Simplification-Quantitative Aptitude for IBPS & SSC Exams

  1. The value of  \frac{0.125+0.027}{0.25-0.15+0.09}

(a) 0.2       (b) 0.25      (c) 0.3        (d) 0.8

Solution: (d) According to the question

\frac{0.125+0.027}{0.25-0.15+0.09}

\frac{0.152}{0.19}    \Rightarrow 0.8    Correct Answer
2. \frac{(7.5)^{3}+1}{(7.5)^{2}-6.5} is equal to

(a) 2.25     (b) 9/5      (c) 4.75      (d) 8.5

Solution:(d). According to the question

\Rightarrow \frac{(7.5)^{3}+1}{(7.5)^{2}-6.5}

[a^{3}+b^{3}=(a+b)(a^{2}+b^{2}-ab)

\frac{(7.5+1)[(7.5)^{2}+1-7.5\times 1]}{(7.5)^{2}-7.5\times 1+1^{2}}

\Rightarrow 8.5        Correct Answer
3. The value of  \frac{(2.697-0.498)^{2}+(2.697+0.498)^{2}}{2.697\times2.697+0.498\times0.498}

(a)  4          (b)2      (c) 2.199          (d) 3.195

Solution (b) according to question

\frac{(2.697-0.498)^{2}+(2.697+0.498)^{2}}{2.697\times2.697+0.498\times0.498}

Let a =2.697 , b = 0.498

\frac{(a-b)^{2}=(a+b)^{2}}{a^{2}+b^{2}}

 \frac{a^{2}+B^{2}-2ab+a^{2}+b^{2}+2ab}{a^{2}+b^{2}}

\frac{2(a^{2}+b^{2})}{a^{2}+b^{2}}\Rightarrow2      Correct Answer
4. \sqrt{\frac{0.081\times0.484}{0.0064\times6.25}} is equal to

(a) 9         (b) .9        (c) 99         (d) .99

Solution: (d). according to the question

\sqrt{\frac{0.081\times0.484}{0.0064\times6.25}}

\frac{9\times 22}{8\times 25} \Rightarrow0.99       Correct Answer

5. Given that \sqrt{13} = 3.6 and \sqrt{130} = 11.4, then  the value of \sqrt{13}+\sqrt{1300}+\sqrt{0.013} is equal to

(a) 36.164                  (b) +637.254

(c) 39.714                   (d) 37.154

Solution: (c). according to the question

\sqrt{13}+\sqrt{1300}+\sqrt{0.013}

3.6+10\sqrt{13}+\frac{\sqrt{130}}{10000}

3.6+10\times 3.6+\frac{11.4}{100}=39.714     Correct Answer

6. The largest number of given digits, which is a perfect square is

(a) 99999    (b) 99976   (c) 99856   (d)99764

Solution: (c) As we know that the square of 316 is 99856

7. The number, whose square is equal to the difference of the squares of the numbers 68 and 32, is

(a) 36          (b) 48         (c) 60         (d) 64

Solution: (c). According to the question

(68)^{2}-(32)^{2}

(68+32)(68-32)

As [a^{2}-b^{2}=(a+b)(a-b)\ ]

100\times 36=3600=(60)^{2}=60     Correct Answer

8. The least fraction to be subtracted from the expression \frac{3\frac{1}{4}-\frac{4}{5}of\frac{5}{6}}{4\frac{1}{3}+\frac{1}{5}-(\frac{3}{10}+21\frac{1}{5})} to make it an integer.

(a)\frac{1}{2}\ \ \ \ (b)\frac{5}{6}\ \ \ \ (c) \frac{1}{4}\ \ \ \ (d)\frac{3}{10}

Solution: (a) According to the question

 \frac{3\frac{1}{4}-\frac{4}{5}of\frac{5}{6}}{4\frac{1}{3}+\frac{1}{5}-(\frac{3}{10}+21\frac{1}{5})}

\frac{\frac{13}{4}-\frac{4}{5}\times \frac{5}{6}}{\frac{13}{3}\times 5-(\frac{3}{10}+\frac{106}{5})}

\frac{\frac{\frac{39-8}{12}}{650-9-636}}{30}    \Rightarrow\frac{31}{12}\times \frac{30}{5}=\frac{31}{2}=15\frac{1}{2}

Therefore, Least fraction number should be subtracted is,

 15\frac{1}{2}-15=\frac{1}{2}   (least fraction number)       Correct Answer

9. If \sqrt[2]{0.014\times0.14x}=0.014*0.14\sqrt[2]{y}, find the value of \frac{x}{y},

(a) 0.000196    (b) 0.00196      (c) 0.0196       (d) 0.196

Solution: (b) According to question

\sqrt[2]{0.014\times 0.14x}=0.014\times 0.14 \sqrt[2]{y}

Squaring both side

0.014\times 0.14x=(0.014)^{2}\times (0.14)^{2}xy

\frac{x}{y}=0.014\times 0.14

\frac{x}{y}=0.00196       Correct Answer

10. The simplified value of  \sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\sqrt{49}}}}}

(a)3                              (b) 2         (c) 4            (d) 6

Solution: (a). According to the question

\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\sqrt{49}}}}}

\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+7 }}}}

 \sqrt{5+\sqrt{11+\sqrt{19+\sqrt{36}}}}

\sqrt{5+\sqrt{11+\sqrt{19+6}}}

\sqrt{5+\sqrt{11+\sqrt{25 }}}\Rightarrow\sqrt{5+\sqrt{11+5}}

\sqrt{5+\sqrt{16}}\Rightarrow\sqrt{5+4 }\Rightarrow\sqrt{9}=3      Correct Answer

11. The smallest number that must be subtracted from 1000 to make the resulting number a perfect square is

(a) 37           (b) 38       (c)39        (d) 40

Solution. (c) As we  know that square of ‘31’ is 961

Therefore,  1000-961 = 39        Correct Answer

12. \frac{4.41\times0.16}{2.1\times1.6\times0.21}  is simplified to

(a) 1            (b) 0.1        (c) 0.01    (d) 10

Solution: (a) According to the question

\frac{4.41\times0.16}{2.1\times1.6\times0.21} = \frac{0.7056}{0.7056} \Rightarrow 1        Correct Answer

13. (0.1\times0.01\times0.01\times10^{7})  is equal to

(a)100        (b) \frac{1}{10}          (c)  \frac{1}{100}      (d) 10

Solution: (a) According to the question

0.1\times 0.01\times 0.01\times 10^{2}=100          Correct Answer

14. \frac{3.25\times3.20-3.20\times3.05}{0.064}  is equal to:

(a)1             (b)  \frac{1}{2}        (c)   \frac{1}{10}          (d) 10

Solution: (d). According to the question

\frac{3.25\times 3.20-3.20\times 3.05}{0.064}\\

\frac{10.4-9.76}{0.064}\Rightarrow\frac{0.64}{0.064}=10          Correct Answer

15. \left \{ \frac{(0.1)^{2}-(0.01)^{2}}{0.0001}\ \right \}+ 1     is equal to

(a)1010       (b) 110       (c) 101     (d) 100

Solution: (d) According to the question

\left [ \frac{(0.1)^{2}-(0.01)^{2}}{0.0001} \right ]+1 \Rightarrow\left [ \frac{(0.1+0.01)(0.1-0.01)}{0.0001}\ \right ]+1

\frac{0.11\times 0.09}{0.0001}+1\Rightarrow99+1=100            Correct Answer

16. (0.5\times5+0.25\times0.5+0.5\times4+0.5\times0.75)    is equal to

(a)5           (b) 10          (c) 15            (d) 20

Solution: (a) According to the question

0.5\times 5+0.25\times 0.5+0.5\times 4+0.5\times 0.75

2.5+0.125+2+0.375=5      Correct Answer

17. \frac{(5+5+5+5)\div 5}{3+3+3+3\div 3}    is equal to

(a) 1           (b) \frac{3}{10}           (c) \frac{4}{9}              (d) \frac{2}{5}

Solution: (d) According to the question

\frac{(5+5+5+5)\div 5}{3+3+3+3\div 3}       \Rightarrow     \frac{20\div 5}{9+1} \Rightarrow\frac{4}{10} \Rightarrow\frac{2}{5}     Correct Answer

18. \frac{(100-1)(100-2)(100-3)\......................(100-200)}{100\times 99\times 98\times .................\times 3\times 2\times 1}    is equal to

(a) \frac{100}{99\times 98\times 97\times \ldots \times 3\times 2\times 1}

(b) -\frac{1}{99\times 98\times 97\times \ldots \times 3\times 2\times 1}

(c) 0

(d) -\frac{2}{99\times 98\times 97\times \ldots \times 3\times 2\times 1}

Solution: (c).According to the question

\frac{(100-1)(100-2)(100-3)\......................(100-200)}{100\times 99\times 98\times .................\times 3\times 2\times 1}

\frac{99\times 98\times 97\times ........ .1\times 0\times 1\times -2\........... .(100-200)}{100\times 99\times 98\times ........... ..\times 3\times 2\times 1}=0      Correct Answer

19. (0.9\times 0.9\times0.9+0.1\times 0.1\times 0.1)  is equal to

(a) 0.73    (b) 0.82    (c) 0.9      (d) 1.00

Solution: (a) According to the question

(0.9\times 0.9\times0.9+0.1\times 0.1\times 0.1) \Rightarrow   0.729+0.001=0.73         Correct Answer

20. \sqrt{\frac{0.009\times 0.036\times 0.016\times 0.08}{0.002\times 0.0008\times 0.0002}}  is equal to

(a) 34     (b) 36       (c) 38        (d) 39

Solution: (b). According to the question

\sqrt{\frac{0.009\times 0.036\times 0.016\times 0.08}{0.002\times 0.0008\times 0.0002}}  \Rightarrow \sqrt{\frac{(9\times 36\times 16\times 8)}{(2\times 8\times 2)}} =3\times 6\times 2=36     Correct Answer

 

 

 

 

 

 

 

 

 

 

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