# Aptitude - Number System Online 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 - The unit digit in the product (536 x 764 x 358)?

A - 4

B - 3

C - 2

D - 1

### Explanation

Unit Digit = Unit Digit in (6 x 4 x 8)
= 2

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

A - 415591

B - 6472

C - 3364

D - 413976

### 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 - Which of the following is a prime number?

A - 7

B - 9

C - 12

D - 20

### Explanation

7 as it has no positive divisors except 1.

Q 4 - The sum of all two digit numbers divisible by 7 is?

A - 215

B - 535

C - 735

D - none of these

### Explanation

7, 14, 21, ..., 98
A.P: a = 7, d = 7, l =98
tn = 98
= a + (n - 1)d
i.e. 98 = 7 + (n - 1)7
n = 14
Sum = n2 (a + l)
= 142 (7 + 98 )
= 735

Q 5 - 22 + 42 + 62 + ... + 142 = ?

A - 260

B - 730

C - 460

D - 560

### Explanation

= (1 x 2) + (2 x 2) + (2 x 3) + ... + (2 x 7)
= (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 72)
= 22 x [ 12 + 22 + 32 + ... + 72 ]
= 4 x 140
= 560

Q 6 - What is the unit digit in 2137754 ?

A - 1

B - 3

C - 7

D - 9

### Explanation

`  unit digit in (2137)754 = unit digit in (7)754 = unit digit in (74)188 x 72 = unit digit in (1 x 49) = 9 Thus Unit digit in (2137)754 is 9.  `

Q 7 - 587 x 999 = y. What is y?

A - 586413

B - 586423

C - 586433

D - 586443

### Explanation

`  y = 587 x 999   = 587 x (1000 - 1)  = 587 x 1000 - 587  = 587000 - 587  = 586413  `

Q 8 - 217 x 217 + 183 x 183 = y. What is y?

A - 79698

B - 80578

C - 80698

D - 81238

### Explanation

`  y = 217 x 217 + 183 x 183    = (217)2 + (183)2  = (200 + 17)2 + (200 -17)2  Using formulae (a+b)2 = a2 + b2 + 2ab and  (a-b)2 = a2 + b2 - 2ab  (a+b)2 + (a-b)2 = 2(a2 + b2)  ∴ y = 2 x [(200)2 + (17)2]  = 2 x [40000 + 289]  = 2 x 40289  = 80578  `

Q 9 - Which of the following will always divide difference between squares of two consecutive even numbers completely?

A - 3

B - 4

C - 6

D - 7

### Explanation

`  let a = 2n , b = 2n + 2  => (b)2  - (a)2 = (2n + 2))2 - (2n)2  = 4[(n + 1)2 - (n)2]  = 4(2n + 1)  Which is always divisible by 4.  `

Q 10 - The product of two numbers is 9375 and quotient is 15. What is the sum of the numbers?

A - 350

B - 400

C - 450

D - 500

`  Let's have numbers as a and b  Thus ab = 9375 and a/b = 15  => ab / (a/b) = 9375 / 15  => (b)2 = 625  => b = 25  => a = 15b = 15 x 25 = 375  ∴ a + b = 375 + 25 = 400  `