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. |

- If the difference between the squares of two consecutive numbers is 29 then find the numbers?
- 16, 17
- 14, 15
- 15, 16
- 13, 14

Answer: (b) 14, 15

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.

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.

- The sum of the two numbers is twice their difference. If one of the numbers is 15 then find the other number?
- 28
- 35
- 45
- 52

Answer: (c) 45

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.

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.

- A number 34*8 is divisible by 3. Find the missing digit in the number?
- 1
- 2
- 3
- 4

Answer: (c) 3

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. $$ = 3 + 4 + * + 8 $$ $$ = 15 + * $$ $$ = 15 + 3 $$ $$ = 18 $$

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. $$ = 3 + 4 + * + 8 $$ $$ = 15 + * $$ $$ = 15 + 3 $$ $$ = 18 $$

- A number, when divided by 55, leaves the remainder 5. If the same number is divided by 7 then the remainder will be?
- 1
- 2
- 3
- 4

Answer: (d) 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.

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.

- On dividing 45372 by a certain number, the quotient is 93 and the remainder is 81 then find the divisor?
- 487
- 478
- 467
- 476

Answer: (a) 487

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

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

Lec 1: Introduction to Number System
Lec 2: Factors of Composite Number
Questions and Answers-1
Lec 3: Basic Remainder Theorem
Questions and Answers-2
Lec 4: Polynomial Remainder Theorem
Questions and Answers-3
Questions and Answers-4
Questions and Answers-5
Lec 5: LCM of Numbers
Questions and Answers-6
Lec 6: HCF of Numbers
Questions and Answers-7
Questions and Answers-8
Lec 7: Divisibility Rules of Numbers
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