This set of Aptitude Questions and Answers (MCQs) focuses on “Simplification – Set 5”.
1. Find the value when \(\frac{1}{2}-\frac{1}{4}+\frac{1}{6}-\frac{1}{8}\) is divided by \(\frac{2}{5}-\frac{4}{9}+\frac{1}{4}-\frac{5}{18}\).
a) -105/26
b) 107/26
c) -105/29
d) -111/31
View Answer
Explanation: \(\frac{(\frac{1}{2}-\frac{1}{4}+\frac{1}{6}-\frac{1}{8})}{\frac{2}{5}-\frac{4}{9}+\frac{1}{4}-\frac{5}{18}}=\frac{\frac{7}{24}}{-\frac{13}{180}}=-\frac{105}{26}\).
2. Which of the following can be used to compute \(\Big(48*5\frac{3}{5}\Big)\)?
a) 40*5+8*5\(\frac{3}{5}\)
b) 48*50+48*\(\frac{3}{5}\)
c) 40*5\(\frac{3}{5}\)+8*5
d) 48*\(\frac{3}{5}\)+40*6
View Answer
Explanation: =48*5\(\frac{3}{5}\)=48*\(\Big(5+\frac{3}{5}\Big)\)
=48*\(\frac{3}{5}\)+48*5=48*\(\frac{3}{5}\)+(40+8)*5=48*\(\frac{3}{5}\)+40*5+5*8.
=48*\(\frac{3}{5}\)+40(5+1)=48*\(\frac{3}{5}\)+40*6.
3. If x=\(\frac{p}{p-1}\) and y=\(\frac{1}{p-1}\) for p≠1, then which of the following is true?
a) x is equal to y
b) x is equal to y only if p<1
c) x is greater than y
d) x is greater than y only if p<1
View Answer
Explanation: Consider p=2 which is greater than 1.
x=\(\frac{2}{2-1}\)=2 and y=\(\frac{1}{2-1}=\frac{1}{2}\).
Consider p=0.5 which is lesser than 1.
x=\(\frac{0.5}{0.5-1}\)=-1 and y=\(\frac{1}{0.5-1}\)=-2.
In both the cases, x is greater than y.
4. If 0<x<1, then which of the following is true for \(\Big(x+\frac{1}{x}\Big)\)?
a) less than 2
b) less than 4
c) greater than 8
d) greater than 2
View Answer
Explanation: For x=\(\frac{3}{4},x+\frac{1}{x}=\frac{3}{4}+\frac{4}{3}=\frac{25}{12}\)=2.083.
For x=\(\frac{1}{4}\),x+\(\frac{1}{x}=\frac{1}{4}+4=\frac{17}{4}\)=4.25.
For x=\(\frac{1}{2}\),x+\(\frac{1}{x}=\frac{1}{2}+2=\frac{5}{2}\)=2.5.
In all the cases, \(\Big(x+\frac{1}{x}\Big)\) is greater than 2, for 0<x<1.
5. If \(\frac{p}{x}+\frac{y}{q}\)=1 and \(\frac{q}{y}+\frac{z}{r}\)=1, then find the value of \(\frac{x}{p}+\frac{r}{z}\).
a) 0
b) 1
c) -1
d) y/q
View Answer
Explanation: \(\frac{p}{x}+\frac{y}{q}\)=1==>\(\frac{p}{x}=\frac{q-y}{q}\)==>\(\frac{x}{p}=\frac{q}{q-y}\).
\(\frac{q}{y}+\frac{z}{r}\)=1==>\(\frac{z}{r}=\frac{y-q}{y}\)==>\(\frac{r}{z}={-y}{q-y}\).
\(\frac{x}{p}+\frac{r}{z}=\frac{q}{q-y}+\frac{-y}{q-y}\)=1.
6. If x=yz and z=x-y, then find the value of x.
a) y2-1
b) \(\frac{y^2}{y-1} \)
c) \(\frac{y}{y-1} \)
d) \(\frac{-2y^2}{y-1} \)
View Answer
Explanation: Given x=yz and z=x-y.
x=y(x-y)=xy-y2.
xy-x=y2==>x=\(\frac{y}{y-1} \).
7. If p+q+r=0, then find the value of \(\frac{p^2}{p^2-qr}+\frac{q^2}{q^2-pr}+\frac{r^2}{r^2-pq}\).
a) 0
b) 1
c) 2
d) 4
View Answer
Explanation: p+q+r=0 🡪 p = -q-r 🡪 p2 = (q+r)2.
\(\frac{p^2}{p^2-qr}+\frac{q^2}{q^2-pr}+\frac{r^2}{r^2-pq}=\frac{(q+r)^2}{(q+r)^2-qr}+\frac{q^2}{q^2-(-q-r)r}+\frac{r^2}{r^2-(-q-r)q}\).
=\(\frac{q^2+r^2+2qr}{q^2+r^2+qr}+\frac{q^2}{q^2+r^2+qr}+\frac{r^2}{q^2+r^2+qr}=\frac{2q^2+2r^2+2qr}{q^2+r^2+qr}\)=2.
8. If \(\frac{a}{b}=\frac{p+2}{p-2}\), then find the value of \(\frac{a^2-b^2}{a^2+b^2}\).
a) \(\frac{8p}{p^2+4} \)
b) \(\frac{4p}{p^2-4} \)
c) \(\frac{8}{p^2} \)
d) \(\frac{4p}{p^2+4} \)
View Answer
Explanation: \(\frac{a}{b}=\frac{p+2}{p-2}\)==>\(\frac{a^2}{b^2}=\frac{(p+2)^2}{(p-2)^2}\).
\(\frac{a^2-b^2}{a^2+b^2} = \frac{\frac{a^2}{b^2}-1}{\frac{a^2}{b^2}+1} = \frac{\frac{(p+2)^2}{(p-2)^2}-1}{\frac{(p+2)^2}{(p-2)^2}+1}=\frac{(p+2)^2-(p-2)^2}{(p+2)^2+(p-2)^2}=\frac{8p}{2p^2+8}=\frac{4p}{p^2+4}\).
9. If 3z+7=z2+A=7z+5, then what is the value of A?
a) 8 \(\frac{1}{4} \)
b) 8 \(\frac{1}{2} \)
c) 6 \(\frac{1}{4} \)
d) 4 \(\frac{1}{8} \)
View Answer
Explanation: 3z+7=7z+5==>4z=2==>z=\(\frac{1}{2} \).
3z+7=z2+A==>\(\frac{3}{2}\)+7=\(\frac{1}{4} \)+A==>A=\(\frac{33}{4}\)=8 \(\frac{1}{4} \).
10. If \(\frac{2p+q}{p+4q}\)=3, then find the value of \(\frac{p+q}{p+2q}\).
a) 2/7
b) 5/9
c) 10/9
d) 10/7
View Answer
Explanation: \(\frac{2p+q}{p+4q}\)=3==>2p+q=3p+12q==>\(\frac{p}{q}\)=-11.
\(\frac{p+q}{p+2q}=\frac{\frac{p}{q}+1}{\frac{p}{q}+2}=\frac{-11+1}{-11+2}=\frac{10}{9}\).
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