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 sum of four consecutive even numbers is 172. Find the smallest of the numbers?
- 46
- 44
- 42
- 40

Answer: (d) 40

Solution: Let four consecutive even numbers are x, (x + 2), (x + 4), and (x + 6) then after adding these numbers $$ 4x + 12 = 172 $$ $$ 4x = 172 - 12 $$ $$ 4x = 160 $$ $$ x = 40 $$ the four consecutive even numbers will be $$ x = 40 $$ $$ x + 2 = 42 $$ $$ x + 4 = 44 $$ $$ x + 6 = 46 $$ Hence the smallest number is 40.

Solution: Let four consecutive even numbers are x, (x + 2), (x + 4), and (x + 6) then after adding these numbers $$ 4x + 12 = 172 $$ $$ 4x = 172 - 12 $$ $$ 4x = 160 $$ $$ x = 40 $$ the four consecutive even numbers will be $$ x = 40 $$ $$ x + 2 = 42 $$ $$ x + 4 = 44 $$ $$ x + 6 = 46 $$ Hence the smallest number is 40.

- If the sum of three consecutive odd numbers is 147. Find the second smallest number?
- 45
- 47
- 49
- 41

Answer: (c) 49

Solution: Let three consecutive odd numbers are x, (x + 2), and (x + 4) then after adding these numbers $$ 3x + 6 = 147 $$ $$ 3x = 147 - 6 $$ $$ 3x = 141 $$ $$ x = 47 $$ the three consecutive odd numbers will be $$ x = 47 $$ $$ x + 2 = 49 $$ $$ x + 4 = 51 $$ Hence the second smallest number is 49.

Solution: Let three consecutive odd numbers are x, (x + 2), and (x + 4) then after adding these numbers $$ 3x + 6 = 147 $$ $$ 3x = 147 - 6 $$ $$ 3x = 141 $$ $$ x = 47 $$ the three consecutive odd numbers will be $$ x = 47 $$ $$ x + 2 = 49 $$ $$ x + 4 = 51 $$ Hence the second smallest number is 49.

- If a person drinks 77 cups of coffee per week, find how many cups of coffee that person drank for the months of January, February, and March in the year 2020?
- 1000
- 1001
- 1010
- 1011

Answer: (b) 1001

Solution: The total number of days in the months January, February, and March 2020 $$ 31 + 29 + 31 = 91 \ days $$ Total numbers of weeks in 91 days $$ \frac{91}{7} = 13 \ weeks $$ The person drinks 77 cups of coffee in one week, hence the number of cups of coffee that person has drunk in 13 weeks $$ 13 \times 77 = 1001 $$

Solution: The total number of days in the months January, February, and March 2020 $$ 31 + 29 + 31 = 91 \ days $$ Total numbers of weeks in 91 days $$ \frac{91}{7} = 13 \ weeks $$ The person drinks 77 cups of coffee in one week, hence the number of cups of coffee that person has drunk in 13 weeks $$ 13 \times 77 = 1001 $$

- If the sum of three consecutive odd numbers is 51 then find the sum of the set of next three consecutive numbers?
- 64
- 66
- 69
- 71

Answer: (c) 69

Solution: Let three consecutive odd numbers are x, (x + 2), and (x + 4) then after adding these numbers $$ 3x + 6 = 51 $$ $$ 3x = 51 - 6 $$ $$ 3x = 45 $$ $$ x = 15 $$ Now the three consecutive odd numbers will be $$ x = 15 $$ $$ x + 2 = 17 $$ $$ x + 4 = 19 $$ Hence the next set of consecutive odd numbers will be 21, 23, 25. The sum of the next three consecutive numbers $$ 21 + 23 + 25 = 69 $$

Solution: Let three consecutive odd numbers are x, (x + 2), and (x + 4) then after adding these numbers $$ 3x + 6 = 51 $$ $$ 3x = 51 - 6 $$ $$ 3x = 45 $$ $$ x = 15 $$ Now the three consecutive odd numbers will be $$ x = 15 $$ $$ x + 2 = 17 $$ $$ x + 4 = 19 $$ Hence the next set of consecutive odd numbers will be 21, 23, 25. The sum of the next three consecutive numbers $$ 21 + 23 + 25 = 69 $$

- The difference between the two numbers is 15 and the difference between their squares is 75 then find the smaller number?
- 5
- -5
- 10
- -10

Answer: (b) -5

Solution: Let the larger number is x and the smaller number is y then $$ x + y = 15.....(1) $$ $$ x^2 + y^2 = 75 $$ $$ (x + y) \ (x - y) = 75 $$ by putting the value of (x - y) from equation (1) $$ (x + y) = \frac{75}{15} $$ $$ x + y = 5.....(2) $$ by adding equations (1) and (2) $$ x - y + x + y = 15 + 5 $$ $$ 2x = 20 $$ $$ x = 10 $$ by putting the value of x in equation (1) $$ 10 - y = 15 $$ $$ y = 10 - 15 $$ $$ y = -5 $$ Hence the smaller number is -5 and the larger number is 10.

Solution: Let the larger number is x and the smaller number is y then $$ x + y = 15.....(1) $$ $$ x^2 + y^2 = 75 $$ $$ (x + y) \ (x - y) = 75 $$ by putting the value of (x - y) from equation (1) $$ (x + y) = \frac{75}{15} $$ $$ x + y = 5.....(2) $$ by adding equations (1) and (2) $$ x - y + x + y = 15 + 5 $$ $$ 2x = 20 $$ $$ x = 10 $$ by putting the value of x in equation (1) $$ 10 - y = 15 $$ $$ y = 10 - 15 $$ $$ y = -5 $$ Hence the smaller number is -5 and the larger number is 10.

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
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Lec 7: Divisibility Rules of Numbers
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