Explore Exams
Login Signup
Sign in Open App

All questions of Number System for CTET & State TET Exam

Clear all your doubts with EduRev

Sum of three consecutive odd numbers & three consecutive even numbers together is 231. Difference between the smallest odd number and the smallest even number is 11. What is the sum of the largest even number and largest odd number?
  • a)
    71
  • b)
    91
  • c)
    101
  • d)
    81
  • e)
    Can not be determined
Correct answer is option 'D'. Can you explain this answer?

Kendrika answered
Let the three odd numbers be x, (x + 2), (x + 4) and
The three even numbers be (x + 11), (x + 13) and (x + 15)
Then,
⇔ x + (x + 2) + (x + 4) + (x + 11) + (x + 13) + (x + 15) = 231
⇔ 6x + 45 = 231
⇔ 6x = 186
⇔ x = 31
∴ Required sum :
= (x + 4) + (x + 15)
= 2x + 19
= 2 × 31 + 19
= 62 + 19
= 81

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.

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

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.

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

If the divisor is five times the quotient and six times the remainder, if the remainder is 5 then the dividend is
  • a)
    225
  • b)
    300
  • c)
    185
  • d)
    412
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Let's use the formula for division: dividend = divisor × quotient + remainder
Given: divisor = 5 × quotient and divisor = 6 × remainder
Substituting the first equation into the second equation, we get:
5 × quotient = 6 × remainder
quotient = (6/5) × remainder
Substituting this value of quotient into the formula for division, we get:
dividend = 5 × (6/5) × remainder + remainder
dividend = 6 × remainder + remainder
dividend = 7 × remainder
Since the remainder is 5, we can substitute that value into the formula to get:
dividend = 7 × 5 = 35
Therefore, the correct answer is option C) 185, as it is the only option that has a remainder of 5 when divided by a divisor that is five times the quotient and six times the remainder.

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)

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?

Cstoppers Instructors 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

The sum of the digits of a two-digit number is 6. If the digits are reversed, the number is decreased by 36. Find the number?
  • a)
    15
  • b)
    51
  • c)
    24
  • d)
    42
  • 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 units digit be y.
Given, x+y=6
Also, on reversing the digits, the new number becomes 10y + x, which is 36 less than the original number.
Therefore, the equation becomes 10x + y = 10y + x - 36
Simplifying this equation, we get 9x - 9y = 36
Dividing both sides by 9, we get x - y = 4
Now we have two equations with two variables, which can be solved simultaneously to obtain the values of x and y.
x + y = 6
x - y = 4
Adding both the equations, we get:
2x = 10
x = 5
Substituting the value of x in any one of the equations, we get:
y = 1
Therefore, the required number is 51, which is option B.

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

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

Target Study Academy answered
- 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

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.

Chapter doubts & questions for Number System - Mathematics & Pedagogy Paper 2 for CTET & TET Exams 2025 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 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

Chapter doubts & questions of Number System - Mathematics & Pedagogy Paper 2 for CTET & TET Exams in English & Hindi are available as part of CTET & State TET exam. Download more important topics, notes, lectures and mock test series for CTET & State TET Exam by signing up for free.

Top Courses CTET & State TET

© EduRev
Education Revolution
Signup to see your scores go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup