Aptitude - Questions & Answers

Aptitude - Number System Online Quiz

Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Number System. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Q 1 - What is the unit digit in 7³⁵ - 3⁴⁸?

Answer : C

Explanation

Unit digit in 7³⁵ = (7⁴)⁸ x 7³
= 1 x 3 = 3
Unit digit in 3⁴⁸ = (3⁴)¹²
= 1
Therefore, unit digit in 7³⁵ - 3⁴⁸ = 3 - 1 = 2

Q 2 - Which of the numbers is exactly divisible by 11?

Answer : A

Explanation

Divisibility by 11: If the difference between the sum of digits at odd places and the sum of its digits at even places is either 0 or a number divisible by 11.
(9 + 5 + 4) - (1 + 5 + 1) = 11 i.e. exactly divisible by 11.
(7 + 6) - (2 + 3) is not divisible by 11.
(6 + 3) - (4 + 3) is not divisible by 11.
(7 + 3 + 4) - (6 + 9 +1) is not divisible by 11.

Q 3 - On dividing a number by 5, we get remainder as 3. What will be the remainder when the square of this number is divided by 5?

Answer : D

Explanation

Let number be p
Dividing p by 5, we get k as quotient and remainder as 3
p = 5k + 3 ->
p² = (5k + 3)² p = (25k² + 30k + 9)
p = 5 (5k² + 6k + 1) + 4
Therefore, we get 4 as remainder on dividing p² by 5.

Q 4 - It is being given that (2³²) + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

Answer : C

Explanation

Let 2³² = p
-> (2³² + 1) = p + 1
Let (p + 1) be completely divisible by natural number Z. Then->
(2⁹⁶ + 1) = [(2³²)³ + 1]
As (p³ + 1) = (p + 1)(p² - p + 1), which is completely divisible by Z, since (p + 1) is completely divisible by Z.

Q 5 - 6 + 15 + 24 + 33 + ... + 123 = ?

Answer : A

Explanation

a = 6, d = 9, l = 123
Let number of terms be n
123 = a + (n - 1)d
123 = 6 + (n - 1)9
123 = 9n - 9
n = 14
S_n = ⁿ⁄₂ (a + l)
= ¹⁴⁄₂ (6 + 123)
= 7 x 129
= 903

Q 6 - If unit digit in 549 x 56 x 28p x 684 is 8 then what is p?

Answer : B

Explanation

  Multiply unit digits of each number. Unit digit in 549 x 56 x 28p x 684 = 8 Unit digit in 9 x 6 x p x 4 = 8 Unit digit in 216 x p = 8 Thus p must be 3.

Q 7 - (45 + 46 + 47 + ... + 114 + 115) = ?

Answer : C

Explanation

  Using formula for sum of natural numbers  (1 + 2 + 3 +... + n) = (1/2)n(n+1)  (45 + 46 + 47 + ... + 114 + 115) = (1 + 2 + 3 +... + 115) - (1 + 2 + 3 + ... + 44)  = (1/2) x 115 x 116 - (1/2) x 44 x 45  = 115 x 58 - 22 x 45  = 6670 - 990  = 5680

Q 8 - 1499 x 1499 = y. What is y?

Answer : C

Explanation

  y = 1499 x 1499  = (1500-1) x (1500 -1)  = (1500-1)^{2^{Using formulae (a-b)^{2^{= a^{2^{+ b^{2^{- 2ab  ∴ y = (1500)^{2^{+ (1)^{2^{- 2 x 1500 x 1  = 2250000 + 1 - 3000  = 2247001}}}}}}}}}}}}

Q 9 - Which of the following is not a prime number?

Answer : D

Explanation

91. As it is divisible by 7.

Q 10 - What is the common factor in (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷)

Answer : B

Explanation

aⁿ + bⁿ is divisible by a + b if n is an odd number. ∴ each number is divisible by (47 + 43).

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