of GSTIN there are ...... alpha-numerals.

  1. $15$
  2. $10$
  3. $16$
  4. $9$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

GSTIN contains 2 digits of state code, followed by 10 alpha-numeric characters of owner's PAN number, then State registration number and letter Z, last digit or alphabet is the checksum. So in total there are 15 alpha-numerals.