Number System Aptitude Questions and Answers:


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

    1. \(\frac{6}{5}\)
    2. \(\frac{3}{5}\)
    3. \(\frac{5}{6}\)
    4. \(\frac{5}{3}\)


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 $$ x = \frac{3}{5} $$

  1. 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?

    1. 260
    2. 290
    3. 310
    4. 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.

  1. Find the sum of all two-digit numbers divisible by 5?

    1. 900
    2. 910
    3. 925
    4. 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

  1. Find the sum of all three-digit numbers divisible by 5?

    1. 98,550
    2. 98,390
    3. 98,320
    4. 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

  1. What number should be divided by \(\sqrt{0.36}\) to give the result as 36?

    1. 22.3
    2. 21.6
    3. 20.5
    4. 18.2


Answer: (b) 21.6

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