Simplification Important Questions For SSC CGL 2018
Attempt the simplification Important questions for SSC CGL 2018 and score the good marks for your competitive exam. Practice more and more…
[math align=”left”]Q1.\quad \overline { 0.142857 } \div \overline { 0.285714 } \quad \quad[/math] is equal to
(a) 10
(b) 2
(c) 1/2
(d) 1/3
Correct Option (d). 1/2
Explaination:
[math align=”left”]\overline { 0.142857 } \div \overline { 0.285714 } =\frac { 142857 }{ 999999 } \div \frac { 285714 }{ 999999 } =\frac { 142857 }{ 285714 } =\frac { 1 }{ 2 }[/math]
Q2. The value [math align=”left”]of\frac { 3.157\times 4126\times 31.98 }{ 63.972\times 2835.121 } [/math]
(a) 0.002
(b) 0.02
(c) 0.2
(d) 2
Correct Option (c). 0.2
Explaination:
Taking approximate values, we have [math align=”left”]Answer:\frac{ 3\times 4126\times 3 }{ 64\times 2835 } =0.2046=0.2[/math]
[math align=”left”]Q3.\frac { { \left( 998 \right) }^{ 2 }-{ \left( 997 \right) }^{ 2 }-45 }{ { \left( 98 \right) }^{ 2 }-{ \left( 97 \right) }^{ 2 } } [/math] is equal to :
(a)1995
(b)195
(c)95
(d)10
Correct Option (d). 10
Explaination:
[math align=”left”]\frac { \left[ { \left( 998 \right) }^{ 2 }-{ \left( 997 \right) }^{ 2 } \right] -45 }{ { \left( 98 \right) }^{ 2 }-{ \left( 97 \right) }^{ 2 } } =\frac { \left( 998+997 \right) (998-997)-45 }{ (98+97)(98-97) } =\frac { 1995-45 }{ 195 } =\frac { 1950 }{ 195 } =10[/math]
Q4. $$The\quad value\quad of\quad { 999 }\frac { 995 }{ 999 } \times 999\quad equal\quad to$$
(a)990809
(b)998996
(c)999824
(d)998999
Correct Option (b). 9989996
Explaination:
$$\left( 999+\frac { 995 }{ 999 } \right) \times 999={ \left( 999 \right) }^{ 2 }+995={ \left( 1000-1 \right) }^{ 2 }+995=1000000+1-2000+995=998996$$
Q5. $$The\quad value\quad of\quad 0.008\times 0.01\times 0.072\div \left( 0.12\times 0.0004 \right) $$
(a) 1.2
(b) 0.12
(c) 0.012
(d) 1.02
Correct Option (b). 0.12
Explaination:
$$0.008\times 0.01\times 0.072+\left( 0.12+0.0004 \right) =0.008\times 0.01\times 0.072+\left( 0.000048 \right) $$
$$=0.008\times 0.01\times \frac { 0.072 }{ 0.000048 } =\frac { 0.000000576 }{ 0.00048 } =0.12$$
Q6. $$Given\quad that\quad \sqrt { 1225 } =35;then\quad \sqrt { 12.25 } +\sqrt { 0.1225 } +\sqrt { 0.001225 } is\quad equal\quad to\quad :$$
(a) 0.3885
(b) 388.5
(c) 38.85
(d) 3.885
Correct Option (d). 3.885
Explaination:
$$Expression\quad =\quad \sqrt { 12.25 } +\sqrt { 0.1225 } +\sqrt { 0.001225 } $$
$$=3.5+0.35+0.035;\left[ ::\quad \sqrt { 1225 } =35 \right] $$
$$=3.885$$
Q7. $$999\frac { 98 }{ 99 } \times 99\quad is\quad equal\quad to\quad :$$
(a) 98999
(b) 99899
(c) 99989
(d) 99998
Correct Option (a). 98999
Explaination:
$$\left( 999+\frac { 98 }{ 99 } \right) \times 99=999\times 99+98 $$
$$=99000-99+98=98999 $$
Q8. $$\left( 999\frac { 999 }{ 1000 } \times 7 \right) \quad is\quad equal\quad to:$$
(a) 6993 7/1000
(b) 7000 7/1000
(c) 6633 7/1000
(d) 6999 993/1000
Correct Option (d). 6999 993/1000
Explaination:
$$999\frac { 999 }{ 1000 } \times 7=\left( 999+\frac { 999 }{ 1000 } \right) \times 7=6993+\frac { 6993 }{ 1000 } =6999+6\frac { 993 }{ 1000 } =6993\frac { 993 }{ 1000 } $$
Q9. $$If\quad \frac { 1120 }{ \sqrt { P } } =80,\quad then\quad P\quad is\quad equal\quad to\quad :$$
(a) 14
(b) 140
(c) 196
(d) 225
Correct Option (c). 196
Explaination:
$$99980\times \sqrt { P } =1120;\rightarrow \sqrt { P } =\frac { 1120 }{ 80 } =14;\rightarrow P={ \left( 14 \right) }^{ 2 }=196 $$
Q10. $$2.8\overline { 768 } \quad is\quad equal\quad to\quad :$$
(a) 2 4394/4995
(b) 2 292/333
(c) 2 9/10
(d) 2 878/999
Correct Option (b). 2 292/333
Explaination:
$$2.8\overline { 768 } =2\frac { 8768-8 }{ 9990 } =2\frac { 8760 }{ 9990 } =2\frac { 292 }{ 333 } $$
Q11. $$\frac { \left( 100-1 \right) \left( 100-2 \right) \left( 100-3 \right) …\left( 100-200 \right) }{ 100\times 99\times 98\times …\times 3\times 2\times 1 } \quad is\quad equal\quad to$$
(a)$$\frac { 100 }{ 100\times 99\times 98\times …\times 3\times 2\times 1 } $$
(b) $$\frac { 1 }{ 99\times 98\times …\times 3\times 2\times 1 } $$
(c) 0
(d) $$\frac { 2 }{ 99\times 98\times …\times 3\times 2\times 1 } $$
Correct Option (c). 0
Explaination:
$$\frac { \left( 100-1 \right) \left( 100-2 \right) \left( 100-3 \right) …\left( 100-100 \right) …\left( 100-200 \right) }{ 100\times 99\times 98\times …\times 3\times 2\times 1 } \quad =\quad 0 $$
Q12. $$\frac { 256\times 256-144\times 144 }{ 112 } \quad is\quad equal\quad to$$
(a) 420
(b) 400
(c) 360
(d) 320
Correct Option (b). 400
Explaination:
$$Tricky\quad approach\quad ;\quad If\quad 256=a\quad and\quad 144=b,\quad then$$
$$Expression\quad =\quad \frac { { a }^{ 2 }-{ b }^{ 2 } }{ a-b } =\frac { \left( a+b \right) \left( a-b \right) }{ a-b } =a+b$$
Q13. Rs. 561 are divided among A,B and C such that A’s share is Rs. 120 more than B’s share and Rs. 120 less than C’s. B’s share will be
(a) Rs. 73
(b) Rs. 80
(c) Rs. 67
(d) Rs. 76
Correct Option (c). Rs. 67
Explaination:
$$Let\quad B’s\quad share\quad =Rs.\quad x$$
$$A’s\quad share=Rs.\left( x+120 \right) ;C’s\quad share=Rs.\left( x+240 \right) ;$$
$$::\quad x+x+120+x+240=561;\rightarrow 3x+360=561;\rightarrow 3x=561-360=201;\rightarrow x=\frac { 201 }{ 3 } =Rs.67$$
Q14. A certain amount of money is distributed among A,B and C, A gets B gets of the whole amount. If C gets Rs. 81, then B gets:
(a) Rs. 30
(b) Rs. 36
(c) Rs. 32
(d) Rs. 40
Correct Option (b). Rs. 36
Explaination:
$$Let\quad the\quad total\quad amount\quad be\quad Rs.\quad x$$
$$::\quad Share\quad of\quad C=x-\frac { 3x }{ 16 } -\frac { x }{ 4 } =\frac { 16x-3x-4x }{ 16 } =\frac { 9x }{ 16 } ;\quad Now\quad \frac { 9x }{ 16 } =81$$
$$\rightarrow x=Rs.\frac { 81\times 16 }{ 9 } =Rs.144;$$
$$\::\quad B’s\quad share=Rs.\frac { 144 }{ 4 } =Rs.36$$
Q15. $$\frac { 3.25\times 3.20\times -3.20\times 3.05 }{ 0.064 } \quad is\quad equal\quad to$$
(a) 1
(b) 15
(c) 13.5
(d) 10
Correct Option (d). 10
Explaination:
$$Expression\quad =\quad \frac { 3.20\left( 3.25-3.05 \right) }{ 0.064 } =\frac { 3.20\times 0.20 }{ 0.064 } =10$$
Q16. $$What\quad is\quad { 5 }^{ \frac { 1 }{ 2 } }.{ 5 }^{ \frac { 1 }{ 4 } }.{ 5 }^{ \frac { 1 }{ 8 } }…..equal\quad to?$$
(a) 6
(b) 1
(c) 0
(d) 5
Correct Option (d). 5
Explaination:
$$Expression\quad =\quad { 5 }^{ \frac { 1 }{ 2 } }.{ 5 }^{ \frac { 1 }{ 4 } }.{ 5 }^{ \frac { 1 }{ 8 } }…..\infty ={ 5 }^{ \frac { 1 }{ 2 } +\frac { 1 }{ 4 } +\frac { 1 }{ 8 } ……+…\infty }={ 5 }^{ \frac { 1 }{ 12 } }=5$$
$$\left[ Sum\quad to\quad infinity\quad of\quad Geometric\quad progression=\frac { a }{ 1-r } \right] $$
Q17. $$\frac { 0.04 }{ 0.03 } of\quad \frac { \left( 3\frac { 1 }{ 3 } -2\frac { 1 }{ 2 } \right) \div \frac { 1 }{ 2 } of\quad 1\frac { 1 }{ 4 } }{ \frac { 1 }{ 3 } +\frac { 1 }{ 5 } of\quad \frac { 1 }{ 9 } } \quad is\quad :$$
(a) 1
(b) 5
(c) 1/5
(d) 1/2
Correct Option (b). 5
Explaination:
$$Expression\quad =\quad \frac { 0.04 }{ 0.03 } \times \quad \frac { \left( \frac { 10 }{ 3 } -\frac { 5 }{ 2 } \right) \div \frac { 1 }{ 2 } \times \frac { 5 }{ 4 } }{ \frac { 1 }{ 3 } +\frac { 1 }{ 5 } \times \frac { 1 }{ 9 } } =\frac { 4 }{ 3 } \times \frac { \frac { 5 }{ 6 } \times \frac { 8 }{ 5 } }{ \frac { 15+1 }{ 45 } } =\frac { 4 }{ 3 } \times \frac { 45 }{ 16 } \times \frac { 4 }{ 3 } =5$$
Q18. $$\frac { 0.3555\times 0.5555\times 2.025 }{ 0.225\times 1.7775\times 0.2222 } \quad is\quad equal\quad to\quad :$$
(a) 5.4
(b) 4.58
(c) 4.5
(d) 5.45
Correct Option (c). 4.5
Explaination:
$$Expression\quad =\frac { 0.3555\times 0.5555\times 2.025 }{ 0.225\times 1.7775\times 0.2222 } =\frac { 3555\times 5555\times 2025 }{ 225\times 17775\times 2222 } =4.5$$
Q19. $$The\quad value\quad of\quad \frac { \sqrt { 80 } -\sqrt { 112 } }{ \sqrt { 45 } -\sqrt { 63 } } \quad is$$
(a) 3/4
(b) 1 3/4
(c) 1 1/3
(d) 1 7/9
Correct Option (c). 1 1/3
Explaination:
$$\frac { \sqrt { 80 } -\sqrt { 112 } }{ \sqrt { 45 } -\sqrt { 63 } } =\frac { \sqrt { 16\times 5 } -\sqrt { 16\times 7 } }{ \sqrt { 9\times 5 } -\sqrt { 9\times 7 } } =\frac { 4\sqrt { 5 } -4\sqrt { 7 } }{ 3\sqrt { 5 } -3\sqrt { 7 } } =\frac { 4\left( \sqrt { 5 } -\sqrt { 7 } \right) }{ 3\left( \sqrt { 5 } -\sqrt { 7 } \right) } =\frac { 4 }{ 3 } =1\frac { 1 }{ 3 } $$
Q20. The product of two numbers is 36 and their sum is 13. The positive difference between the two numbers is
(a) 1
(b) 3
(c) 5
(d) 9
Correct Option (c). 5
Explaination:
$$Let\quad the\quad number\quad be\quad x\quad and\quad y;\quad ::\quad x+y=13;\rightarrow xy=36;::{ \left( x-y \right) }^{ 2 }={ \left( x+y \right) }^{ 2 }-4xy$$
$$={ \left( 13 \right) }^{ 2 }-4\times 36=169-144=25;\rightarrow x-y=5$$
Q21. $$The\quad least\quad one\quad among\quad the\quad following\quad 12\frac { 1 }{ 2 } %\quad of\quad 100,\quad 12.\overline { 55 } ,{ \left( \frac { 18 }{ 5 } \right) }^{ 2 },\quad \sqrt { 160 } \quad is$$
(a) $$12\frac { 1 }{ 2 } %\quad of\quad 100$$
(b) $$12.\overline { 55 } $$
(c) $${ \left( \frac { 18 }{ 5 } \right) }^{ 2 }$$
(d) $$\sqrt { 160 } $$
Correct Option (b). $$12.\overline { 55 } $$
Explaination:
$$12\frac { 1 }{ 2 } %\quad of\quad 100\quad =\frac { 25 }{ 2 } =12.5;12.\overline { 55 }=12\frac { 59 }{ 99 } =12.05;{ \left( \frac { 18 }{ 5 } \right) }^{ 2 }={ \left( 3.6 \right) }^{ 2 }=12.96;\sqrt { 160 }=12.649 $$
Q22. $$\frac { 0.\overline { 83 } \div 7.5 }{ 2.3\overline { 21 } -0.0\overline { 98 } } \quad is\quad equal\quad to\quad :$$
(a) 0.6
(b) 0.1
(c) 0.06
(d) 0.05
Correct Option (d). 0.05
Explaination:
$$\frac { 0.\overline { 83 } \div 7.5 }{ 2.3\overline { 21 } -0.0\overline { 98 } } =\frac { \frac { 88-8 }{ 90 } +7.5 }{ 2\frac { 321-3 }{ 990 } -\frac { 98 }{ 990 } } =\frac { \frac { 75 }{ 90 } +7.5 }{ 2\frac { 318 }{ 990 } -\frac { 98 }{ 990 } } =\frac { \frac { 75 }{ 90 } +7.5 }{ 2\frac { 220 }{ 990 } } =\frac { 7.5 }{ 90\times 7.5 } \times \frac { 990 }{ 2200 } =\frac { 1 }{ 20 } =0.05$$
Q23. $$\left[ 2\sqrt { 54 } -6\sqrt { \frac { 2 }{ 3 } } -\sqrt { 96 } \right] \quad is\quad equal\quad to$$
(a) 0
(b) 1
(c) 2
(d) 3
Correct Option (a). 0
Explaination:
$$Expression=2\sqrt { 54 } -6\sqrt { \frac { 2 }{ 3 } } -\sqrt { 96 } =2\sqrt { 9\times 6 } -\sqrt { \frac { 2\times 6\times 6 }{ 3 } } -\sqrt { 16\times 6 } =2\times 3\sqrt { 6 } -2\sqrt { 6 } -4\sqrt { 6 } =0$$
Q24. $$The\quad Value\quad of\quad 99\frac { 95 }{ 99 } \times 99\quad is$$
(a) 9798
(b) 9997
(c) 9898
(d) 9896
Correct Option (d). 9896
Explaination:
$$Expression=\left( 99+\frac { 95 }{ 99 } \right) \times 99=99\times 99+95=9896$$
Q25. $$\left( \frac { \sqrt { 625 } }{ 11 } \times \frac { 14 }{ \sqrt { 25 } } \times \frac { 11 }{ \sqrt { 196 } } \right) \quad is\quad equal\quad to$$
(a) 6
(b) 5
(c) 8
(d) 11
Correct Option (b). 5
Explaination:
$$\left( \frac { \sqrt { 625 } }{ 11 } \times \frac { 14 }{ \sqrt { 25 } } \times \frac { 11 }{ \sqrt { 196 } } \right) \quad =\left( \frac { 25 }{ 11 } \times \frac { 14 }{ 5 } \times \frac { 11 }{ 14 } \right) =5$$
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