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Number System Aptitude Questions

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.



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