This set of Aptitude Questions and Answers (MCQs) focuses on “Formula Based Problems”.
1. What is the value of \(\frac{3.48*3.48-1.52*1.52}{1.96}\)?
a) 5
b) 1.96
c) 1.52
d) 9.8
View Answer
Explanation: We know that, a2-b2 = (a+b) (a-b).
\(\frac{3.48*3.48-1.52*1.52}{1.96}=\frac{(3.48+1.52)(3.48-1.52)}{1.96}=\frac{5*1.96}{1.96}\)=5.
2. What is the value of 375*375 + 125*125?
a) 145250
b) 156250
c) 165250
d) 155250
View Answer
Explanation: We know that, a2+b2 = ½ [(a+b)2 + (a-b)2]
3752 + 1252 = ½ [5002 + 2502] = ½ [250000 + 62500] = 156250.
3. What is the value of 615*615 + 215*215 – 615*430?
a) 160000
b) 360000
c) 250000
d) 120000
View Answer
Explanation: We know that (a-b)2 = a2 + b2 – 2ab.
6152 + 2152 – 2*615*215 = (615 -215)2 = 4002 = 160000.
4. Find the square root of 4a2 + 9b2 + c2 + 12ab – 6bc – 4ac.
a) 2a + b – 3c
b) 2a – 3b – c
c) 2a – 3b + c
d) 2a + 3b – c
View Answer
Explanation: We know that, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca.
4a2 + 9b2 + c2 + 12ab – 6bc – 4ac = (2a)2 + (3b)2 + (-c)2 + 2(2a)(3b) + 2(3b)(-c) + 2(2a)(-c) = (2a + 3b – c)2
Therefore, square root of (2a + 3b – c)2 is 2a + 3b – c
5. Find the value of \(\frac{756*756*756+244*244*244}{756*756-756*244+244*244}\).
a) 1000
b) 512
c) 900
d) 712
View Answer
Explanation: We know that, a3 + b3 = (a + b) (a2 – ab + b2)
i.e., (a3 + b3)/ (a2 – ab + b2) = a + b.
\(\frac{756*756*756+244*244*244}{756*756-756*244+244*244}=\frac{756^3+244^3}{756^2-756*244+244^2}\)=756+244=1000.
6. Find the value of \(\frac{(973+786)^2-(973-786)^2}{973*786}\).
a) 2
b) 6
c) 4
d) 8
View Answer
Explanation: We know that, (a + b)2 – (a – b)2 = 4ab
or [(a + b)2 – (a – b)2]/(ab) = 4.
\(\frac{(973+786)^2-(973-786)^2}{973*786}\)=4.
7. Find the value of \(\frac{(576+276)^2+(576-276)^2}{576*576+276*276}\).
a) 2
b) 4
c) 852
d) 300
View Answer
Explanation: We know that, (a+b)2+(a-b)2 = 2(a2+b2)
i.e., [(a+b)2+(a-b)2]/ (a2+b2) = 2.
\(\frac{(576+276)^2+(576-276)^2}{576*576+276*276}\)=2.
8. If x + y + z = 0, then what is the value of (x + y)(y + z)(z + x) ?
a) x2 + y2 + z2
b) (x + y + z)2
c) -xyz
d) xyz
View Answer
Explanation: Given, x + y + z = 0
i.e., x+y=-z, y+z=-x, z+x=-y
(x + y)(y + z)(z + x) = -xyz.
9. If a+b+c = 0, then what is the value of a3 + b3 + c3?
a) 0
b) -3abc
c) 3abc
d) 3
View Answer
Explanation: We know that, a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
Since, a+b+c = 0
a3 + b3 + c3 – 3abc = 0
and a3 + b3 + c3 = 3abc.
10. If x = 15 and y = 12, then find the value of \(\frac{x^2+y^2+xy}{x^3-y^3}\).
a) 3
b) 2
c) 1/2
d) 1/3
View Answer
Explanation: We know that, x3 – y3 = (x – y) (x2 + xy + y2)
Or, \(\frac{x^2+y^2+xz}{x^3-y^3} = \frac{1}{x-y}=\frac{1}{15-12} = \frac{1}{3} \)
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