MCQ: Number System - 2 - SSC CGL MCQ

# MCQ: Number System - 2 - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Number System - 2

MCQ: Number System - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Number System - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Number System - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Number System - 2 below.
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MCQ: Number System - 2 - Question 1

### How many factors does 120 contains ?

Detailed Solution for MCQ: Number System - 2 - Question 1

Factors of composite number = (P1 +1)(P2+1)(P3+1)......(Pn+1).
Where P1,P2,P3... Pn are the powers of respective prime factors.
So,
120= 23 x 31 x 51
Factors=(3+1)(1+1)(1+1)=16.

MCQ: Number System - 2 - Question 2

### 76n - 66n, where n is an integer greater than 0, is divisible by

Detailed Solution for MCQ: Number System - 2 - Question 2

For n =1
76n - 66n = 76 - 66
⇒ ( 73 )2 - ( 63 )2
⇒ ( 73 - 63 )( 73 + 63 )
= ( 343 - 216 )( 343 + 216 )
= 127 x 559
=127×13×43
∴ it is clearly divisible by 127.

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MCQ: Number System - 2 - Question 3

### Find the sum of square of first 35 natural numbers.

Detailed Solution for MCQ: Number System - 2 - Question 3

Sum of the square of first n natural numbers = n(n+1)(2n+1) / 6
Given n = 35
∴ Required sum = ( 35 x 36 x 71 ) / 6
= 14910

MCQ: Number System - 2 - Question 4

Find the sum of first 84 even numbers

Detailed Solution for MCQ: Number System - 2 - Question 4

Sum of first n even numbers = n( n +1 )
Given n = 84
∴ Required sum = 84 ( 84 + 1 )
= 84 x 85
= 7140

MCQ: Number System - 2 - Question 5

Sum of first 15 multiple of 8 is

Detailed Solution for MCQ: Number System - 2 - Question 5

First 15 multiple of 8 are 8, 16, 24, ......, 120
Sum = 8 (1 + 2 + 3 + 4 ......+ 15)
= 8 [ n(n + 1) / 2]
= 8 x 15 x 8
960

MCQ: Number System - 2 - Question 6

What is th unit digit in ( 365x659x771 ) ?

Detailed Solution for MCQ: Number System - 2 - Question 6

Unit digit in 34 = 1
∴ Unit digit in ( 34 )16 = 1
∴ Unit digit in 365 = 3
Unit digit in 659 = 6
Unit digit in 771 = 3
∴ Required unit digit = Unit digit in ( 3 x 6 x 3 )
= Unit digit in 54
= 4

MCQ: Number System - 2 - Question 7

On dividing a certain number by 357, the remainder is 39. On dividing the same number by 17, what will be the remainder ?

Detailed Solution for MCQ: Number System - 2 - Question 7

MCQ: Number System - 2 - Question 8

A number when divided by a divisor leaves remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor ?

Detailed Solution for MCQ: Number System - 2 - Question 8

Let the divisor be x and quotient be y.
Then, the number = xy + 24
Twice the number = 2xy + 48
Now 2xy is completely divisible by x.
On dividing 48 by x remainder is x
∴ x = 48 - 11
= 37

MCQ: Number System - 2 - Question 9

How many numbers between -11 and 11 are multiple of 2 or 3

Detailed Solution for MCQ: Number System - 2 - Question 9

Number between 0 and 11 which are multiple of 2 or 3
= 11/2 + 11/3 - 11/6 = 5 + 3 - 1
= 7
Number between 0 and -11 which are multiple of 2 or 3
= 11/2 + 11/3 - 11/6 = 5 + 3 - 1
= 7
∴ Number be 15, including 0

MCQ: Number System - 2 - Question 10

When 17200 divided by 18, find the remainder.

Detailed Solution for MCQ: Number System - 2 - Question 10

We know that, ( xm - am ) is divisible by ( x + a ), for even value of m.
∴ 17200 - 1200 is divisible by 17 +1
⇒ 17200 - 1 is divisible by 18.
Hence when 17200 divided by 18 the remainder is 1.

MCQ: Number System - 2 - Question 11

A common factor of (4143 + 4343 ) and ( 4141 + 4341) is ...

Detailed Solution for MCQ: Number System - 2 - Question 11

We know that when m is a odd number ( xm + am ) is divisible by ( x + a ).
∴ Each one is divisible by (41 + 43).
So Common factor = (41 + 43).

MCQ: Number System - 2 - Question 12

What will be remainder when 19100 is divided by 20 ?

Detailed Solution for MCQ: Number System - 2 - Question 12

19100 = ( 20 -1 )100
⇒ ( -1 )100 / 20
⇒ 1 / 20
∴ Required Remainder = 1

MCQ: Number System - 2 - Question 13

712 - 412 is exactly divisible by which of the following number ?

Detailed Solution for MCQ: Number System - 2 - Question 13

xn - yn is divisible by x + y and x - y for all n.
712 - 412 is divisible by 7 + 4 and 7 - 4
⇒ 712 - 412 is divisible by 11 x 3 = 33

MCQ: Number System - 2 - Question 14

195 + 215 is divisible by

Detailed Solution for MCQ: Number System - 2 - Question 14

We can check divisibility of 195 + 215 by 10 by adding the unit digit of 95 + 15 which is equal to 9 + 1 = 10.
So it must be divisible by 10.
Now, for divisibility by 20 we add 19 and 21 which is equal to 40. So, it is clear that it is also divisible by 20.
So 195 + 215 is divisible by both 10 and 20

MCQ: Number System - 2 - Question 15

If N, N + 2, and N + 4 are prime numbers, then the number of possible solutions for N are

Detailed Solution for MCQ: Number System - 2 - Question 15

When N is a natural number, then there is only one possible case that N, N + 2, N + 4 are prime numbers.
When N = 3, then N, N + 2, N + 4 = 3, 5, 7 all are primes.
so for only 1 value of n this is posiible

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## Quantitative Aptitude for SSC CGL

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