This set of Aptitude Questions and Answers (MCQs) focuses on “Simplification – Set 2”.
1. If \(\frac{a}{b}=\frac{4}{3}\) and \(\frac{p}{q}=\frac{9}{14}\), then find the value of \(\frac{3ap-bq}{4bq-7ap}\).
a) -11/14
b) 11/14
c) -5/4
d) -11/2
View Answer
Explanation:\(\frac{3ap-bq}{4bq-7ap}=\frac{bq(3*\frac{a}{b}*\frac{p}{q}-1)}{bq(4-7*\frac{a}{b}*\frac{p}{q})} = \frac{3*\frac{4}{3}*\frac{9}{14}-1}{4-7*\frac{4}{3}*\frac{9}{14}}=-\frac{11}{14}\).
2. If p+\(\frac{1}{q}\)=1 and q+\(\frac{1}{r}\)=1, then find the value of r+\(\frac{1}{p}\).
a) 0
b) 1
c) 1/2
d) 2
View Answer
Explanation: p+\(\frac{1}{q}\)=1.
p=\(\frac{q-1}{q}\).
\(\frac{1}{p}=\frac{-q}{1-q}\)…… (i)
q+\(\frac{1}{r}\)=1.
r=\(\frac{1}{1-q}\)…… (ii)
r+\(\frac{1}{p}=\frac{1}{1-q}+\frac{-q}{1-q}\)=1.
3. If a-16=b, then determine the value of |a-b|-|b-a|.
a) 4
b) 8
c) 32
d) 0
View Answer
Explanation: |a-b|-|b-a|=|a-b|-|-(a-b)|=|a-b|-|a-b|=0.
4. If \(\frac{x}{y+z}=\frac{y}{z+x}=\frac{z}{x+y}\)=k, then determine the value of k.
a) -1
b) 1/2
c) -1 or \(\frac{1}{2} \)
d) ±\(\frac{1}{2} \)
View Answer
Explanation: \(\frac{x}{y+z}=\frac{y}{z+x} \)
xz + x2 = y2 + yz
x2 – y2 = yz – xz
(x+y)(x-y) = -z(x-y)
x + y = -z …… (i)
\(\frac{z}{x+y}=\frac{z}{-z}\)=-1=k.
Or
\(\frac{x}{y+z}\)=k==>x=k(y+z)…… (ii)
\(\frac{y}{z+x}\)=k==>y=k(x+z)…… (iii)
\(\frac{z}{x+y}\)=k==>z=k(x+y)…… (iv)
On adding (ii), (iii) and (iv), we get,
x + y + z = k(2x + 2y + 2z)
k = 1/2.
Therefore, k = -1 or 1/2.
5. Find x, if \(\frac{x}{7}-\frac{x}{9}\)=2.
a) 63
b) 126
c) 36
d) 116
View Answer
Explanation: \(\frac{x}{7}-\frac{x}{9}\)=2
\(\frac{(9x-7x)}{63}\)=2.
2x = 2*63.
Therefore, x = 63.
6. If 4a+5b=83 and \(\frac{3a}{2b}=\frac{21}{22}\), then find the value of (b-a).
a) 3
b) 4
c) 7
d) 11
View Answer
Explanation: \(\frac{3a}{2b}=\frac{21}{22}\)==>\(\frac{a}{b}=\frac{21}{22}*\frac{2}{3}=\frac{7}{11}\)==>a=\(\frac{7b}{11}\).
4a+5b=4*\(\frac{7b}{11}\)+5b=\(\frac{28b+55b}{11}\)=83.
83b = 83*11 → b = 11.
a=\(\frac{7b}{11}\)=7*\(\frac{11}{11}\)=7.
Therefore, b-a = 4.
7. Which of the following pairs of fraction adds up to a number greater than 6?
a) \(\frac{15}{7}\) and \(\frac{21}{9}\)
b) \(\frac{17}{6}\) and \(\frac{5}{3}\)
c) \(\frac{17}{4}\) and \(\frac{5}{2}\)
d) \(\frac{15}{6}\) and \(\frac{21}{8}\)
View Answer
Explanation:\(\frac{17}{4}+\frac{5}{2}=\frac{27}{4}\)=6.75.
Therefore, \(\frac{17}{4}\) and \(\frac{5}{2}\) pair of fraction adds up to a number greater than 6.
8. If x+3y=8 and xy=6, then find the value of \(\frac{9}{x}+\frac{3}{y}\).
a) 4/3
b) 3/4
c) 2
d) 4
View Answer
Explanation: \(\frac{9}{x}+\frac{3}{y}=\frac{9y+3x}{xy}=\frac{3(x+3y)}{xy}=\frac{3*8}{6}\)=4.
9. If \(\frac{p}{4}=\frac{q}{5}=\frac{r}{9}\), then find the value of \(\frac{p+q+r}{r}\).
a) 2
b) 1/2
c) 17/9
d) 9
View Answer
Explanation: Let \(\frac{p}{4}=\frac{q}{5}=\frac{r}{9}\)=k.
P = 4k, q = 5k and r = 9k.
\(\frac{p+q+r}{r}=\frac{4k+5k+9k}{9k}=\frac{18k}{9k}\)=2.
10. -8m-[7n-{9m-(5n-12m)}] simplifies to which of the following?
a) 13m+12n
b) 13m-12n
c) -13m-12n
d) -13m+12n
View Answer
Explanation: =-8m-[7n-{9m-(5n-12m)}]
=-8m-[7n-{9m-5n+12m}]
=-8m-[7n-21m+5n]
=-8m-12n+21m
=13m-12n.
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