# Simplification - 1

1. By how much is 12% of 24.2 more than 10% of 14.2?
a. 0.1484
b. 14.84
c. 1.484
d. 2.762
Correct Option: C
Explanation:
It is more by $\left( {\displaystyle\frac{{12}}{{100}} \times 24.2 - \displaystyle\frac{{10}}{{100}} \times 14.2} \right)$=2.904-1.420=1.484

2. The value of $4.1\overline 2$ is
a. $4\displaystyle\frac{{11}}{{99}}$
b. $5\displaystyle\frac{2}{9}$
c. $4\displaystyle\frac{{11}}{{90}}$
d. None of these
Correct Option: C
Explanation:
$4.1\overline 2$ = 4+$0.1\overline 2$ = $4 + \displaystyle\frac{{12 - 1}}{{90}} = 4\displaystyle\frac{{11}}{{90}}$

3. The greatest fraction out of  $\displaystyle\frac{2}{5},\displaystyle\frac{5}{6},\displaystyle\frac{{11}}{{12}}$ and $\displaystyle\frac{7}{8}$ is
a. $\displaystyle\frac{7}{8}$
b. $\displaystyle\frac{{11}}{{12}}$
c. $\displaystyle\frac{5}{6}$
d. $\displaystyle\frac{2}{5}$
Correct Option: B
Explanation:
$\displaystyle\frac{2}{5} = 0.4;\displaystyle\frac{5}{6} = 0.833;\displaystyle\frac{{11}}{{12}} = 0.916$ and $\displaystyle\frac{7}{8} = 0.875$
$\displaystyle\frac{{11}}{{12}}$ is largest number.

4.  $2.53 \times 0.154$ is the same as
a. $253 \times 0.00154$
b. $25.3 \times 1.54$
c. $253 \times 0.0154$
d. $253 \times 0.154$
Correct Option: A
Explanation:
Both contain same number of decimal places.

5. $\displaystyle\frac{{0.23 - 0.023}}{{0.0023 \div 23}} = ?$
a. 0.207
b. 207
c. 2070
d. 0.0207
Correct Option: C
Explanation:
$\displaystyle\frac{{0.2070}}{{\displaystyle\frac{{0.0023}}{{23}}}}$ = $\displaystyle\frac{{0.2070}}{{0.0001}}$ = $\dfrac{{0.2070 \times 10000}}{{0.0001 \times 10000}}$ = 2070

6. $\displaystyle\frac{{? - 0.11}}{{1.6}} = 1.6$
a. 2.56
b. 1.76
c. 0.267
d. None of these
Correct Option: D
Explanation:
Let $\displaystyle\frac{{x - 0.1}}{{1.6}} = 16,$ then $x - 0.11 = 1.6 \times 1.6 = 2.56$
$\Rightarrow x \Rightarrow 2.56 + 0.11 = 2.67$

7. If 1.5x=0.04y, then the value of  $\displaystyle\frac{{y - x}}{{y + x}}$ is
a. $\displaystyle\frac{{730}}{{77}}$
b. $\displaystyle\frac{{73}}{{77}}$
c. $\displaystyle\frac{{7.3}}{{77}}$
d. None of these
Correct Option: B
Explanation:
$\displaystyle\frac{x}{y} = \displaystyle\frac{{0.04}}{{15}} = \displaystyle\frac{2}{{75}}$
$\displaystyle\frac{{y - x}}{{y + x}} = \displaystyle\frac{{1 - x/y}}{{1 + x/y}} = \displaystyle\frac{{1 - 2/75}}{{1 + 2/75}}$
=$\left( {\displaystyle\frac{{73}}{{75}} \times \displaystyle\frac{{75}}{{77}}} \right) = \displaystyle\frac{{73}}{{77}}$

8. $0.\overline 6 + 0.\overline 7 + 0.\overline 8 + 0.\overline 3$ = ?
a. $2\displaystyle\frac{3}{{10}}$
b. $2\displaystyle\frac{{33}}{{10}}$
c. $2\displaystyle\frac{2}{3}$
d. 2.35
Correct Option: C
Explanation:
$0.\overline 6 + 0.\overline 7 + 0.\overline 8 + 0.\overline 3$  = $\left( {\displaystyle\frac{6}{9} + \displaystyle\frac{7}{9} + \displaystyle\frac{8}{9} + \displaystyle\frac{3}{9}} \right)$ = $\displaystyle\frac{{24}}{9}$ = $\displaystyle\frac{8}{3}$ = $2\displaystyle\frac{2}{3}$

9. The square root of  $\displaystyle\frac{{0.320 \times 0.081 \times 4.624}}{{1.5625 \times 0.0289 \times 72.9 \times 64}}$ is
a. 24
b. 2.4
c. 0.024
d. None of these
Correct Option: C
Explanation:
$\sqrt {\dfrac{{0.320 \times 0.081 \times 4.624}}{{1.5625 \times 0.0289 \times 72.9 \times 64}}}$
$\sqrt {\dfrac{{324 \times 81 \times 4624}}{{15625 \times 289 \times 729 \times 64}}}$
= $\sqrt {\dfrac{{{{18}^2} \times {9^2} \times {{68}^2}}}{{{{125}^2} \times {{17}^2} \times {9^3} \times {8^2}}}}$
$\dfrac{{18 \times 9 \times 68}}{{125 \times 17 \times 9 \times 3 \times 8}}$ = $\dfrac{9}{{375}}$ = 0.024

10.Which of the following fractions are in ascending order?
a. $\dfrac{{16}}{{19}},\dfrac{{11}}{{14}},\dfrac{{17}}{{22}}$
b. $\dfrac{{11}}{{14}},\dfrac{{16}}{{19}},\dfrac{{17}}{{22}}$
c. $\dfrac{{17}}{{22}},\dfrac{{11}}{{14}},\dfrac{{16}}{{19}}$
d. $\dfrac{{16}}{{19}},\dfrac{{17}}{{22}},\dfrac{{11}}{{14}}$
Correct Option: C
Explanation:
$\displaystyle\frac{{16}}{{19}}$ = 0.842; $\displaystyle\frac{{11}}{{14}} = 0.785$
and $\displaystyle\frac{{17}}{{22}} = 0.772$
0.772<0.785<0.842

$\Rightarrow \displaystyle\frac{{17}}{{22}} < \displaystyle\frac{{11}}{{14}} < \displaystyle\frac{{16}}{{19}}$

11. $\displaystyle\frac{{20 + 8 \times 0.5}}{{20 - ?}} = 12$
a. 8
b. 18
c. 2
d. None of these
Correct Option: B
Explanation:
Let $\displaystyle\frac{{20 + 8 \times 0.5}}{{20 - x}} = 12$ $\Rightarrow$ 20 + 4 = 12(20 - x)
$\Rightarrow$ 24 = 240 - 12x  $\Rightarrow$ 12x=216  $\Rightarrow$x=18

12. $0.15 \div \displaystyle\frac{{0.5}}{{15}} = ?$
a. 4.5
b. 45
c. 0.03
d  0.45
Correct Option: A
Explanation:
$0.15 \div \displaystyle\frac{{0.5}}{{15}}$ = $\displaystyle\frac{{15}}{{100}} \div \displaystyle\frac{5}{{150}}$ = $\displaystyle\frac{{15}}{{100}} \times \displaystyle\frac{{150}}{5}$ = 4.5

13. If $\sqrt {15} = 3.88$,  the value of $\sqrt {\displaystyle\frac{5}{3}}$ is
a. 0.43
b. 1.89
c. 1.29
d. 1.63
Correct Option: C
Explanation:
$\sqrt {\displaystyle\frac{5}{3}} = \sqrt {\displaystyle\frac{5}{3}} \times \sqrt {\displaystyle\frac{3}{3}}$  = $\sqrt {\displaystyle\frac{{15}}{{{3^2}}}}$  = $\displaystyle\frac{{\sqrt {15} }}{3}$ =$\displaystyle\frac{{3.88}}{3}$ = 1.29

14.If 12276$\div$155=79.2, then the value of 122.76$\div$15.5 is
a. 7.092
b. 7.92
c. 79.02
d. 79.2
Correct Option: B
Explanation:
$\displaystyle\frac{{122.76}}{{15.50}}$ = $\displaystyle\frac{{12276}}{{1550}}$ = $\displaystyle\frac{{12276}}{{155}} \times \displaystyle\frac{1}{{10}}$ = $\displaystyle\frac{{79.2}}{{10}}$ = 7.92

15. What decimal of an hour is a second ?
a. 0.0025
b. 0.0256
c. 0.00027
d. 0.000126
Correct Option: C
Explanation:
One second is 3600 part of an hour.
The decimal is $\displaystyle\frac{1}{{60 \times 60}} = 0.00027$

16. $15.60 \times 0.30 = ?$
a. 4.68
b. 0.458
c. 0.468
d. 0.0468
Correct Option: A
Explanation:
$1560 \times 30 = 46800$
$15.60 \times 0.30 = 4.6800 = 4.68$

17.$\displaystyle\frac{{3420}}{{19}} = \displaystyle\frac{?}{{0.01}} \times 7$
a. $\displaystyle\frac{{35}}{9}$
b. $\displaystyle\frac{{18}}{7}$
c. $\displaystyle\frac{{63}}{5}$
d. None of these
Correct Option: D
Explanation:
$x = \displaystyle\frac{{3420}}{{19}} \times \displaystyle\frac{{0.01}}{7}$ = $180 \times \displaystyle\frac{1}{{700}}$ = $\dfrac{9}{{35}}$

18.$\displaystyle\frac{{17.28 \div x}}{{3.6 \times 0.2}} = 200$
a. 120
b. 1.20
c. 12
d. 0.12
Correct Option: D
Explanation:
Let $\displaystyle\frac{{17.28 \div x}}{{3.6 \times 0.2}} = 200$
$\Rightarrow \displaystyle\frac{{17.28}}{x} = 200 \times 3.6 \times 0.2$
$\Rightarrow x = \displaystyle\frac{{17.28}}{{200 \times 3.6 \times 0.2}} = 0.12$

19. If $\sqrt 5 = 2.24$ then the value of $\displaystyle\frac{{3\sqrt 5 }}{{2\sqrt 5 - 0.4}}$ is
a. 0.168
b. 1.68
c. 1.29
d. 1.63
Correct Option: B
Explanation:
$\displaystyle\frac{{3\sqrt 5 }}{{2\sqrt 5 - 0.48}} = \displaystyle\frac{{3 \times 2.24}}{{2 \times 2.24 - 0.48}}$
=$\displaystyle\frac{{6.72}}{{4.48 - 0.48}} = \displaystyle\frac{{6.72}}{4} = 1.68$

20. $\sqrt {\displaystyle\frac{{0.289}}{{0.00121}}} = ?$
a. $\displaystyle\frac{{170}}{{11}}$
b. $\displaystyle\frac{{17}}{{110}}$
c. $\displaystyle\frac{{17}}{{1100}}$
d. $\displaystyle\frac{{17}}{{11}}$
Correct Option: A
Explanation:
$\sqrt {\displaystyle\frac{{0.289}}{{0.00121}}}$  = $\sqrt {\displaystyle\frac{{0.289 \times 100000}}{{0.00121 \times 100000}}}$  = $\sqrt {\displaystyle\frac{{289 \times 100}}{{121}}}$  = $\displaystyle\frac{{170}}{{11}}$

21. $\left\{ {\displaystyle\frac{{{{(0.1)}^2} - {{(0.01)}^2}}}{{0.0001}} + 1} \right\}$ is equal to
a. 100
b. 101
c. 1010
d. 1101
Correct Option: A
Explanation:
$\left( {\displaystyle\frac{{0.01 - 0.0001}}{{0.0001}} + 1} \right)$ = $\left( {\displaystyle\frac{{0.0099}}{{0.0001}} + 1} \right)$ = (99 + 1) = 100

22. $\displaystyle\frac{{0.5 \times 0.5 \times 0.5 + 0.6 \times 0.6 \times 0.6}}{{0.5 \times 0.5 \times - 0.3 + 0.6 \times 0.6}}$ = ?
a. 0.3
b. 1.1
c. 0.1
d. 0.61
Correct Option: B
Explanation:
$\displaystyle\frac{{{{(0.5)}^3} + {{(0.6)}^3}}}{{{{(0.5)}^2} - 0.5 \times 0.6 + {{(0.6)}^2}}}$
$\left( {\displaystyle\frac{{{p^3} + {q^3}}}{{{p^2} - pq + {q^2}}}} \right) = (p + q)$
=(0.5+0.6)=1.1

23. $\displaystyle\frac{{{{(0.87)}^3} + {{(0.13)}^3}}}{{{{(0.87)}^2} + {{(0.13)}^2} - 0.87 \times 0.13}} = ?$
a. 0.13
b. 0.74
c. 0.87
d. 1
Correct Option: D
Explanation:
Given expression resembles $\displaystyle\frac{{{p^3} + {q^3}}}{{{p^2} + {q^2} - pq}}$
where p = 0.87 ; q=0.13
$\Rightarrow \displaystyle\frac{{{p^3} + {q^3}}}{{({p^2} + {q^2} - pq)}}$ = $\displaystyle\frac{{(p + q)({p^2} + {q^2} - pq)}}{{({p^2} + {q^2} - pq)}}$ =  p + q
$\Rightarrow$ (p+q) = (0.87 + 0.13)=1

24. $\displaystyle\frac{{{{(0.05)}^2} + {{(0.14)}^2} + {{(0.073)}^2}}}{{{{(0.005)}^2} + {{(0.041)}^2} + {{(0.0073)}^2}}} = ?$
a. 0.1
b. 10
c. 100
d. 1000
Correct Option: C
Explanation:
Given expression resembles $\displaystyle\frac{{{p^2} + {q^2} + {r^2}}}{{{{\left( {\displaystyle\frac{p}{{10}}} \right)}^2} + {{\left( {\displaystyle\frac{q}{{10}}} \right)}^2} + {{\left( {\displaystyle\frac{r}{{10}}} \right)}^2}}}$
=$\displaystyle\frac{{100({p^2} + {q^2} + {r^2})}}{{({p^2} + {q^2} + {r^2})}} = 100$

25. $\left[ {\displaystyle\frac{{104 \times 104 + 104 \times 0.04 + 0.04 \times 0.04}}{{104 \times 104 \times 104 - 0.04 \times 0.04 \times 0.04}}} \right]$ = ?
a. 0.10
b. 0.1
c. 1
d. 0.01
Correct Option: C
Explanation:
Given expression resembles $\displaystyle\frac{{{{(104)}^2} + 14 \times 0.04 + {{(0.04)}^2}}}{{{{(104)}^3} - {{(0.04)}^3}}}$ $\Rightarrow$ $\displaystyle\frac{{{p^2} + pq + {q^2}}}{{{p^3} - {q^3}}}$
= $\displaystyle\frac{{{p^2} + pq + {q^2}}}{{(p - q)({p^2} + pq + {q^2}}}$
$\Rightarrow \displaystyle\frac{1}{{p - q}} = \displaystyle\frac{1}{{104 - 0.04}} = 1$