Quantitative Aptitude · Mathematics

Number and Polynomial Division

133 Questions

Number and polynomial division tests your skill in finding quotients, remainders, and applying theorems to algebraic expressions. These calculations are a staple in quantitative aptitude exams. Solving these problems enhances speed and accuracy for competitive tests.

Number remaindersPolynomial divisionQuotient and remainderFactor and remainder theoremSuccessive division

Number and Polynomial Division Questions

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

If the quotient is terminating decimal, the division is complete only when ...............

  1. we get the remainder $1$

  2. we get the remainder zero

  3. we get the remainder as the repeated numbers

  4. All of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Any division is complete only when we get the remainder zero.
Therefore, $B$ is the correct answer.
Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

When the division process does not end and the remainder is not equal to zero; then such decimal is known as ............... decimal

  1. terminating

  2. non-terminating

  3. recurring

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

The division is completed when we get the remainder zero. In this division process we do not get a zero and it is never ending. This process of division is called a non- terminating decimal.
Therefore, $B$ is the correct answer.

Multiple choice maths logarithms more about logarithms a relation between logarithmic functions properties of logarithms

The remainder when ${75^{{{75}^{75}}}}$ is divided by $37$.

  1. $0$
  2. $1$
  3. $3$

  4. can't be determine
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Since $75 ≅ 1 modulo 37$

$75 \times 75 ≅ 1 *1 (=1) modulo 37$

$75 \times 75\times 75 ≅ 1*1*1 (=1) modulo 37$

So $75 ^{\ any \ integer}≅ $1$ modulo $37$
So$\ {75^{{75}^{75}}}$ ≅ $1 $modulo $37$

The remainder is 1.
*The digits (=1) are the remainders when divided by 37.
Multiple choice

DIV returns the

  1. Whole number of a multiplication

  2. Whole number of a division

  3. Remainder of a multiplication

  4. Remainder of a division
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In many programming contexts, DIV (or integer division) performs division and returns only the whole number quotient, discarding the remainder.

Multiple choice

MOD returns the

  1. Whole number of a multiplication

  2. Whole number of a division

  3. Remainder of a multiplication

  4. Remainder of a division
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The MOD (modulo) operator returns the remainder left over after a division operation is performed.

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

Find the greatest number which divides 120, 165 and 210 exactly leaving remainders 5, 4 and 3 respectively

  1. 7

  2. 5

  3. 23

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

The required number will be the H.C.F of (120 - 5), (165 - 4) and (210 - 3) i.e. H.C.F. of 115
161 and 207
$\displaystyle \therefore $ Required number = H.C.F. of 115, 161 and 207 = 23

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

Greatest number which divided $926$ and $2313$, leaving $2$ and $3$ remainders, respectively, is?

  1. $462$
  2. $54$
  3. $152$
  4. $154$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A number divides 926 and 2313 leaving remainders 2 and 3 respectively.

This means that the number perfectly divides 926 - 2 = 924 as well as 2313 - 3 = 2310.

Now we simply need to find the HCF of 924 and 2310 

On calculating the HCF , we get it as  462

Hence, the answer is 462

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

The greatest integer that divides 358, 376, 334 leaving the same remainder in each case is

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The difference between each set of two numbers is respectively 18, 42 and 24.
Now, as the remainder should be the same in each case, the number is the greatest common divisor of 18, 24 and 42.
$18=2\times 3\times 3$
$24=2\times 2\times 2\times 3$
$42=2\times 3\times 7$
$\therefore HCF=2\times 3=6$
$\therefore$ The required number is 6.

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

On dividing 4996 by a certain number the quotient is 62 and the the remainder is 36 what is the divisor ? 

  1. 80

  2. 85

  3. 90

  4. 95
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the divisor number is x

Then$ quotient \times divisor +reminder =number$
$\therefore 62x+36=4996$
$\Rightarrow 62x=4996-36$
$\Rightarrow 62x=4960$
$\Rightarrow x=80$
Then divisor is 80

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

The sum of all three-digit natural numbers which leave a remainder $2$ when divided by $3$

  1. $168450$
  2. $168850$
  3. $165840$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
First three digit number leaves remainder $2$ is $101$
The next being $104, 107, 110$,...…
Last $3$ digit number $=998$
$\therefore 101, 104, …… 998$
$a=101, d=3$
$n^{th}$ term $\Rightarrow 998=a+(n-1)d$
$998=101+(n-1)3$
$(n-1)\not{3}={\not{897}} _{299}$
$n=300$.
$S _n=\dfrac{300}{2}(2(101)+(300-1)3)=\dfrac{300}{2}(202+897)$
$=164850$.
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

A number when divided by $14$ leaves a remainder of $8$, but when the same number is divided by $7$, it will leave the remainder ?

  1. 3

  2. 2

  3. 1

  4. can't be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We have,

When the number is divided by $14$ it gives a remainder of $8$,

The number $= 14N + 8 (14N$ is divisible by $14)$

When same number is divided by $7$ it will give remainder $1.$

hence, this is the answer.

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

The sum of all two digit numbers which when divided by 4 , yield unity as remainder is 

  1. $1012$
  2. $1201$
  3. $1212$
  4. $1210$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

number should be of the form $4k+1$


Smallest 2 digit number that gives remainder $1$ when divided by $4$ $\Rightarrow$ $13 (when \ k=3)$ first term of A.P

Largest 2 digit number that gives remainder $1$ when divided by $4$ $\Rightarrow$ $97 (when \ k=24)$ last term of AP

Series: $13,17,21,....97$

$97=a+(n-1)d$

$97=13+(n-1)4$

$89=(n-1)4$

$(n-1)=21$

$n=22$

Sum of series $=\cfrac{n}{2}$[first term  + last term]

$=\cfrac{22}{2}[13+97]$

$=11\times (110)$

$=1210$