Model 4 Simplification with continued fraction Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 4 EXERCISES
The following question based on simplification topic of quantitative aptitude
(a) $101/100$
(b) $20/101$
(c) $90/101$
(d) $100/101$
The correct answers to the above question in:
Answer: (b)
$1 + 1/{10 + {1/10}} = 111/101 = a$
and, $1 - 1/{10 + {1/10}} = 91/101 = b$
${a^2 - b^2}/{(a + b)} = {(a+b)(a-b)}/(a+b)$ = (a-b)
$= 111/101 - 91/101 = 20/101$
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Read more problems based on continued fraction Based Quantitative Aptitude Questions and Answers
Question : 1
The value of $1/{3 + 1/{2 - 1/{7/9}}} + 17/22$ is :
a) 1
b) $5/22$
c) $22/5$
d) $12/22$
Answer »Answer: (a)
$1/{3 + 1/{2 - {1/{7/9}}}} + 17/22$
= $1/{3 + 1/{2 - {9/7}}} + 17/22$
= $1/{3 + 1/{{14 - 9}/7}} + 17/22$
= $1/{3 + {1/{5/7}}} + 17/22 = 1/{3 + {7/5}} + 17/22$
= $1/{{15+7}/5} + 17/22$
= $5/22 + 17/2 = 22/22 = 1$
Question : 2
The value of $3+3/{3+1/{3+{1/3}}}$ is
a) $41/11$
b) $46/11$
c) $43/11$
d) $40/11$
Answer »Answer: (c)
Expression = $3+3/{3+{1/{{9+1}/3}}}$
= $3+3/{3+{3/10}} = 3+3/{{30+3}/10}$
= $3+{30/33} = 3+{10/11}$
= ${33+10}/11 = 43/11$
Question : 3
$1 + 1/{1 + {1/5}}$ = ?
a) None of the above
b) $15/6$
c) $13/6$
d) $11/6$
Answer »Answer: (d)
Expression = $1+1/{1+{1/5}}$
= $1+1/{{5+1}/5} = 1+{5/6}$
= ${6+5}/6 = 11/6$
Question : 4
$√{{4{1/7} - 2{1/4}}/{3{1/2} + 1{1/7}} ÷ {2/{2+1/{2+1/{5-{1/5}}}}}}$ is equal to
a) 2
b) 3
c) 4
d) 1
Answer »Answer: (d)
${4{1/7} - 2{1/4}}/{3{1/2}+1{1/7}} = {29/7 - 9/4}/{7/2 +8/7}$
= ${{116 - 63}/28}/{{49+16}/14} = 53/28 ×14/65 = 53/130$
Again,
$1/{2+1/{2+{1/{{25 - 1}/5}}}} =1/{2+1/{2+{5/24}}}$
= $1/{2+{1/{{48+5}/24}}} = 1/{2+{24/53}}$
$1/{{106+24}/53} = 53/130$
Expression = $√{{53/130} ÷ {53/130}} = 1$
Question : 5
If $[4-5/{1+1/{3+1/{2+{1/4}}}}]^{th}$ part of a journey takes 10 minutes, then to complete $3/5$ th of that journey, it will take
a) 36 minutes
b) 48 minutes
c) 45 minutes
d) 40 minutes
Answer »Answer: (b)
$4 - 5/{1+1/{3+{1/{9/4}}}} = 4 - 5/{1+{1/{3+{4/9}}}}$
= $4 - 5/{1+{1/{{27+4}/9}}} = 4 - 5/{1+{9/31}}$
= $4 - 5/{40/31} = 4 - {5×31}/40$
= $4 - 31/8 = {32-31}/8 = 1/8$
Since, Time taken in completing $1/8$ part = 10 minutes
Time taken in completing $3/5$ part
= 10 × 8 × $3/5$ = 48 minutes
GET simplification PRACTICE TEST 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
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