# Number System

Quantitative Aptitude Questions and Answers section on “Number-system” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.

1.

The least number of five digits which has 123 as a factor is :
[A]10063
[B]10037
[C]10086
[D]10081

10086
The smallest number of 5 digits = 10000
Remainder on dividing 10000 by 123 = 37
∴ Required number = 10000 + (123 – 37) = 10086
Hence option [C] is the right answer.

2.

The largest among the numbers :
$\left ( 0.1 \right )^{2}, \sqrt{0.0121}, 0.12$ and $\sqrt{0.0004}$ is
[A]$\sqrt{0.0121}$
[B]0.12
[C]$\sqrt{0.0004}$
[D]$\left ( 0.1 \right )^{2}$

0.12
$\because \left ( 0.1 \right )^{2}=0.001$
$\sqrt{0.0121}=\sqrt{0.11\times0.11}=0.11$
$\sqrt{0.0004}=0.02$
∵ 0.01 < 0.02 < 0.11 < 0.12
Hence option [B] is the right answer.

3.

Which of the following fraction is the smallest?
$\frac{7}{6}$, $\frac{7}{9}$, $\frac{4}{5}$, $\frac{5}{7}$
[A]$\frac{4}{5}$
[B]$\frac{5}{7}$
[C]$\frac{7}{9}$
[D]$\frac{7}{6}$

$\frac{5}{7}$
$\frac{7}{6}=1.166$; $\frac{7}{9}=0.777$
$\frac{4}{5}=0.8$ and $\frac{5}{7}=0.714$
Therefore, the smallest number is $\frac{5}{7}$
Hence option [B] is the right answer.

4.

Which of the following fraction is the smallest?
$\frac{8}{15}$, $\frac{14}{33}$, $\frac{7}{13}$, $\frac{11}{13}$
[A]$\frac{11}{13}$
[B]$\frac{14}{33}$
[C]$\frac{8}{15}$
[D]$\frac{7}{13}$

$\frac{11}{13}$
$\frac{8}{15}=0.5333$
$\frac{14}{33}=0.4242$
$\frac{7}{13}=0.538$
$\frac{11}{13}=0.846$
$\therefore \frac{11}{13}> \frac{7}{13}> \frac{8}{15}> \frac{14}{33}$
Hence option [A] is the right answer.

5.

Which of the following fraction is smallest?
$\frac{9}{13}, \frac{17}{26}, \frac{28}{29}, \frac{33}{52}$
[A]$\frac{9}{13}$
[B]$\frac{17}{26}$
[C]$\frac{28}{29}$
[D]$\frac{33}{52}$

$\mathbf{ \frac{33}{52}}$
$\frac{9}{13} = \frac{9\times 4}{13\times 4} = \frac{36}{52}$
$\frac{17}{26} = \frac{17\times 2}{26\times 2} = \frac{34}{52}$
$\frac{33}{52} = \frac{33}{52}$
$\frac{28}{29} = \frac{28\times 2}{29\times 2} = \frac{56}{58}$
Now it is clear that the smallest fraction is : $\frac{33}{52}$
Hence option [D] is the right answer.

6.

Which of the following is the largest fraction?
$\frac{6}{7}$, $\frac{5}{6}$, $\frac{7}{8}$, $\frac{4}{5}$
[A]$\frac{7}{8}$
[B]$\frac{5}{6}$
[C]$\frac{4}{5}$
[D]$\frac{6}{7}$

$\mathbf{\frac{7}{8}}$
The decimal equivalents of :
$\frac{6}{7}=0.857$, $\frac{5}{6}=0.8$
$\frac{7}{8}=0.875$, $\frac{4}{5}=0.8$
Obviously, 0.875 is the greatest.
∴ The largest fraction is $\frac{7}{8}$
Hence option [A] is the right answer.

7.

The least number among $\frac{4}{9}, \sqrt{\frac{9}{49}}, 0.\overline{45}$ and $\left ( 0.8 \right )^{2}$ is :
[A]$0.\overline{45}$
[B]$\left ( 0.8 \right )^{2}$
[C]$\frac{4}{9}$
[D]$\sqrt{\frac{9}{49}}$

$\mathbf{\sqrt{\frac{9}{49}}}$
Decimal equivalents :
$\frac{4}{9} = 0.\bar4 ,$
$\sqrt{\frac{9}{49}} = \frac{3}{7} = 0.43$
$0.\overline{45},$
$\left ( 0.8 \right )^{2} = 0.64$
∴ Least Number is,
$= 0.43 = \sqrt{\frac{9}{49}}$
Hence option [D] is the right answer.

8.

Which of the following number is the greatest of all?
$0.9, 0.\overline9, 0.0\overline9, 0.\overline{09}$
[A]$0.\overline{09}$
[B]$0.\overline9$
[C]$0.9$
[D]$0.0\overline9$

$\mathbf{0.\overline9}$
$0.9 = \frac{9}{10},$
$0.\bar9 = \frac{9}{9} = 1,$
$0.0\bar9 = \frac{9}{90} = \frac{1}{10},$
$0.\overline{09} = \frac{9}{99} = \frac{1}{11}$
Hence option [B] is the right answer.

9.

The greatest value among the fractions $\frac{2}{7}, \frac{1}{3}, \frac{5}{6}, \frac{3}{4}$ is :
[A]$\frac{2}{7}$
[B]$\frac{3}{4}$
[C]$\frac{1}{3}$
[D]$\frac{5}{6}$

$\mathbf{\frac{5}{6}}$
$\frac{2}{7} = 0.286,$
$\frac{1}{3} = 0.33$,
$\frac{5}{6} = 0.833,$
$\frac{3}{4} = 0.75$
Hence option [D] is the right answer.

10.

The greatest among the following numbers
$(3)^{\frac{1}{3}}, (2)^{\frac{1}{2}}, 1, (6)^{\frac{1}{6}}$
[A] $1$
[B]$(2)^{\frac{1}{2}}$
[C]$(3)^{\frac{1}{3}}$
[D]$(6)^{\frac{1}{6}}$

$\mathbf{(3)^{\frac{1}{3}}}$
LCM of 3, 2 and 6 = 6
$\therefore (3)^{\frac{1}{3}} = (3^{2})^{\frac{1}{6}} = (9)^{\frac{1}{6}}$
$(2)^{\frac{1}{2}} = (2^{3})^{\frac{1}{6}} = (8)^{\frac{1}{6}}$
$(1)^\frac{1}{6} = 1$
$(6)^\frac{1}{6} = (6)^\frac{1}{6}$
Hence option [C] is the right answer.