Model 4 Simplification with continued fraction Practice Questions Answers Test with Solutions & More Shortcuts
simplification PRACTICE TEST [4 - EXERCISES]
Model 1 Simplification using VBODMAS
Model 2 Simplification based on square & square root
Model 3 Simplification based on cube & cube root
Model 4 Simplification with continued fraction
Question : 6
The value of $1+1/{1+1/{1+1/{1+1/{1+{2/3}}}}$ is
a) $8/5$
b) $34/21$
c) $17/3$
d) $21/13$
Answer »Answer: (b)
Expression
$1+1/{1+1/{1+1/{1+1/{1+{2/3}}}}$
= $1+1/{1+1/{1+1/{1+{1/{3+2}/3}}}}$
= $1+1/{1+1/{1+1/{1+ {3/5}}}}$
= $1+1/{1+1/{1+{1/{{5+3}/5}}}}$
= $1+1/{1+1/{1+{5/8}}}$
= $1+1/{1+{1/{{8+5}/8}}}$
= $1+1/{1+{8/13}} = 1+1/{{13+8}/13}$
= $1+{13/21} = {21+13}/21 = 34/21$
Question : 7 [SSC CPO S.I.2006]
$13/48$ is equal to
a) $1/{3+1/{1+1/{2+{1/4}}}}$
b) $1/{3+1/{1+1/{1+{1/8}}}}$
c) $1/{2+1/{1+{1/8}}}$
d) $1/{3+1/{1+{1/16}}}$
Answer »Answer: (a)
Check through options
$1/{3+1/{1+{1/{2 + {1/4}}}}}$
= $1/{3+1/{1+1/{{8+1}/4}}} = 1/{3+1/{1+{4/9}}}$
= $1/{3+{1/{{9 + 4}/9}}}= 1/{3+{9/13}}$
= $1/{{39+9}/13} = 13/48$
Question : 8 [SSC CPO S.I.2003]
The simplification of $5/{3+3/{1-{2/3}}}$ gives
a) $3/5$
b) $5/12$
c) $5/3$
d) 5
Answer »Answer: (b)
$5/{3+3/{1-{2/3}}}$
$5/{3+3/{{3 - 2}/3}} = 5/{3 + {3/{1/3}}}$
$5/{3 + 3 × 3} = 5/{3 + 9} = 5/12$
Question : 9
On simplification, the expression ${{4{1/7} - 2{1/7}}/{3{1/2} + 1{1/7}} ÷ {1/{2+1/{2+1/{5-{1/5}}}}}}$ is equal to
a) $14/65$
b) $56/53$
c) $24/53$
d) $28/65$
Answer »Answer: (b)
First part = ${4{1/7} - 2{1/7}}/{3{1/2} + 1{1/7}}$
= ${{29/7} - 15/7}/{{7/2}+ 8/7} = {14/7}/{{49+16}/14}$
= $2/{65/14} = {2×14}/65 = 28/65$
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 = ${28/65} ÷ {53/130}$
= $28/65 × 130/53 = 56/53$
Question : 10 [SSC CGL Tier-II 2015]
The value of $4 - 5/{1+1/{3+1/{2+{1/4}}}}$ is
a) $1/32$
b) $1/16$
c) $1/64$
d) $1/8$
Answer »Answer: (d)
Expression = $4 - 5/{1+1/{3+1/{2+{1/4}}}}$
= $4 - 5/{1+1/{3+{1/{{8+1}/4}}}}$
= 4 - $5/{1+1/{3+{4/9}}} = 4 - 5/{1+{1/{{27+4}/9}}}$
= $4 - 5/{1+{9/31}} = 4 - 5/{{31+9}/31}$
= $4 - {5×31}/40 = {160-155}/40$
= $5/40 = 1/8$
IMPORTANT quantitative aptitude EXERCISES
Model 4 Simplification with continued fraction Shortcuts »
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