Number System Test

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Number System Test - 2

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Question 1
2 / -0.83

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

A
15,51

B
41, 14

C
30, 31

D
32, 23

E
None of these

Solution

Let the digits be x and y respectively.
Therefore, x + y = 5 ----------- (1)
Original Number : 10x + y
Reversed Number : 10y + x
10x + y - (10y + x) = 27
10x + y - 10y - x = 27
9x - 9y = 27
9 (x - y) = 27
x - y = 3 ------------ (2)
Adding equation (1) and (2)
2x = 8
x = 4
Substituting value for x in equation (1), we get
4 + y = 5
y = 1
The numbers are 41 and 14.
Question 2
2 / -0.83

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?

A
17

B
27

C
36

D
34

E
None of these
Solution
Define the Digits:
Let the digit in the ten ’s place be x.
Then, the digit in the unit ’s place is x + 5.
Form the Two-Digit Number:
The two-digit number can be expressed as 10x + (x + 5) = 11x + 5.
The sum of the Digits:
The sum of the digits is x + (x + 5) = 2x + 5.
Set Up the Ratio:
According to the problem, the ratio of the number to the sum of its digits is 3:1.
Therefore, we have:
11x + 5 / 2x + 5 = 3
Solve for x:
Multiply both sides by 2x + 5:
11x + 5 = 3(2x + 5)
Expand the right side:
11x + 5 = 6x + 15
Subtract 6x from both sides:
5x + 5 = 15
Subtract 5 from both sides:
5x = 10
Divide by 5:
x = 2
Find the Unit ’s Place Digit:
The unit ’s place digit is x + 5 = 2 + 5 = 7.
Form the Number:
The two-digit number is 10x + (x + 5) = 10(2) + 7 = 27.
Question 3
2 / -0.83

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

A
39

B
40

C
41

D
42

E
None of these

Solution

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.
Question 4
2 / -0.83

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

A
1

B
2

C
4

D
9

E
None of these
Solution
To determine the units digit of 12958129^{58}, focus on the units digit of the base, which is 9. The pattern of units digits for powers of 9 is as follows:
9¹ =9 (units digit: 9)
9² =81 (units digit: 1)
9³ =729 (units digit: 9)
9⁴ =6561 (units digit: 1)
The pattern (9, 1) repeats every two powers.
Since 58 is even, it corresponds to 9² , where the units digit is 1.
Thus, the units digit of 129⁵⁸ is 1 .
Question 5
2 / -0.83

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?

A
1

B
2

C
4

D
3

E
None of these

Solution

Le the number be 5a + 4
square of the number = 25a² + 16 + 40a
so remainder = 1 (16 divided by 5 leaves a remainder 1)
Question 6
2 / -0.83

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

A
2

B
3

C
4

D
7

E
None of these

Solution

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
Question 7
2 / -0.83

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

A
20

B
21

C
22

D
24

E
None of these

Solution

(a +4)/b = 1/3 and a/(b+3) = 1/6 solve both the equations, u will get a = 5 and b = 27
Question 8
2 / -0.83

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

A
24

B
32

C
36

D
48

E
None of these
Solution
Let the number be x.
According to the given condition:
- (1/4)x + 16 = (3/4)x
Solve for x:
(1/4)x + 16 = (3/4)x
16 = (3/4)x - (1/4)x
16 = (2/4)x
16 = (1/2)x
x = 32
Therefore, the number is 32.
Answer: B: 32
Question 9
2 / -0.83

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

A
856

B
866

C
876

D
886

E
896

Solution

Let total marks = M
(3/8)*M = 300 + 36 = 336
M = 112*8 = 896
Question 10
2 / -0.83

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?

A
20

B
24

C
25

D
26

E
None of these

Solution

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
Question 11
2 / -0.83

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?

A
33,583

B
37,587

C
39,589

D
36,586

E
None of these

Solution

561 = 3*11*17
So the number must be divided by 3, 11 and 17
Only B option is divided by all.
Question 12
2 / -0.83

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

A
1 and 5

B
6 and 0

C
5 and 0

D
2 and 5

E
None of these

Solution

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
Question 13
2 / -0.83

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.

A
60

B
15

C
42

D
33

E
24

Solution

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
Question 14
2 / -0.83

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?

A
85

B
130

C
65

D
90

E
105

Solution

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)
Question 15
2 / -0.83

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

A
5

B
4

C
3

D
7

E
9

Solution

- Divide 103876 by 16.
- The quotient is 6492 with a remainder of 4.
- To make 103876 divisible by 16, subtract the remainder.
- Therefore, subtract 4 from 103876.
- The resulting number, 103872, is divisible by 16.
Answer: b) 4
Question 16
2 / -0.83

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?

A
2594

B
2680

C
2851

D
2654

E
2632

Solution

Smaller no = x, then larger = x+2577
Now x+2577 = 26x + 2
Solve, x = 103
So larger no is = 103+2577
Question 17
2 / -0.83

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.

A
94

B
61

C
72

D
49

E
27

Solution

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
Question 18
2 / -0.83

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

A
9

B
5

C
12

D
11

E
15
Solution
Let the number be N .
From the given information:
When N is divided by 462, the remainder is 25. This means:
N = 462k + 25
where k is an integer.
Now, we need to find the remainder when N is divided by 14. Substituting N = 462k + 25 :
First, divide 462 by 14:
462 ÷14 = 33 (remainder 0)
So, 462k is divisible by 14, leaving us with:
N = 462k + 25
Now, divide 25 by 14:
25 ÷14 = 1 (remainder 11) .
Therefore, the remainder when N is divided by 14 is 11 .
Answer: The remainder is 11 .
Question 19
2 / -0.83

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?

A
15

B
34

C
32

D
36

E
33

Solution

Let she attend x correct answers out of 40, then incorrect = 40-x
So x*3 –(40-x)*1 = 96
Solve, x = 34
Question 20
2 / -0.83

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.

A
4/19

B
3/16

C
5/17

D
2/15

E
None of these

Solution

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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Re-Attempt Weekly Quiz Competition

Number System Test - 2

Result

Number System Test - 2

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SHARING IS CARING

Question 1

15,51

41, 14

30, 31

32, 23

None of these

Solution

Question 2

17

27

36

34

None of these

Solution

Question 3

39

40

41

42

None of these

Solution

Question 4

1

2

4

9

None of these

Solution

Question 5

1

2

4

3

None of these

Solution

Question 6

2

3

4

7

None of these

Solution

Question 7

20

21

22

24

None of these

Solution

Question 8

24

32

36

48

None of these

Solution

Question 9

856

866

876

886

896

Solution

Question 10

20

24

25

26

None of these

Solution

Question 11

33,583