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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.

If three numbers are added in pairs, the sums equal to 11,16 and 23.Find the three numbers
  • a)
    8,6,16
  • b)
    9,2,14
  • c)
    9,5,14
  • d)
    7,2,8
Correct answer is option 'B'. Can you explain this answer?

Preeti Khanna answered
X+y = 11 - (1)
Y+z = 16 - (2)
Z+x = 23 -(3)
Add (1), (2), and (3)
2(x + y + z) = 50
X+y+z = 25
X = 25 – 16 = 9
y = 25 – 23 = 2
z = 25 – 11 = 14

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.

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 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.

If the numerator of a fraction is increased by 100% and the denominator is increased by 200%. The resultant fraction is 1 (1/15), What was the original fraction ?
  • a)
    1(4/3)
  • b)
    1(5/3)
  • c)
    1(3/5)
  • d)
    1(3/2)
Correct answer is option 'C'. Can you explain this answer?

Aarav Sharma answered
Given:
- Numerator of a fraction increased by 100%
- Denominator of the same fraction increased by 200%
- Resultant fraction is 1 (1/15)

To find: Original fraction

Approach:
1. Let the original fraction be x/y
2. According to the given condition, (2x/y) / (3y) = 1(1/15)
3. Simplifying the above equation, we get 2x = 5y
4. Dividing both sides by y, we get 2x/y = 5
5. Therefore, the original fraction is 1(3/5)

Answer: Option C (1(3/5))

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)

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

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

Aarav Sharma answered
Solution:

Let the number be x.

When x is divided by 527, the remainder is 21.

So, x = 527k + 21, where k is a positive integer.

We need to find the remainder when x is divided by 17.

Let's try to express x in terms of 17.

527 can be written as 17 x 31.

So, x = (17 x 31 x k) + 21

We can write (17 x 31 x k) as 527k - 10k.

So, x = 527k - 10k + 21

Now, we can see that x leaves a remainder of 21 when divided by 17 if and only if 10k leaves a remainder of 4 when divided by 17.

Let's try to find such a value of k.

10k leaves a remainder of 4 when divided by 17 means: 10k = 17n + 4, where n is a positive integer.

Solving for k, we get:

k = (17n + 4)/10

We can see that k is an integer only when n leaves a remainder of 8 when divided by 10.

Let n = 10m + 8, where m is a positive integer.

Substituting in the above equation, we get:

k = (17 x (10m + 8) + 4)/10

Simplifying, we get:

k = 17m + 14

So, for any positive integer m, k leaves a remainder of 14 when divided by 17.

Substituting in the equation for x, we get:

x = 527k - 10k + 21

x = (527 - 10)k + 21

x = 517k + 21

x leaves a remainder of 4 when divided by 17.

Therefore, the correct answer is option C (4).

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 number of prime factors of 510510
  • a)
    4
  • b)
    5
  • c)
    6
  • d)
    7
Correct answer is option 'D'. Can you explain this answer?

Aarav Sharma answered
Solution:

Prime factorization of 510510 can be written as:

510510 = 2 × 3 × 5 × 7 × 11 × 13

Therefore, the number of prime factors of 510510 is 6.

However, we can also count the prime factors in a different way:

- 2 is a prime factor of 510510
- 3 is a prime factor of 510510
- 5 is a prime factor of 510510
- 7 is a prime factor of 510510
- 11 is a prime factor of 510510
- 13 is a prime factor of 510510
- 17 is not a prime factor of 510510

Therefore, the number of prime factors of 510510 is 7 (counting each prime factor only once).

Hence, the correct option is (D) 7.

The sum of 3 consecutive even number is 40 more than the average of these numbers. Which of the following is the 2 largest number ?
  • a)
    18
  • b)
    20
  • c)
    22
  • d)
    24
Correct answer is option 'B'. Can you explain this answer?

Aarav Sharma answered
Solution:
Let's assume the first even number to be x.
Then, the next two consecutive even numbers will be x+2 and x+4.

According to the given condition,
x + (x+2) + (x+4) = (x + x+2 + x+4)/3 + 40

Simplifying this equation, we get:
3x + 6 = (3x + 6)/3 + 40

Multiplying both sides by 3, we get:
9x + 18 = 3x + 6 + 120

Simplifying this equation further, we get:
6x = 96

Therefore, x = 16

So, the 3 consecutive even numbers are 16, 18, and 20.

Therefore, the largest two numbers are 20 and 18.

Hence, the correct answer is option B (20).

Chapter doubts & questions for Number System - Quantitative Aptitude for Competitive Exams 2025 is part of SSC MTS / SSC GD exam preparation. The chapters have been prepared according to the SSC MTS / SSC GD exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for SSC MTS / SSC GD 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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