This set of Aptitude Questions and Answers (MCQs) focuses on “Simplification”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.
1. If x+y=21 and xy=110, find the value of x2+y2.
a) 221
b) 241
c) 331
d) 321
View Answer
Explanation: We know that, (x + y)2 = x2 + y2 + 2xy.
212 = x2 + y2 + 2*110.
x2 + y2 = 221.
2. If a-b=16 and a2-b2=544, find the value of 2ab.
a) 350
b) 450
c) 500
d) 550
View Answer
Explanation: a – b = 16 …… (i)
a2-b2 = (a+b) * (a-b) = 544.
a + b = 34 …… (ii)
On solving (i) and (ii), we get,
a = 25 and b = 9.
Therefore, 2ab = 2*25*9 = 450.
3. Find the value of p, if pq = 24 and p2 + q2 = 52.
a) 8 or 3
b) 12 or 2
c) 6 or 4
d) 1 or 24
View Answer
Explanation: pq = 24 …… (i)
(p + q)2 = p2 + q2 +2pq
(p + q)2 = 52 + 48 = 100.
p + q = 10 …… (ii)
On solving (i) and (ii), we get,
p2 – 10p + 24 = 0.
p = 6 or 4.
4. Find the value of \(\frac{4}{1+\frac{2}{5+\frac{2}{3+\frac{5}{7}}}}\).
a) 129/47
b) 157/37
c) 136/41
d) 144/49
View Answer
Explanation: \(\frac{4}{1+\frac{2}{5+\frac{2}{3+\frac{5}{7}}}}=\frac{4}{1+\frac{2}{5+\frac{2*7}{26}}}=\frac{4}{1+\frac{2*13}{72}}=\frac{4}{1+\frac{2*13}{72}}=\frac{4*36}{49}=\frac{144}{49}\).
5. If X + Y = 174, and X is half of Y, then find the value of X.
a) 58
b) 116
c) 57
d) 114
View Answer
Explanation: X + Y = 174 …… (i)
Y = 2X …… (ii)
On solving (i) and (ii), we get,
X = 58.
6. If a, b, c, ……, x, y, z are 26 natural numbers, then what is the value of (t-a)(t-b)(t-c)……(t-y)(t-z)?
a) 26
b) 13
c) 1
d) 0
View Answer
Explanation: t is also a natural number among 26 natural numbers of a, b, c, ……, x, y, z.
(t-t) is an element in (t-a)(t-b)(t-c)……(t-y)(t-z).
(t-t) = 0. Hence, (t-a)(t-b)(t-c)……(t-y)(t-z) = 0.
7. If (x2 + y2)3 = (x3 + y3)2 and xy≠0, then find the value of \(\frac{x}{y}+\frac{y}{x}\).
a) 2/3
b) 7/3
c) 2
d) 4
View Answer
Explanation: (x2 + y2)3 = (x3 + y3)2
x6 + y6 + 3x2y2(x2 + y2) = x6 + y6 + 2x3y3
\(\frac{x^2 y^2 (x^2+y^2)}{x^3 y^3}=\frac{2}{3}\)
\(\frac{x^2+y^2}{xy}=\frac{2}{3}\)
\(\frac{x}{y}+\frac{y}{x}=\frac{2}{3}\).
8. If 2\(\frac{x}{7}\)*3 \(\frac{y}{5}\)=12, then find the values of x and y respectively.
a) 8, 4
b) 4, 6
c) 6, 6
d) 3, 7
View Answer
Explanation: 2\(\frac{x}{7}\)*3 \(\frac{y}{5}\)=12.
\(\frac{14+x}{7}*\frac{15+y}{5}\)=12.
210 + 15x + 14y + xy = 420.
15x + 14y + xy = 210.
By trial and error, x = 6 and y = 6.
9. Find the difference of 3\(\frac{3}{4}\) and its reciprocal.
a) 209/60
b) 203/60
c) 209/120
d) 203/30
View Answer
Explanation: 3\(\frac{3}{4}=\frac{15}{4}\).
\(\frac{15}{4}-\frac{4}{15}=\frac{209}{60}\).
10. If b+\(\frac{1}{c}\)=1 and a+\(\frac{1}{b}\)=1, the find the value of abc.
a) 0
b) 1
c) -1
d) -2
View Answer
Explanation: b+\(\frac{1}{c}\)=1.
bc – c = -1.
c = \(\frac{1}{1-b}\).
a+\(\frac{1}{b}\)=1.
ab – b = -1.
b = \(\frac{1}{1-a}\).
Therefore, abc=a\(\Big(\frac{1}{1-a}\Big)\Big(\frac{1}{1-b}\Big)=a\Big(\frac{1}{1-a}\Big)\bigg(\frac{1}{1-\frac{1}{1-a}}\bigg)=a\Big(\frac{1}{1-a}\Big)\Big(\frac{1-a}{-a}\Big)\)=-1.
More Aptitude Questions and Answers on Simplification:
- Simplification Questions (Set 2)
- Simplification Questions (Set 3)
- Simplification Questions (Set 4)
- Simplification Questions (Set 5)
- Simplification Questions (Set 6)
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
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