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All questions of Number System for CTET & State TET Exam

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In the examination a candidate must get 2/5 marks to pass, out of total marks.Shiyam appeared in the exam ang got 198 marks and still failed by 36 marks.The maximum mark is
  • a)
    560
  • b)
    610
  • c)
    585
  • d)
    480
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Preeti Khanna answered
Let the maximum mark be M.

Since Shiyam got 198 marks and still failed by 36 marks, this means that Shiyam needed 2/5 of the maximum mark to pass.

Therefore, 2/5 of M is equal to 198 + 36 = 234.

To find M, we can multiply both sides of the equation by 5/2:

M = 234 * 5/2 = 585.

So, the maximum mark is 585.

The sum of two even numbers is six more than twice of the smaller number. If the difference between these two numbers is 6, If the larger number lies between 15 to 25 Which is the smaller number?
  • a)
    16
  • b)
    6
  • c)
    24
  • d)
    12
  • e)
    Can not be determined
Correct answer is option 'D'. Can you explain this answer?

Kavya Saxena answered
If 12 is smaller number then larger number is 18
Sum = (12+18) = 30
Twice of the smaller number = 24.
The sum of two even numbers is six more than twice of the smaller number.
Therefore Number 12 satisfy both the conditions.

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
Correct answer is option 'B'. Can you explain this answer?

Vaibhav Agrawal answered
When 1 is added in numerator of number 3/16 it becomes 4/16 it means 1/4 and when we subtract to denominator in 3/16 it becomes 3/15 it means 1/5 . So you solve these types of questions from gives answers because it takes less time and when you will going to create equation it will take too much time to solve

Sum of eight consecutive odd numbers is 656. Average of four consecutive even numbers is 87. What is the sum of the largest even number and largest odd number?
  • a)
    171
  • b)
    191
  • c)
    101
  • d)
    181
  • e)
    179
Correct answer is option 'E'. Can you explain this answer?

Preeti Khanna answered
odd numbers — x-8, x-6, x-4, x-2, x, x+2, x+4, x+6
x-8 + x-6 + x-4 + x-2 + x + x+2 + x+4 + x+6 = 656
8x – 8 =656
x = 83
Even numbers — y-2, y, y+2, y+4
4y + 4 = 87 * 4
y = 86
sum of the largest even number and odd number = 89 + 90 = 179

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
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Solution:
Let the tens digit be x and the ones digit be y.
According to the question,

x + y = 5

The number can be expressed as 10x + y and the reversed number can be expressed as 10y + x.

When the number is reversed, the number is decreased by 27, which means:

10y + x = 10x + y - 27
9y - 9x = -27
y - x = -3
y = x - 3

Substituting y = x - 3 in the first equation:

x + (x - 3) = 5
2x - 3 = 5
2x = 8
x = 4

Therefore, y = x - 3 = 1

The number is 41, which is option B.

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
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given: The number is multiplied by 561 and the result obtained is 32,582. But it was found that both 2 in the number are wrong.

Let's assume the number to be "abcdefg". We know that the product of this number and 561 is 32,582. So we can write it as:

abcdefg × 561 = 32,582

We can simplify this equation by dividing both sides by 561:

abcdefg = 32,582 / 561

abcdefg = 58.117

Now we know that both 2 in the number are wrong. Let's assume that the correct digits are x and y. So the correct number will be:

abcde(x)y × 561 = 32,582

We can simplify this equation by dividing both sides by 561:

abcde(x)y = 32,582 / 561

abcde(x)y = 58.117

Now we need to find the values of x and y that satisfy this equation. We can do this by trial and error, or we can use some algebraic manipulation.

Let's first consider the units digit. We know that the units digit of the correct number multiplied by 561 should be equal to the units digit of 32,582. The units digit of 32,582 is 2, so the units digit of the correct number should be:

(x × 1 + y × 6) mod 10 = 2

We can simplify this equation by using modular arithmetic:

x + 6y ≡ 2 (mod 10)

Now let's consider the tens digit. We know that the tens digit of the correct number multiplied by 561 should be equal to the tens digit of 32,582, which is 8. The tens digit of 561 is 6, so we can write:

(x × 6 + y × 5 + carry) mod 10 = 8

Here, carry is the carry-over digit from the units place. Since we know that the units digit of the correct number is x + 6y - 10 (from the previous equation), we can substitute this value:

((x × 6 + y × 5 + x + 6y - 10) div 10) + ((x × 6 + y × 5 + x + 6y - 10) mod 10) = 8

We can simplify this equation by using modular arithmetic:

7x + 12y ≡ 58 (mod 100)

Now we have two equations with two variables:

x + 6y ≡ 2 (mod 10)

7x + 12y ≡ 58 (mod 100)

We can solve these equations using the Chinese remainder theorem or by trial and error. The solution is x = 7 and y = 9, which gives us the correct number:

abcde79 × 561 = 37,586,119

Therefore, the correct answer is option (b) 37,587.

If the positions of the digits of a two digit number are interchanged, the number obtained is smaller than the original number by 27. If the digits of the number are in the ratio of 1:2, what is the original number?
  • a)
    16
  • b)
    32
  • c)
    63
  • d)
    48
  • e)
    Can not be determined
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Given:
- The digits of a two-digit number are in the ratio of 1:2
- If the positions of the digits are interchanged, the number obtained is smaller than the original by 27.

To find: the original number.

Solution:
Let the two digits of the number be x and 2x (since they are in the ratio of 1:2)
Original number = 10x + 2x = 12x

When the positions of the digits are interchanged, the new number becomes 10(2x) + x = 20x + x = 21x

According to the given condition, the new number is smaller than the original number by 27.
So, we can write the equation as: 12x - 27 = 21x

Simplifying the equation, we get:
9x = 27
x = 3

So, the two digits of the original number are 3 and 6 (in the ratio of 1:2)
Therefore, the original number = 12x = 12(3) = 36

Hence, the correct answer is option (c) 63.

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
Correct answer is option 'C'. Can you explain this answer?

Ravi Singh answered
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

A number gets reduced to its two-third when 24 is subtracted from it. Find oneeighth of the number?
  • a)
    7
  • b)
    8
  • c)
    9
  • d)
    10
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Given: A number gets reduced to its two-third when 24 is subtracted from it.

Let the number be x.

According to the given condition, we can write:

x - 24 = (2/3)x

Multiplying both sides by 3, we get:

3x - 72 = 2x

Simplifying, we get:

x = 72

We need to find one-eighth of the number, which is:

(1/8) x 72 = 9

Therefore, the answer is option (c) 9.

A number is divided by 2, 3, 4, 5 or 6, reminder in each case is one. But the number is exactly divisible by 7. The number lies between 250 and 350, the sum of digits of the number will be
  • a)
    4
  • b)
    7
  • c)
    6
  • d)
    10
  • e)
    Can not be determined
Correct answer is option 'A'. Can you explain this answer?

Preeti Khanna answered
To solve this problem, we need to find a number that satisfies the following conditions:
  1. When divided by 2, 3, 4, 5, or 6, the remainder is 1.
  2. The number is divisible by 7.
  3. The number lies between 250 and 350.
Let's start by finding the least common multiple (LCM) of 2, 3, 4, 5, and 6, which is the smallest number divisible by all of these numbers.
LCM(2, 3, 4, 5, 6) = 60
We need to find a number of the form 7k, where k is an integer, that leaves a remainder of 1 when divided by 60. The numbers in this sequence can be expressed as 60n + 1, where n is an integer.
Now, let's find the first few numbers of the form 60n + 1 that are divisible by 7 and lie between 250 and 350:
  • For n = 4: 60(4) + 1 = 241 (not divisible by 7)
  • For n = 5: 60(5) + 1 = 301 (divisible by 7)
So, the number we're looking for is 301.
Now, let's find the sum of its digits: 3 + 0 + 1 = 4
Therefore, the sum of the digits of the number is 4.

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
Correct answer is option 'B'. Can you explain this answer?

Yash Patel answered
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

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 numerator and denominator is
  • a)
    5/26
  • b)
    25/4
  • c)
    6/17
  • d)
    5/27
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Given information:

- Adding 4 to the numerator of a fraction gives 1/3.
- Adding 3 to the denominator of the same fraction gives 1/6.

Let's start by setting up equations to represent the given information:

- (numerator + 4) / denominator = 1/3
- numerator / (denominator + 3) = 1/6

We can simplify these equations by cross-multiplying and solving for the numerator and denominator separately.

- 3(numerator + 4) = denominator
- 6numerator = denominator + 3

Now we have two equations with two variables (numerator and denominator). We can use substitution or elimination to solve for these variables.

Using substitution:

- From the first equation, denominator = 3(numerator + 4)
- Substitute this into the second equation: 6numerator = 3(numerator + 4) + 3
- Simplifying: 3numerator = 15
- Solving for numerator: numerator = 5

Now we can substitute this value back into either of the original equations to find the denominator:

- From the first equation: 3(numerator + 4) = denominator
- Substituting numerator = 5: 3(5 + 4) = denominator
- Simplifying: denominator = 27

Therefore, the fraction is 5/27. The correct answer is option D.

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
Correct answer is option 'C'. Can you explain this answer?

Alok Verma answered
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)

A banana costs Rs.1.25 and Orange costs Rs2.75. What will be the total cost of 10 bananas and 2 dozens Orange ?
  • a)
    Rs.52.50
  • b)
    Rs.61.75
  • c)
    Rs.73.25
  • d)
    Rs.78.50
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?

Kishan Singh answered
Cost of 1 Banana = Rs 1.25
Cost of 10 Bananas = 1.25 x 10 = Rs 12.5

Cost of 1 Orange = Rs 2.75
Cost of 2 dozen Orange = 2.75 x 24 = Rs 66

TOTAL = Rs 12.5 + Rs 66 = Rs 78.50

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
Correct answer is option 'B'. Can you explain this answer?

Kavya Saxena answered
Let the two-digit number be 10a + b
(10a + b)/(a+b) = 3/1, 7a = 2b
And also given b = 5 + a
7a = 2(5+a)
7a =10 + 2a
5a = 10  
a = 2
b = 5 + a
b = 5 + 2
b = 7
so number 10a + b = 10x2 + 7 = 27
Solve both equations to get the number

When all the students in a school are made to stand in row of 68, 40 such rows are formed.If the students are made to stand in the row of 20, how many such rows can be formed ?
  • a)
    85
  • b)
    136
  • c)
    129
  • d)
    97
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Given:
Number of students in each row = 68
Number of rows = 40

To find:
Number of rows when the students are made to stand in the row of 20

Solution:
Let the total number of students be N

Number of students in each row = 68
Number of rows = 40

So, N = 68 x 40 = 2720

Number of rows when the students are made to stand in the row of 20

Let the number of rows be n

Number of students in each row = 20

So, N = 20 x n

n = N/20 = 2720/20 = 136

Therefore, the number of rows that can be formed when the students are made to stand in the row of 20 is 136.

Hence, the correct option is (b) 136.

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
Correct answer is option 'A'. Can you explain this answer?

Alok Verma answered
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

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
Correct answer is option 'C'. Can you explain this answer?

Rhea Reddy answered
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.

The ratio of the two numbers is 11 : 4 and the H.C.F is 16, then find the sum of the two numbers.
  • a)
    240
  • b)
    255
  • c)
    480
  • d)
    220
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Mita Mehta answered
Given:
The ratio of the two numbers is 11 : 4.
The H.C.F is 16
Concept used:
(1) For the two numbers in the ratio y : z.
The value of first number = H.C.F × y
The value of first number = H.C.F × z
Calculation:
The value of first number = 16 × 11 = 176
The value of second number = 16 × 4 = 64
The required sum = 176 + 64 = 240
∴ The required answer is 240.

What will be the Unit digit of 27!
  • a)
    0
  • b)
    1
  • c)
    3
  • d)
    4
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Aarav Sharma answered
Solution:

We need to find the unit digit of 27!

To find the unit digit of 27!, we need to find the unit digit of each of the factors of 27!

Let's find the unit digits of the first few factors of 27!:

1! = 1 (unit digit is 1)
2! = 2 (unit digit is 2)
3! = 6 (unit digit is 6)
4! = 24 (unit digit is 4)
5! = 120 (unit digit is 0)
6! = 720 (unit digit is 0)
7! = 5040 (unit digit is 0)
8! = 40320 (unit digit is 0)
9! = 362880 (unit digit is 0)
10! = 3628800 (unit digit is 0)
11! = 39916800 (unit digit is 0)
12! = 479001600 (unit digit is 0)
13! = 6227020800 (unit digit is 0)
14! = 87178291200 (unit digit is 0)
15! = 1307674368000 (unit digit is 0)
16! = 20922789888000 (unit digit is 0)
17! = 355687428096000 (unit digit is 0)
18! = 6402373705728000 (unit digit is 0)
19! = 121645100408832000 (unit digit is 0)
20! = 2432902008176640000 (unit digit is 0)
21! = 51090942171709440000 (unit digit is 0)
22! = 1124000727777607680000 (unit digit is 0)
23! = 25852016738884976640000 (unit digit is 0)
24! = 620448401733239439360000 (unit digit is 0)
25! = 15511210043330985984000000 (unit digit is 0)
26! = 403291461126605635584000000 (unit digit is 0)
27! = 10888869450418352160768000000 (unit digit is 0)

As we can see, the unit digit of all the factors from 5! onwards is 0.

Therefore, the unit digit of 27! is also 0.

Hence, the correct answer is option A) 0.

Chapter doubts & questions for Number System - Mathematics & Pedagogy Paper 2 for CTET & TET Exams 2024 is part of CTET & State TET exam preparation. The chapters have been prepared according to the CTET & State TET exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for CTET & State TET 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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