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 operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

What number should be subtracted from each of the numbers 54, 71, 75 and 99, so that the remainders may be in proportion?

  1. 5

  2. 4

  3. 3

  4. 2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number to be subtracted is $x$

$(54-x),  (71-x),   (75-x)$  and $ (99-x)$ are in proportion

$\Rightarrow \dfrac{54-x}{71-x}=\dfrac{75-x}{94-x}$ Which is true if $x=3$


$\Rightarrow \dfrac{54-3}{71-3}=\dfrac{75-3}{94-3}$

$\Rightarrow \dfrac{51}{68}=\dfrac{72}{91}$

i.e $\Rightarrow \dfrac{3}{4}=\dfrac{3}{4}$

Then subtracted $3$ in these number may be in proportion  

Multiple choice

In binary division, when dividing a 1-bit number by another 1-bit number, what is the result when the dividend is 1 and the divisor is 1?

  1. 0 with a remainder of 1

  2. 1 with a remainder of 0

  3. 1 with a remainder of 1

  4. 0 with a remainder of 0
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In binary division, when dividing a 1-bit number by another 1-bit number, if the dividend is 1 and the divisor is 1, the result is 1 with a remainder of 0.

Multiple choice

What is the remainder when 123456789 is divided by 11?

  1. 1

  2. 2

  3. 3

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

We can use the divisibility rule for 11 to find the remainder. The rule states that a number is divisible by 11 if the alternating sum of its digits is divisible by 11. In this case, the alternating sum of the digits of 123456789 is (1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9) = 3. Therefore, the remainder when 123456789 is divided by 11 is 3.

Multiple choice

What is the rule for division of fractions according to Harivamsha?

  1. Invert the divisor and multiply

  2. Multiply the divisor and dividend

  3. Add the divisor and dividend

  4. Subtract the divisor from the dividend
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Harivamsha stated that to divide two fractions, one should invert the divisor and multiply it with the dividend.

Multiple choice

What is the result of dividing (3x^2 + 6x - 9) by (x - 3)?

  1. \(3x + 9\)
  2. \(3x - 9\)
  3. \(x + 3\)
  4. \(x - 3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To divide (3x^2 + 6x - 9) by (x - 3), we can use polynomial long division. The result is (3x + 9) with a remainder of 0.

Multiple choice

What is the result of dividing (4x^2 - 9) by (2x + 3)?

  1. \(2x - 3\)
  2. \(2x + 3\)
  3. \(2x - 6\)
  4. \(2x + 6\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using synthetic division, we find that the quotient is (2x - 3) with a remainder of 0.

Multiple choice

What is the result of dividing (4x^2 - 9) by (2x + 3)?

  1. \(2x - 3\)
  2. \(2x + 3\)
  3. \(2x - 6\)
  4. \(2x + 6\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using synthetic division, we find that the quotient is (2x - 3) with a remainder of 0.

Multiple choice

What is the result of dividing (4x^2 - 9) by (2x + 3)?

  1. \(2x - 3\)
  2. \(2x + 3\)
  3. \(2x - 6\)
  4. \(2x + 6\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using synthetic division, we find that the quotient is (2x - 3) with a remainder of 0.

Multiple choice

Find the remainder when 7^25 is divided by 13.

  1. 1

  2. 3

  3. 7

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

Using modular arithmetic, we can calculate 7^25 mod 13 by raising 7 to the power of 25 mod 13: 7^25 mod 13 = (7^4)^6 * 7 mod 13 = 1 * 7 mod 13 = 3.

Multiple choice

Find the remainder when 11^100 is divided by 13.

  1. 1

  2. 3

  3. 7

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

Using modular arithmetic, we can calculate 11^100 mod 13 by raising 11 to the power of 100 mod 13: 11^100 mod 13 = (11^4)^25 * 11 mod 13 = 1 * 11 mod 13 = 1.

Multiple choice

What is the remainder theorem?

  1. If a polynomial \(f(x)\) is divided by \(x - a\), the remainder is \(f(a)\).
  2. If a polynomial \(f(x)\) is divided by \(x - a\), the remainder is \(f(-a)\).
  3. If a polynomial \(f(x)\) is divided by \(x + a\), the remainder is \(f(a)\).
  4. If a polynomial \(f(x)\) is divided by \(x + a\), the remainder is \(f(-a)\).
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The remainder theorem states that if a polynomial (f(x)) is divided by (x - a), the remainder is (f(a)).