Number System - MCQ 2

# Number System - MCQ 2

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## 20 Questions MCQ Test Quantitative Techniques for CLAT | Number System - MCQ 2

Number System - MCQ 2 for Quant 2022 is part of Quantitative Techniques for CLAT preparation. The Number System - MCQ 2 questions and answers have been prepared according to the Quant exam syllabus.The Number System - MCQ 2 MCQs are made for Quant 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Number System - MCQ 2 below.
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Number System - MCQ 2 - Question 1

### The sum of the digits of two-digit number is 5. If the number is reversed, the number is decreased by 27. Find the number?

Detailed Solution for Number System - MCQ 2 - Question 1

Let the number be (10a + b)
given, a +b = 5 and (10a + b) – (10b +a) = 27
a – b = 3 and a +b = 5

Number System - MCQ 2 - Question 2

### The ratio between a two-digit number and the sum of the digits of that number is 3:1. If the digit in the unit’s place is 5 more than digit at ten’s place, what is the number?

Detailed Solution for Number System - MCQ 2 - Question 2

Let the two-digit number be 10a + b
(10a + b)/(a+b) = 3/1, 7a = 2b
And also given b = 5 + a
Solve both equations to get the number

Number System - MCQ 2 - Question 3

### How many numbers are there up to 1000 which are divisible by 4, 6 and 8 together?

Detailed Solution for Number System - MCQ 2 - Question 3

LCM of 4,6 and 8 is 24
Divide 1000 by 24, we get quotient = 41 and 16 as remainder
so 41 numbers are there which are divisible by 4,6 and 8 together.

Number System - MCQ 2 - Question 4

What is the number in the unit place of the number (129)58?

Detailed Solution for Number System - MCQ 2 - Question 4

[(129)2]29 = (1)29 = 1 (92 always result in 1 on unit place)

Number System - MCQ 2 - Question 5

A number when divided by 5 leaves a remainder 4. What is the remainder when the square of the same number is divided by 5?

Detailed Solution for Number System - MCQ 2 - Question 5

Le the number be 5a + 4
square of the number = 25a2 + 16 + 40a
so remainder = 1 (16 divided by 5 leaves a remainder 1)

Number System - MCQ 2 - Question 6

When a number is divided by 527 gives the remainder as 21. When the same number is divided by 17, the remainder will be?

Detailed Solution for Number System - MCQ 2 - Question 6

Let the number be 527a + 21
when divided by 17, 527a is divisible by 17 and leaves remainder as 4 when 21 is divided by 17

Number System - MCQ 2 - Question 7

If 4 is added to the numerator of a fraction it becomes 1/3 and if 3 is added to the denominator it becomes 1/6 then find the difference between numerator and denominator is

Detailed Solution for Number System - MCQ 2 - Question 7

(a +4)/b = 1/3 and a/(b+3) = 1/6 solve both the equations, u will get a = 5 and b = 27

Number System - MCQ 2 - Question 8

When one-fourth of a number is added to 16, it becomes three-fourth of itself. Find the number?

Detailed Solution for Number System - MCQ 2 - Question 8

a/4 + 16 = 3a/4,
2a/4 = 16, so a = 32

Number System - MCQ 2 - Question 9

In the examination a candidate must get 3/8 marks to pass, out of total marks. Shyam appeared in the exam and got 300 marks and still failed by 36 marks. The maximum mark is

Detailed Solution for Number System - MCQ 2 - Question 9

Let total marks = M
(3/8)*M = 300 + 36 = 336
M = 112*8 = 896

Number System - MCQ 2 - Question 10

Two different numbers are divided by the same divisor and left remainder 11 and 21 respectively and when their sum was divided by the same divisor, remainder was 4. What is the divisor?

Detailed Solution for Number System - MCQ 2 - Question 10

Let us say that the two numbers are 'a' and 'b' and the divisor is 'd'

We are given that

Rem [a/d] = 11 and Rem [b/d] = 21

We are also given that the Remainder [(a + b)/d] = 4

=> Rem[(11 + 21)/d] = 4

=> Rem[32/d] = 4

=> 32 - 4 = 28 is divisible by 'd' or 'd' is a factor of 28

=> 'd' could be 1, 2, 4, 7, 14, or 28

We also know that 'd' is greater than 21 because 'b' when divided by 'd' leaves a remainder of 21.

=> The value of 'd' is 28

Number System - MCQ 2 - Question 11

A number is multiplied by 561, and the result obtained is 32,582. But it was found that both 2 in the number are wrong, what should be the correct answer?

Detailed Solution for Number System - MCQ 2 - Question 11

561 = 3*11*17
So the number must be divided by 3, 11 and 17
Only B option is divided by all.

Number System - MCQ 2 - Question 12

If the number 10*47* is divisible by both 5 and 11, then the missing digits are respectively

Detailed Solution for Number System - MCQ 2 - Question 12

Check the options in the number 10x47y
all numbers will be divisible by 5 because in end it is 5 and 0
for number to be divisible by 11, (y+4+0) – (7+x+1) should be divisible by 11
from option A, y = 5, x = 1 gives (y+4+0) – (7+x+1) as 0 which is divisible by 11

Number System - MCQ 2 - Question 13

The sum of digits of a two digit number is 6. The ratio of the original number to the number formed by interchanging its digits is 4 : 7. Find the number.

Detailed Solution for Number System - MCQ 2 - Question 13

Let the number is 10x+y
So x+y = 6
And (10x+y)/(10y+x) = 4/7
Solve, 2x = y and from above we have x+y = 6
Solve both equations, x = 2, y = 4

Number System - MCQ 2 - Question 14

When a number is multiplied by 13 and 13 is added to the product, the resultant is divisible by 5. Find the smallest product possible?

Detailed Solution for Number System - MCQ 2 - Question 14

13x + 13 which is divisible by 5, or 13(x+1) should be divisible by 5. The smallest value of x = 4 to be put here to make it divisible by 5. So the number is 13(4+1)

Number System - MCQ 2 - Question 15

Find the least number which must be subtracted from 103876 to make the obtained number divisible by 16.

Detailed Solution for Number System - MCQ 2 - Question 15

103876/16 gives remainder 4, so 4 should be subtracted

Number System - MCQ 2 - Question 16

The difference between two numbers is 2577. The quotient and remainder are respectively 26 and 2 when the larger number is divided by the smaller one. What is the largest number?

Detailed Solution for Number System - MCQ 2 - Question 16

Smaller no = x, then larger = x+2577
Now x+2577 = 26x + 2
Solve, x = 103
So larger no is = 103+2577

Number System - MCQ 2 - Question 17

The difference between the digits of a two digit number is 5. Also the original number is 18 more than two times the number obtained by reversing its digits. Find the original number.

Detailed Solution for Number System - MCQ 2 - Question 17

Let number is 10x+y
Then x-y = 5 or y-x = 5
Now given that, 10x+y = 2(10y+x) + 18 Solve, 8x – 19y = 18
Now solve: 8x – 19y = 18 and x-y = 5. In this y = 2, x = 7
And also solve; 8x – 19y = 18 and y-x = 5. In this y come to be negative which is not possible so discard this
So number is 10*7 + 2

Number System - MCQ 2 - Question 18

A number when divided by 462 gives the remainder as 25. When same number is divided by 14, the remainder will be?

Detailed Solution for Number System - MCQ 2 - Question 18

Let x be the quotient, then that number becomes 462*x + 25
Which = (22x * 14) + (14*1)+11
Which = 14 (22x + 1) + 11

Number System - MCQ 2 - Question 19

Kavya attends 40 questions and get 96 marks. If 3 marks are given for each correct answer and 1 mark is deducted for each wrong answer, find the number of question she attended correct?

Detailed Solution for Number System - MCQ 2 - Question 19

Let she attend x correct answers out of 40, then incorrect = 40-x
So x*3 – (40-x)*1 = 96
Solve, x = 34

Number System - MCQ 2 - Question 20

When 1 is added to the numerator of a fraction it becomes 1/4 and 1 is subtracted from the denominator of that fraction it becomes 1/5. Find the fraction.

Detailed Solution for Number System - MCQ 2 - Question 20

Let fraction = x/y
Then (x+1)/y = 1/4
And x/(y-1) = 1/5
Solve both equations, x = 3, y = 16

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## Quantitative Techniques for CLAT

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