Pratice Number System Questions and answers.

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Which of the following is the smallest fraction?

\[\frac{7}{6},\frac{7}{9},\frac{4}{5},\frac{5}{7}\]
\[\frac{7}{6}\]

\[\frac{7}{9}\]

\[\frac{4}{5}\]

\[\frac{5}{7}\]

\[\frac{7}{6}=1.166\]

\[\frac{7}{9}=0.777\]

\[\frac{4}{5}=0.8\]

\[\frac{5}{7}=0.714\]

Therefore, the smallest number is \[\frac{5}{7}\]

Which of the following is the largest fraction?

\[\frac{6}{7},\frac{5}{6},\frac{7}{8},\frac{4}{5}\]
\[\frac{6}{7}\]

\[\frac{4}{5}\]

\[\frac{5}{6}\]

\[\frac{7}{8}\]

The decimal equivalents of :

\[\frac{6}{7}=0.857\]

\[\frac{5}{6}=0.833\]

\[\frac{7}{8}=0.875\]

\[\frac{4}{4}=0.8\]

Obviously, \[0.875\] is the greatest.

\[\frac{7}{8}\] is the largest fraction.

Which of the following is the least number?

\[\frac{4}{9},\ \sqrt{\frac{9}{49}},\ 0.45,\ (0.8)^2\]
\[\frac{4}{9}\]

\[\sqrt{\frac{9}{49}}\]

\[0.45\]

\[(0.8)^2\]

Decimal equivalents :

\[\frac{4}{9}=0.4\]

\[\sqrt{\frac{9}{49}}=\frac{3}{7}=0.43\]

\[0.45\]

\[(0.8)^2=0.64\]

\[\therefore\] Least nmber \[= 0.43\]

\[=\sqrt{\frac{9}{49}}\]

Which of the following number is the greatest of all ?

\[0.9,\ 0.\overline{9},\ 0.0\overline{9},\ 0.\overline{09}\]
\[0.9\]

\[0.\overline{9}\]

\[0.0\overline{9}\]

\[0.\overline{09}\]

\[0.9=\frac{9}{10}\]

\[0.\overline{9}=\frac{9}{9}=1\]

\[0.0\overline{9}=\frac{9}{10}=\frac{1}{10}\]

\[0.\overline{09}=\frac{9}{99}=\frac{1}{11}\]

When a number is divided by \[56\], the remainder obtained is \[29\]. What will be the remainder when the number is divided by \[8\] ?

3

4

5

6

**Rule :** When the second divisor is factor of first divisor, the second remainder is obtained by dividing the first remainder by the second divisor. Hence, on dividing \[29\] by \[8\], the remainder is \[5\].

\[\frac{1}{5}\] of a number exceeds \[\frac{1}{7}\] of the same number by \[10\]. The number is :

125

150

175

200

Let the number be \[x\].

\[\therefore\] According to question,

\[\frac{x}{5}-\frac{x}{7}=10\]

\[\Rightarrow\frac{\left\{7x-5x\right\}}{35}=10\]

\[\Rightarrow\frac{2x}{35}=10\]

\[\Rightarrow x=\frac{\left\{10\times35\right\}}{2}=175\]

If the difference between the reciprocal of a positive proper fraction and the fraction itself be \[\frac{9}{20}\], then the fraction is

\[\frac{3}{5}\]

\[\frac{3}{10}\]

\[\frac{4}{5}\]

\[\frac{5}{4}\]

The required fraction is \[\frac{4}{5}\],

because \[\frac{5}{4}-\frac{4}{5}=\frac{\left\{25-16\right\}}{20}=\frac{9}{20}\]

A tree increases annually by \[\frac{1}{8}\] of its height. By how much will it increase after \[2\] years, if it stands today \[64\] cm high?

\[72\] cm

\[74\] cm

\[75\] cm

\[81\] cm

Height of tree after 1 year

\[=64+\Bigg(64\times\frac{1}{8}\Bigg)=72\]

Height of tree after 2 year

\[=72+\Bigg(72\times\frac{1}{8}\Bigg)\]

\[=72+9=81\] cm

In a class, there are '\[z\]' students. Out of them '\[x\]' are boys. What part of the class is composed of girls ?

\[\frac{x}{z}\]

\[\frac{z}{x}\]

\[1-\frac{x}{z}\]

\[\frac{x}{z}-1\]

Boys \[= x\]

Girls \[= z - x\]

\[\therefore\] Part of girls \[=\frac{\left\{z-x\right\}}{z}=1-\frac{x}{z}\]

Six numbers are arranged in decreasing order. The average of the first five numbers is \[30\] and the average of the last five numbers is \[25\]. The difference of the first and the last numbers is :

15

20

25

30

Numbers are :

\[a > b > c > d > e > f\]

According to the question,

\[a + b + c + d + e = 5 × 30 = 150 \rightarrow (i)\]

\[b + c + d + e + f = 5 × 25 = 125 \rightarrow (ii)\]

By equation \[(i) - (ii)\]

\[a – f = 150 – 125 = 25\]

The product of two positive numbers is \[2500\]. If one number is four times the other, then the sum of the two numbers is :

25

125

225

250

Let one of the positive numbers be \[x\].

The other will be \[4x\]

Now, \[4x \times x = 2500\]

\[\implies x^2 = 2500 \div 4 = 625\]

\[x = \sqrt{625} = 25\]

\[\therefore\] Sum of the two numbers

\[= 5x = 5 \times 25 = 125\]