model 1 find largest and smallest value Practice Questions Answers Test with Solutions & More Shortcuts

Question : 31 [SSC CHSL 2013]

Out of the numbers 0.3, 0.03, 0.9, 0.09 the number that is nearest to the value of $√{0.9}$ is

a) 0.9

b) 0.3

c) 0.03

d) 0.09

Answer: (a)

Question : 32 [SSC CGL Tier-I 2014]

Arranging the following in descending order, we get $√^3{4}, √2, √^6{3}, √^4{5}$

a) $√2>√^6{3}>√^3{4}>√^4{5}$

b) $√^3{4}>√^4{5}>√2>√^6{3}$

c) $√^4{5}>√^3{4}>√^6{3}>√2$

d) $√^6{3}>√^4{5}>√^3{4}>√2$

Answer: (b)

$√^3{4}, √2, √^6{3}, √^4{5}$

LCM of indices = LCM of 3,6, 4 and 2 = 12

$√^3{4}=(4)^{1/3}=(4)^{1/12}=√^12{4^4}=√^12{256}$

$√2=(2)^{1/2}=√^12{2^6}=√^12{64}$

$√^6{3}=√^12{3^2}=√^12{9}$

$√^4{5}=√^12{5^3}=√^12{125}$

Clearly,$√^3{4}>√^4{5}>√2>√^6{3}$

Question : 33 [SSC CGL Prelim 2008]

Which of the following is the largest number ? $√2, √^3{3}, √^4{4}, √^6{6}$

a) $√^4{4}$

b) $√2$

c) $√^3{3}$

d) $√^6{6}$

Answer: (c)

$√2, √^3{3}, √^4{4}, √^6{6}$

LCM of 2, 3, 4 and 6 = 12

$√2 =(2)^{1/2} =(2)^{6/12}$

$= (2^6)^{1/12}=√^12{2^6}=√^12{64}$

$√^3{3}=√^12{3^4}=√^12{81}$

$√^4{4}=√^12{4^4}=√^12{64}$

$√^6{6}=√^12{6^2}=√^12{36}$

Question : 34 [SSC CGL Prelim 1999]

Which one of the following is the least? $√3, √^3{2}, √2$ and $√^3{4}$

a) $√3$

b) $√2$

c) $√^3{4}$

d) $√^3{2}$

Answer: (d)

$√3, √^3{2}, √2$ and $√^3{4}$

LCM of 2 and 3 = 6

$√3 = (3)^{1/2}=3^{3/6}=(3^3)^{1/6}=√^6{27}$

$√^3{2} = √^6{2^2} =√^6{4}$

$√{2} = √^6{2^3} =√^6{8}$

$√^3{4} = √^6{4^2} =√^6{16}$

Question : 35 [SSC CHSL 2014]

The greatest number among the following is $4/9, √ {9/49}, 0.47↖{..}, (0.7)^2$

a) $0.47↖{..}$

b) $4/9$

c) $√{9/49}$

d) $(0.7)^2$

Answer: (d)

$4/9, √ {9/49}, 0.47, (0.7)^2$

Decimal equivalents of fractions :

$4/9=0.44; √{9/49}=3/7=0.43;$

$(0.7)^2=0.49$

IMPORTANT quantitative aptitude EXERCISES

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