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

Which of the following statements is incorrect?

  1. All even numbers when divided by 2 leaves 1 as remainder.

  2. When two odd numbers are added, the result is an even number.

  3. When two even numbers are added, the result is an even number.

  4. When one odd number and one even number are added together, the result is always an odd number.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

All even numbers when divided by 2 do not leave remainder.

Multiple choice

Two numbers when divided by a certain divisor leave remainders 4375 and 2986 respectively, but when the sum of the two numbers is divided by the same divisor, the remainder is 2361. What is the divisor?

  1. 5000

  2. 4050

  3. 4000

  4. 4500
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let n be the divisor and the numbers be a and b. We have a ≡ 4375 (mod n) and b ≡ 2986 (mod n). So (a+b) ≡ 4375+2986 ≡ 7361 (mod n). But we're told (a+b) ≡ 2361 (mod n). Therefore 7361 ≡ 2361 (mod n), meaning n divides (7361-2361) = 5000. Since n > 4375 (remainder must be less than divisor), n = 5000.

Multiple choice

If 96 and 120 have remainders 5 and 3 respectively when divided by a positive integer m, find the value of m.

  1. 7

  2. 9

  3. 1<font size="2">1</font>

  4. 13

  5. 19
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the division of 96 by m leaves the remainder 5, then 91 must be divisible by m without remainder.  Similarly, if the division of 120 by m leaves the remainder 3, then 117 must be divisible by m without  remainder. So, m must be a divisor of both 91 and 117. Among the choices, it is only 13 which satisfies this  condition.

Multiple choice

Which of the following operators is used for modulus or remainder?

  1. /

  2. //

  3. %

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

The modulus operator % returns the remainder after division of one number by another. For example, 10 % 3 = 1 because 10 divided by 3 is 3 with remainder 1. Option C correctly identifies % as the modulus operator. The / operator performs division, // is not a standard C++ operator (it's used in Python for floor division), and %% has no special meaning in C++.