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Parin Sir > Quantitative Aptitude (Maths) > Fundamental (Numbers) > Fundamental(Numbers) Examples > Examples 1 to 10 of Fundamental(Numbers)

Examples 1 to 10 of Fundamental(Numbers)

May 28, 2020
Category: Fundamental(Numbers) Examples

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(1) Evaluate : 25 – | – 8 | – | 7 | + | – 31 |.

Soln. 25 – | – 8 | – | 7 | + | – 31 | = 25 – 8 – 7 + 31 = 41

(2) Find the value of i¹⁸.

Soln. i¹⁸ = $\left (i^{2} \right )^{9}$ = $\left (-1 \right )^{9}$ = – 1

(3) If [n] denotes the greatest integer < n, and (n) denotes the smallest integer > n where n is any real number, find $\left (4\frac{8}{9} \right )$ – $\left [4\frac{8}{9} \right ]$ .

Soln. $\left (4\frac{8}{9} \right )$ – $\left [4\frac{8}{9} \right ]$ . = 5 – 4 = 1.

(4) Simplify : $\frac{1.80\times0.81}{1.62\times 0.5 \times6}+\frac{\left (0.723 \right )^{2}}{\left (7.23 \right )^{2}}$

Soln. $\frac{1.80\times0.81}{1.62\times 0.5 \times6}+\frac{\left (0.723 \right )^{2}}{\left (7.23 \right )^{2}}$ = $\frac{18 \times 81}{162 \times5\times6}$ + $\left (\frac{723}{7230} \right )^{2}$

= $\frac{3}{10}$ + $\left (\frac{1}{10} \right )^{2}$

= 0.3 + 0.01

= 0.31

(5) Simplify : 1.8 + 2 $\sqrt{5}$ + 3 $\sqrt{3}$ + 2.8 + 5 $\sqrt{5}$

Soln. 1.8 + 2 $\sqrt{5}$ + 3 $\sqrt{3}$ + 2.8 + 5 $\sqrt{5}$ = 4.6 + 3 $\sqrt{3}$ + 7 $\sqrt{5}$

(6) Simplify : (2 + 3 $\sqrt{3}$ ) (1 + 2 $\sqrt{3}$ ).

Soln. (2 + 3 $\sqrt{3}$ ) (1 + 2 $\sqrt{3}$ ) = 2 + 4 $\sqrt{3}$ + 3 $\sqrt{3}$ + 6 $\times$ $\sqrt{3\times3}$ = 20 + 7 $\sqrt{3}$

(7) There are three tanks of volumes 980 m³, 490 m³ and 700 m³ respectively. If they have to be filled up using a bucket, what could be the maximum volume of the bucket ? (The bucket should always be full.)

Solution. Since we have to fill up the tank, volume of the bucket that we select must exactly divide each of the given volume. The only number which would divide each of the above values exactly would be the Highest Common Factor of the numbers.

980 = 70 14; 490 = 70 7; 700 = 70 10

HCF = 70.

Hence, maximum volume of the bucket is 70 m³.

(8) Simplify : 1 1 + 1 $\div$ 1 – 1

Soln. 1 $\times$ 1 + 1 $\div$ 1 – 1 = 1 $\times$ 1 + 1 – 1 = 1 + 1 – 1 = 2 – 1 = 1.

(9) Simplify : ( $\overline{7-5}$ + 3) 4 $\div$ 5 + 3

Soln. ( $\overline{7-5}$ + 3) 4 5 + 3 = (2 + 3) $\times$ 4 $\div$ 5 + 3 = 5 $\times$ $\frac{4}{5}$ + 3 = 4 + 3 = 7

The following are four different uses for bar ( ).

1) $\overline{10-4}$ = 6

2) $0.\overline{73}$ = $\frac{73}{99}$ & $0.3\overline{75}$ = $\frac{375-3}{990}$ = $\frac{372}{990}$ = $\frac{62}{165}$

3) $\overline{3}$ .5214 = – 3 + 0.5234 = – 2.4766

4) For a complex No., the conjugate of ( a + ib ) = $\overline{a+ib}$ = ( a – ib )

(10) Simplify : 0.8 $\div$ $0.\overline{4}$ of $\frac{9}{5}$ + 90

Soln. $0.\overline{4}$ = 0.4444…. = $\frac{4}{9}$

Now, 0.8 $\div$ $0.\overline{4}$ of $\frac{9}{5}$ + 90 = 0.8 $\div$ $\frac{4}{9}\times\frac{9}{4}$ + 90 = 0.8 $\div \frac{4}{5}$ + 90 = 1 + 90 = 91.

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Examples 1 to 10 of Fundamental(Numbers)

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