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 numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Find the greatest number that will divide $400$, $435$ and $541$ leaving $9$, $10$ and $14$ as remainders respectively

  1. $17$
  2. $4$
  3. $55$
  4. $11$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$400-9=391$


$435-10=425$


$541-14=527$

$391=17\times23$

$425=5\times5\times17$

$527=17\times31$

 HCF of $391,425$ and $527=17$ 

Required number$=17$ 

Multiple choice validating statements proofs in mathematics mathematical reasoning maths

Choose the incorrect statements

  1. Digit at the units place of $3^{51}$ is $9$
  2. If $i-f=(9-\sqrt{82})^{11}$ and $< f < 1 $, then $'i'$ is an even integers
  3. If $7^{80}$ is divided by $13$, then the remainder is $9$
  4. If only $6^{th}$ term in the expression of $\left(\dfrac{x}{5}+\dfrac{2}{5}\right)^{n} $ ahs numerically greatest coefficient, then $n=7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths four operations division trick division multiply and divide

Choose the correct answers from the alternatives given.
$9^6$ -  11 when divided by 8 would leave a remainder of _______________.

  1. 0

  2. 6

  3. 2

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

We want (9^6 - 11) mod 8. Since 9 mod 8 = 1, then 9^6 mod 8 = 1^6 = 1. Thus, (1 - 11) mod 8 = -10 mod 8. Since -10 = -16 + 6, the remainder is 6.

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?

  1. $2404$
  2. $4808$
  3. $3648$
  4. $4848$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Divisor $= 5$  $\displaystyle \times $ Remainder = 5 $\displaystyle \times $ $48 = 240$
$\displaystyle \therefore $ Quotient = $\displaystyle \frac{1}{12}\times 240=20$
$\displaystyle \Rightarrow $ Dividend = Divisor $\displaystyle \times $Quotient + Remainder
$= 240 $ $\displaystyle \times $  $ 20 + 48 = 4800 + 48$
$=4848 $

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given numbers $x,y$ 

Let us assume $a$ is the quotient when $x$ is divided by $7$ and $b$ is the quotient when $y$ is divided by $7$ 

$x = 7$ $\displaystyle \times $$ a + 1 $   and  $y = 7 $ $\displaystyle \times $$ b + 2$

 $\displaystyle \therefore $ $ x + y = 7a + 7b + 1 + 2 = 7(a + b) + 3$

$\displaystyle \Rightarrow $$ (x + y)$ when divided by $7$ leaves a remainder $3$.

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

A number when divided by  $156$  gives  $29$  as remainder. If the same number is divided by  $13$ , what will be the remainder?

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

Given number = 156x + 29
=156x + 26 + 3
= 13 $\displaystyle \times $ 12x + 13 $\displaystyle \times $ 2 + 3
= 13(12x + 2) + 3
$\displaystyle \therefore $  When the number is divided by 13 the remainder will be 3

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

In a question on division the divisor is  $7$  times the quotient and  $3 $ times the remainder. If the remainder is  $28$  then what is the dividend?

  1. $1008$
  2. $1516$
  3. $1036$
  4. $2135$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Divisor $ = 3$ $\displaystyle \times $ Remainder = 3$\displaystyle \times $ $28=84$
Quotient = $\displaystyle \frac{1}{7}\times Divisor=\frac{1}{7}\times 84=12$
$\displaystyle \therefore $ Dividend = Divisor $\displaystyle \times $ Quotient + Remainder
$= 84$ $\displaystyle \times $  $12+ 28 = 1008 + 28 = 1036$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

When $31513$ ad $34369$ are divided by a certain three digit number, the remainders are equal, then the remainder is ______.

  1. $86$
  2. $97$
  3. $374$
  4. $113$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the divisor be $a$ and remainder be $r$

Let $31513 = am+r$
and $34369 = an+r$
Then, $a(n-m) = 2856 = 24\times119 = 12\times238 = 8\times357= 6\times476=4\times714$
All three digit numbers give same remainder $=$ $97$

Multiple choice computer and ms office mathematical methods for economics economics

_________ is the largest number which when divides $100$ and $83$ leaves a remainder of $4$ and $3$ in each case.

  1. $14$
  2. $12$
  3. $16$
  4. $20$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We need the HCF of (100-4) and (83-3), which is the HCF of 96 and 80. The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The greatest common factor is 16.

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

Consider the following quotients:
I.   $368.39$ divided by $17$.
II.  $170.50$ divided by $62$.
III. $875.65$ divided by $83$.
Their correct sequence in decreasing order is ?

  1. I, III, II

  2. II, I, III

  3. II, III, I

  4. III, I, II
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(I) $\displaystyle\frac{368.39}{17} = 21.67$


(II) $\displaystyle\frac{170.50}{62} = 2.75$
(III) $\displaystyle\frac{875.65}{83} = 10.55$
$\therefore$ The correct sequence in decreasing order is (I), (III), (II).