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

Find the remainder of 2100 when divided by 3.

  1. 2

  2. 1

  3. 4

  4. 7

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

2 ^ {100} = 2 ^ {4} ^ {25} = (4.4) ^ {25} = (15 + 1) ^ {25} = (3.5 + 1) ^ {25} Now, as we divide the expression, (3.5 + 1) ^ {25} by 3, the first part, i.e. 3.5 is divisible by 3. The second part 1 will remain as a remainder, i.e. (1) ^ {25} = 1. So, the remainder is 1. Therefore, option 2 is correct.

Multiple choice

Which of the following statement correctly obtains the remainder on dividing 5.5 by 1.3?

  1. Rem = 5.5 % 1.3

  2. Rem = modf(5.5,1.3)

  3. Rem = fmod(5.5,1.3)

  4. We cannot determine the reminder while doing floating point division.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The standard modulo operator (%) in C only works with integer types. To find the remainder of a division involving floating-point numbers like 5.5 and 1.3, the fmod function from the math.h library must be used.

Multiple choice

What is the remainder of 2^60 divided by 10?

  1. 6

  2. 7

  3. 10

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

2^1 = 2, 2 ^ 2 = 4, 2 ^ 3 = 8, 2 ^ 4 = 16, 2 ^ 5 = 32, 2 ^ 6 = 64…  We can find out that the units digit of 2^n is the same as the units digit of 2^ (n + 4) So the units digit of 2^60 would be the same as the units digit of 2^4, which is 6. Hence, the remainder of 2^60 divided by 10 will be 6.

Multiple choice

x is a multiple of 5 and is a positive integer. What is the remainder of x divided by 7? 1) The remainder of x divided by 4 is 3 2) The remainder of x divided by 14 is 1

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

x = 5n, n is a positive integer. 1)  only, assume x = 4m + 3, m is a positive integer, so 5n = 4m + 3. If m = 3, n = 3, x = 15, the remainder will be 1. But if m = 8, n = 7, x = 35, the remainder will be 0. We don't know the value of x, so we don't know the remainder of x divided by 7, insufficient. 2)  only, assume x = 14p + 1, p is a positive integer, so x/7 = (14p + 1)/7 = 2p + 1/7, the remainder is 1, sufficient.

Multiple choice

What is the remainder of 3(4n + 3) divided by 5?

  1. 0.25

  2. 1

  3. 4

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

31 = 3, 32 = 9, 33 = = 27, 34 = 81, 35 = 243, 36 = 729…
We can find out that the units digit of 3(4n + 3) should be the same as the units digit of 33, which should be 7. Hence, the units digit of 3(4n + 3) - 7 should be 0, which means 3(4n + 3) - 7 can be divided by 5. So the remainder of 3(4n + 3) would be the same as the remainder of 7 divided by 5, which is 2.