This set of Aptitude Questions and Answers (MCQs) focuses on “Simplification – Set 4”.
1. If \(\frac{a}{b+c}\)=x, \(\frac{b}{c+a}\)=y and \(\frac{c}{a+b}\)=z, then find the value of \(\frac{1}{1+x}+\frac{1}{1+y}+\frac{1}{1+z}\).
a) 2
b) 1
c) 3
d) 6
View Answer
Explanation: \(\frac{1}{1+x}+\frac{1}{1+y}+\frac{1}{1+z}=\frac{1}{1+\frac{a}{b+c}}+\frac{1}{1+\frac{b}{c+a}}+\frac{1}{1+\frac{c}{a+b}}=\frac{b+c}{a+b+c}+\frac{c+a}{a+b+c}+\frac{a+b}{a+b+c}=\frac{2a+2b+2c}{a+b+c}\)=2.
2. If y = (x+4)2, then find the value of (-3x-12)2.
a) 9y2
b) 9y
c) -9y2
d) -3y
View Answer
Explanation: (-3x-12)2 = [-3(x+4)]2 = 9y.
3. Find the value of 2a3-[3a3+4a2-{2a3-7a3}+5a3-7a2].
a) -11a3+3a2
b) 7a2+3a3
c) 11a3-3a2
d) -11a3-3a2
View Answer
Explanation: 2a3-[3a3+4a2-{2a3-7a3}+5a3-7a2] = 2a3-[3a3+4a2+5a3+5a3-7a2] = 2a3-[13a3-3a2] = -11a3+3a2.
4. Find the value of x if \(\frac{\frac{7\frac{1}{2}-5\frac{3}{4}}{3\frac{1}{2}+x}}{\frac{\frac{1}{2}+1 \frac{1}{4}}{1 \frac{1}{5}+3 \frac{1}{2}}}=\frac{3}{5}\).
a) 4 \(\frac{1}{2}\)
b) 4 \(\frac{1}{3}\)
c) 4 \(\frac{2}{7}\)
d) 4 \(\frac{2}{3}\)
View Answer
Explanation: \(\frac{7\frac{1}{2}-5\frac{3}{4}}{3\frac{1}{2}+x}=\frac{3}{5}*\frac{\frac{1}{2}+1 \frac{1}{4}}{1 \frac{1}{5}+3 \frac{1}{2}}\).
\(\frac{\frac{15}{2}-\frac{23}{4}}{\frac{7}{2}+x}=\frac{3}{5}*\frac{\frac{1}{2}+\frac{5}{4}}{\frac{6}{5}+\frac{7}{2}}\).
\(\frac{\frac{7}{4}}{\frac{7}{2}+x}=\frac{3}{5}*\frac{\frac{7}{4}}{\frac{47}{10}}\).
\(\frac{\frac{7}{4}}{\frac{7}{2}+x}=\frac{21}{94}\).
\(\frac{\frac{7}{4}}{\frac{21}{94}}=\frac{7}{2}\)+x.
\(\frac{47}{6}-\frac{7}{2}\)=x.
x=\(\frac{13}{3}\)=4\(\frac{1}{3}\).
5. If [p] means the greatest integer less than or equal to p, then find the value of \(\Big[-\frac{1}{8}\Big]+\Big[5 \frac{2}{3}\Big]-\Big[3 \frac{3}{4}\Big]\).
a) 5
b) 8
c) 1
d) 2
View Answer
Explanation: \(\Big[-\frac{1}{8}\Big]+\Big[5 \frac{2}{3}\Big]-\Big[3 \frac{3}{4}\Big]\)=-1+5-3=1.
6. If R = xS – 4, when S = 5 and R = 16. Then find the value of R when S = 8.
a) 28
b) 36
c) 34
d) 32
View Answer
Explanation: R = xS – 4 🡪 16 = 5x – 4 🡪 x = 4.
R = 4*8 – 4 = 28.
7. How many \(\frac{1}{16}\)s are there in 43\(\frac{3}{4}\)?
a) 400
b) 600
c) 700
d) 500
View Answer
Explanation: =\(\frac{43\frac{3}{4}}{\frac{1}{16}}=\frac{175}{4}\)*16=700.
8. If x = (5 ÷ 4) ÷ 4 ÷ 5, y = 5 ÷ (4 ÷ 4) ÷ 5 and z = 5 ÷ 4 ÷ (4 ÷ 5). Which of the following three number is/are maximum?
a) x
b) y
c) z
d) y & z
View Answer
Explanation: x = (5 ÷ 4) ÷ 4 ÷ 5 = \(\frac{\frac{5}{4}}{4}\)÷5=\(\frac{\frac{5}{16}}{5}=\frac{1}{16}\).
y = 5 ÷ (4 ÷ 4) ÷ 5 = 5÷\(\frac{4}{4}\)÷5=1.
z = 5 ÷ 4 ÷ (4 ÷ 5) = 5÷4÷\(\frac{4}{5}=\frac{\frac{\frac{5}{4}}{4}}{5}=\frac{25}{16}\).
Therefore, z is the maximum.
9. A student was asked to solve the fraction \(\frac{\frac{7}{4}+2 \frac{4}{5} \, of \, \frac{15}{7}}{3+1 \frac{2}{5}}\) and his answer was 1/8. By how much was his answer wrong?
a) 15/11
b) 17/11
c) 12/11
d) 18/11
View Answer
Explanation: \(\frac{\frac{7}{4}+2 \frac{4}{5} \, of \, \frac{15}{7}}{3+1 \frac{2}{5}}=\frac{\frac{7}{4}+\frac{14}{5}*\frac{15}{7}}{3+\frac{7}{5}}=\frac{155}{88}\).
\(\frac{155}{88}-\frac{1}{8}=\frac{18}{11}\).
Therefore, the correct answer was 18/11 wrong from his answer.
10. Find the value of \(\frac{1}{4}\)÷2\(\frac{3}{4}\) of \(\frac{5}{4}-\frac{\frac{1}{2}-\frac{1}{3}}{\frac{1}{2}+\frac{1}{3}}\)*5 \(\frac{1}{4}+\frac{7}{4}\).
a) 15/22
b) 18/23
c) 17/22
d) 13/23
View Answer
Explanation:\(\frac{1}{4}\)÷2\(\frac{3}{4}\) of \(\frac{5}{4}-\frac{\frac{1}{2}-\frac{1}{3}}{\frac{1}{2}+\frac{1}{3}}\)*5 \(\frac{1}{4}+\frac{7}{4}=\frac{\frac{1}{4}}{\frac{11}{4}*\frac{5}{4}}-\frac{\frac{1}{6}}{\frac{5}{6}}*\frac{21}{4}+\frac{7}{4}=\frac{4}{55}-\frac{1}{5}*\frac{21}{4}+\frac{7}{4}=\frac{4}{55}-\frac{21}{20}+\frac{7}{4}=\frac{17}{22}\).
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