Practice Simplification - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) The value of $5/{1{7/8} of 1{1/3}} × {2{1/10}}/{3{1/2}} of 1{1/4}$
(a)
(b)
(c)
(d)
Using Rule 1,
$5/{15/8 × 4/3} × {21/10}/{7/2} of {5/4}$
=$5 × 2/5 × 21/10 × 2/7 × 5/4$
=$3/2 = 1{1}/2$
Q-2) On simplification of ${(2.644)^2 - (2.356)^2}/{0.288}$ we get :
(a)
(b)
(c)
(d)
? = ${(2.644)^2 - (2.356)^2}/{0.288}$
= ${(2.644 - 2.356)(2.644 + 2.356)}/{0.288}$
= ${0.288 × 5}/{0.288} = 5$
Using Rule 8,${a^2 - b^2}/{a - b} = a+b or, {a^2 - b^2}/{a + b} = a-b$
${(2.644)^2 - (2.356)^2}/{0.288}$
= ${(2.644)^2 - (2.356)^2}/{2.644 + 2.356}$
= (2.644 + 2.356) = 5
Q-3) The value of $√{5+ √{11 + √{19 + √{29 + √{49}}}}}$ is
(a)
(b)
(c)
(d)
$√{5+ √{11 + √{19 + √{29 + √{49}}}}}$
$√{5+ √{11 + √{19 + √{29 + 7}}}}$
$√{5+ √{11 + √{19 + 6}}}$
$√{5+ √{11 + √{25}}}$
$√{5+ √{11 + 5}}$
$√{5+ 4} = √9$ = 3
Q-4) The value of $(3 + √{8}) + 1/{3 - √{8}} - (6 + 4√{2})$ is
(a)
(b)
(c)
(d)
${1/{3 - √8}} = {3 + √8}/{(3 - √8)(3 + √8)}$
(Rationalising the denominator)
= ${3 + √8}/{9 - 8} = 3 + √8$
Expression
= $3 + √{8} + 3 + √{8} - 6 - 4√{2}$
= $6 + 2√{8} - 6 - 4√{2} = 2√{8} - 4√{2}$
= $2 × 2√{2} - 4√{2} = 0$
Q-5) The square root of : ${(0.75)^3}/{1 - 0.75} + [0.75 + (0.75)^2 + 1]$ is :
(a)
(b)
(c)
(d)
Expression
= ${(0.75)^3 + (1 - 0.75)((0.75)^2 + 0.75 × 1 + {1}^2)}/{1 - 0.075}$
= ${(0.75)^3 + 1^3 - (0.75)^3}/{0.25}$
= $1/{0.25} = 100/25 = 4$
Required square root = $√{4} = 2$
Q-6) The value of ${(75.8)^2 - (55.8)^2}/20$ is
(a)
(b)
(c)
(d)
${(75.8)^2 - (55.8)^2}/20$
= ${(75.8 - 55.8)(75.8 + 55.8)}/20$
= ${20 × 131.6}/20$ = 131.6
Using Rule 8,
${(75.8)^2 - (55.8)^2}/{(75.8 - 55.8)}$
= 75.8 + 55.8 = 131.6
Q-7) The value of $√{{(0.1)^2 + (0.01)^2 + (0.009)^2}/{(0.01)^2 + (0.001)^2 + (0.0009)^2}}$ is :
(a)
(b)
(c)
(d)
$√{{(0.1)^2 + (0.01)^2 + (0.009)^2}/{(0.01)^2 + (0.001)^2 + (0.0009)^2}}$
= $√{{0.01 + 0.0001 + 0.000081}/{0.0001 + 0.000001 + 0.00000081}}$
= $√{{0.010181}/{0.00010181}} = √{100}$ = 10
Q-8) $√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$ is equal to
(a)
(b)
(c)
(d)
Expression
= $√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$
= $√{{9 × 36 × 16 × 8}/{2 × 8 × 2}}$
= 3 × 2 × 3 × 2 = 36
Q-9) The value of $√{{(0.03)^2 + (0.21)^2 + (0.065)^2}/{(0.003)^2 + (0.021)^2 + (0.0065)^2}}$ is :
(a)
(b)
(c)
(d)
Let 0.03 = x ⇒ 0.003 = $x/10$
0.21 = y ⇒ 0.021 = $y/10$
and 0.065 = z ⇒ 0.0065= $z/10$
Expression
= $√{{x^2 + y^2 + z^2}/{(x/10)^2 + (y/10)^2 + (z/10)^2}}$
= $√{100{(x^2 + y^2 + z^2)}/ {(x^2 + y^2 + z^2)}}$
= $√{100}$ = 10
Q-10) $√^3{(333)^3 + (333)^3 + (334)^3 - 3 × 333 × 333 × 334}$ is equal to
(a)
(b)
(c)
(d)
We know that
$a^3 + b^3 + c^3$ - 3abc
= (a+b+c)$(a^2+b^2+c^2$ - ab - bc - ca)
= $1/2 (a + b + c) [(a - b)^2 + (b - c)^2 + (c - a)^2 ]$
∴ $√^3{(333)^3 + (333)^3 + (334)^3 - 3 × 333 × 333 × 334}$
= $√^3{1/2 (333 + 333 + 334)[(333 - 333)^2 + (333 - 334)^2 + (334 - 333)^2]}$
= $√^3{1/2 × 1000 × 2} = √^3{1000}$
= $√^3{10 × 10 × 10}$ = 10
Q-11) The value of 0.008 × 0.01 × 0.072 ÷ (0.12 × 0.0004) is :
(a)
(b)
(c)
(d)
Using Rule 1,
0.008 × 0.01 × 0.072 ÷ (0.12 × 0.0004)
= 0.008 × 0.01 × 0.072 ÷ (0.000048)
= 0.008 × 0.01 × ${0.072}/{0.000048}$
= ${0.00000576}/{0.000048}$ = 0.12
Q-12) On simplification 3034 - (1002 ÷ 20.04) is equal to
(a)
(b)
(c)
(d)
Using Rule 1,
3034 - (1002 ÷ 20.04)
= 3034 - $1002/{20 .04}$
= 3034 - $1002/2004 × 100$
= 3034 - 50 = 2984
Q-13) ${(3.63)^2 - (2.37)^2}/{3.63 + 2.37}$ is simplified to
(a)
(b)
(c)
(d)
Using Rule 8,
Let 3.63 = a and 2.37 = b
Expression = ${a^2 - b^2}/{a + b}$
= ${(a - b)(a + b)}/{a + b}$
= a - b = 3.63 - 2.37 = 1.26
Q-14) The square root of ${0.342 × 0.684}/{0.000342 × 0.000171}$ is :
(a)
(b)
(c)
(d)
$√{{0.342 × 0.684}/{0.000342 × 0.000171}}$
= $√{{342 × 684 × {10}^6}/{342 × 171}}$
= $√{4 × {10}^6} = 2 × {10}^3$ = 2000
Q-15) What is the square root of 0.09?
(a)
(b)
(c)
(d)
$√{0.09} = √{0.3 × 0.3} = 0.3$
Q-16) The value of $√^3{7/875}$ is equal to
(a)
(b)
(c)
(d)
$√^3{7/875} = (7/875)^{1/3}$
= $(1/125)^{1/3} = 1/5$
Q-17) ${4{2/7} - {1/2}}/{3{1/2} + 1{1/7}}$ ÷ $1/{2+1/{2+1/{5-{1/5}}}}$ is equal to
(a)
(b)
(c)
(d)
First part = ${30/7 - 1/2}/{7/2 + 8/7}$
= ${{60 - 7}/14}/{{49+16}/14} = {53/14} × 14/65 = 53/65$
Second part = $1/{2+1/{2+{1/{{25 - 1}/5}}}}$
= $1/{2+1/{2+{5/24}}} = 1/{2+{1/{{48+5}/24}}}$
= $1/{2+{24/53}} = 1/{{106+24}/53} = 53/130$
Expression = ${53/65} ÷ {53/130} = 53/65 × 130/53 = 2$
Q-18) The value of $1+1/{1+1/{1+1/{1+1/{1+{2/3}}}}$ is
(a)
(b)
(c)
(d)
Expression
$1+1/{1+1/{1+1/{1+1/{1+{2/3}}}}$
= $1+1/{1+1/{1+1/{1+{1/{3+2}/3}}}}$
= $1+1/{1+1/{1+1/{1+ {3/5}}}}$
= $1+1/{1+1/{1+{1/{{5+3}/5}}}}$
= $1+1/{1+1/{1+{5/8}}}$
= $1+1/{1+{1/{{8+5}/8}}}$
= $1+1/{1+{8/13}} = 1+1/{{13+8}/13}$
= $1+{13/21} = {21+13}/21 = 34/21$
Q-19) The simplification of $5/{3+3/{1-{2/3}}}$ gives
(a)
(b)
(c)
(d)
$5/{3+3/{1-{2/3}}}$
$5/{3+3/{{3 - 2}/3}} = 5/{3 + {3/{1/3}}}$
$5/{3 + 3 × 3} = 5/{3 + 9} = 5/12$
Q-20) $1 + 1/{1+{1/2}}$ is equal to
(a)
(b)
(c)
(d)
Expression = $1 + 1/{1 + {1/2}}$
= $1 + 1/{{2+1}/2} = 1+{2/3}$
= ${3 + 2}/3 = 5/3$