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 a positive proper fraction and its reciprocal is \(\frac{16}{15}\) then find the fraction?
- \(\frac{6}{5}\)
- \(\frac{3}{5}\)
- \(\frac{5}{6}\)
- \(\frac{5}{3}\)

Answer: (b) \(\frac{3}{5}\)

Solution: Let the fraction is \(x\) then. $$ \frac{1}{x} - x = \frac{16}{15} $$ $$ \frac{1 - x^2}{x} = \frac{16}{15} $$ $$ 15 - 15 \ x^2 = 16 \ x $$ $$ 15 \ x^2 + 16 \ x - 15 = 0 $$ $$ 15 \ x^2 + 25 \ x - 9 \ x - 15 = 0 $$ $$ 5x \ (3x + 5) - 3 \ (3x + 5) = 0 $$ $$ (3x + 5) \ (5x - 3) = 0 $$ According to the question fraction is positive, hence $$ x = \frac{3}{5} $$

Solution: Let the fraction is \(x\) then. $$ \frac{1}{x} - x = \frac{16}{15} $$ $$ \frac{1 - x^2}{x} = \frac{16}{15} $$ $$ 15 - 15 \ x^2 = 16 \ x $$ $$ 15 \ x^2 + 16 \ x - 15 = 0 $$ $$ 15 \ x^2 + 25 \ x - 9 \ x - 15 = 0 $$ $$ 5x \ (3x + 5) - 3 \ (3x + 5) = 0 $$ $$ (3x + 5) \ (5x - 3) = 0 $$ According to the question fraction is positive, hence $$ x = \frac{3}{5} $$

- The difference between the two numbers is 945. On dividing the larger number by the smaller, we get 4 as quotient and 15 as the remainder. Find the smaller number?
- 260
- 290
- 310
- 322

Answer: (c) 310

Solution: Let the smaller number is \(x\) then the larger number should be \(x + 945\). $$ dividend = divisor \times quotient \\ + remainder $$ $$ x + 945 = 4 \times x + 15 $$ $$ 3 \ x = 930 $$ $$ x = \frac{930}{3} $$ $$ x = 310 $$ Hence the smaller number is 310.

Solution: Let the smaller number is \(x\) then the larger number should be \(x + 945\). $$ dividend = divisor \times quotient \\ + remainder $$ $$ x + 945 = 4 \times x + 15 $$ $$ 3 \ x = 930 $$ $$ x = \frac{930}{3} $$ $$ x = 310 $$ Hence the smaller number is 310.

- Find the sum of all two-digit numbers divisible by 5?
- 900
- 910
- 925
- 945

Answer: (d) 945

Solution: Two-digit numbers divisible by 5 are 10, 15, 20, 25,.....95.

These numbers are making an arithmetic progression series, hence $$ a = 10 $$ $$ d = 5 $$ $$ l = T_n = 95 $$ Let the number of terms in the series are "n" then. $$ T_n = a + (n - 1) \ d $$ $$ 95 = 10 + (n - 1) \ 5 $$ $$ 85 = (n - 1) \ 5 $$ $$ n - 1 = \frac{85}{5} $$ $$ n - 1 = 17 $$ $$ n = 18 $$ Hence the sum of all two-digit numbers divisible by 5. $$ S = \frac{n}{2} \ (a + l) $$ $$ = \frac{18}{2} \ (10 + 95) $$ $$ = 9 \times 105 $$ $$ S = 945 $$ Learn Arithmetic Progression Click Here

Solution: Two-digit numbers divisible by 5 are 10, 15, 20, 25,.....95.

These numbers are making an arithmetic progression series, hence $$ a = 10 $$ $$ d = 5 $$ $$ l = T_n = 95 $$ Let the number of terms in the series are "n" then. $$ T_n = a + (n - 1) \ d $$ $$ 95 = 10 + (n - 1) \ 5 $$ $$ 85 = (n - 1) \ 5 $$ $$ n - 1 = \frac{85}{5} $$ $$ n - 1 = 17 $$ $$ n = 18 $$ Hence the sum of all two-digit numbers divisible by 5. $$ S = \frac{n}{2} \ (a + l) $$ $$ = \frac{18}{2} \ (10 + 95) $$ $$ = 9 \times 105 $$ $$ S = 945 $$ Learn Arithmetic Progression Click Here

- Find the sum of all three-digit numbers divisible by 5?
- 98,550
- 98,390
- 98,320
- 98,000

Answer: (a) 98,550

Solution: Three-digit numbers divisible by 5 are 100, 105, 110, 115,.....995.

These numbers are making an arithmetic progression series, hence $$ a = 100 $$ $$ d = 5 $$ $$ l = T_n = 995 $$ Let the number of terms in the series are "n" then. $$ T_n = a + (n - 1) \ d $$ $$ 995 = 100 + (n - 1) \ 5 $$ $$ 895 = (n - 1) \ 5 $$ $$ n - 1 = \frac{895}{5} $$ $$ n - 1 = 179 $$ $$ n = 180 $$ Hence the sum of all three-digit numbers divisible by 5. $$ S = \frac{n}{2} \ (a + l) $$ $$ = \frac{180}{2} \ (100 + 995) $$ $$ = 90 \times 1095 $$ $$ S = 98,550 $$ Learn Arithmetic Progression Click Here

Solution: Three-digit numbers divisible by 5 are 100, 105, 110, 115,.....995.

These numbers are making an arithmetic progression series, hence $$ a = 100 $$ $$ d = 5 $$ $$ l = T_n = 995 $$ Let the number of terms in the series are "n" then. $$ T_n = a + (n - 1) \ d $$ $$ 995 = 100 + (n - 1) \ 5 $$ $$ 895 = (n - 1) \ 5 $$ $$ n - 1 = \frac{895}{5} $$ $$ n - 1 = 179 $$ $$ n = 180 $$ Hence the sum of all three-digit numbers divisible by 5. $$ S = \frac{n}{2} \ (a + l) $$ $$ = \frac{180}{2} \ (100 + 995) $$ $$ = 90 \times 1095 $$ $$ S = 98,550 $$ Learn Arithmetic Progression Click Here

- What number should be divided by \(\sqrt{0.36}\) to give the result as 36?
- 22.3
- 21.6
- 20.5
- 18.2

Answer: (b) 21.6

Solution: Let the number is \(x\) then. $$ \frac{x}{\sqrt{0.36}} = 36 $$ $$ \frac{x}{0.6} = 36 $$ $$ x = 36 \times 0.6 $$ $$ x = 21.6 $$

Solution: Let the number is \(x\) then. $$ \frac{x}{\sqrt{0.36}} = 36 $$ $$ \frac{x}{0.6} = 36 $$ $$ x = 36 \times 0.6 $$ $$ x = 21.6 $$

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
Questions and Answers-9
Questions and Answers-10
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Questions and Answers-12
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