# Number System Solved Questions in Aptitude:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Number System Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. If the difference between the squares of two consecutive numbers is 29 then find the numbers?

1. 16, 17
2. 14, 15
3. 15, 16
4. 13, 14

Solution: Let the two consecutive numbers are $$x$$ and $$(x + 1)$$ then $$(x + 1)^2 - x^2 = 29$$ $$x^2 + 1 + 2x - x^2 = 29$$ $$1 + 2x = 29$$ $$2x = 29 - 1$$ $$2x = 28$$ $$x = \frac{28}{2}$$ $$x = 14$$ and $$(x + 1) = 15$$ Hence the two consecutive numbers are 14 and 15.

1. The sum of the two numbers is twice their difference. If one of the numbers is 15 then find the other number?

1. 28
2. 35
3. 45
4. 52

Solution: Let the other number is $$x$$ then $$x + 15 = 2 \ (x - 15)$$ $$x + 15 = 2x - 30$$ $$15 + 30 = 2x - x$$ $$x = 45$$ Hence the other number is 45.

1. A number 34*8 is divisible by 3. Find the missing digit in the number?

1. 1
2. 2
3. 3
4. 4

Solution: A number is divisible by 3 if the sum of all the digits of any number is divisible by 3. Hence if consider 3 as the missing digit then the sum of the number will be 18, which is divisible by 3 and the number will also be divisible by 3. $$= 3 + 4 + * + 8$$ $$= 15 + *$$ $$= 15 + 3$$ $$= 18$$

1. A number, when divided by 55, leaves the remainder 5. If the same number is divided by 7 then the remainder will be?

1. 1
2. 2
3. 3
4. 4

Solution: Let the number is $$x$$ and the quotient is 1 then $$dividend = divisor \times quotient \\ + remainder$$ $$x = 55 \times 1 + 5$$ $$x = 60$$ Hence the number is 60. Now if 60 is divided by 7 then the remainder will be 4.

1. On dividing 45372 by a certain number, the quotient is 93 and the remainder is 81 then find the divisor?

1. 487
2. 478
3. 467
4. 476

Solution: $$dividend = divisor \times quotient \\ + remainder$$ $$Divisor = \frac{dividend - remainder}{quotient}$$ $$= \frac{45372 - 81}{93}$$ $$Divisor = 487$$