Aptitude :: Equation ProblemsPage 2
9.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. 2X² + 11X + 14 = 0
2. 4Y² + 12y + 9 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X = Y 

Answer is: ASolve:
2X² + 11X + 14 = 0
2X² + 7X + 4X + 14 = 0
X(2X + 7) + 2(2X +7) = 0
(X + 2)(X + 7/2) = 0
X = 2, 7/2
Again
4Y² + 12y + 9 = 0
4Y² + 6y + 6Y + 9 = 0
2Y(2Y + 3) + 3(2Y + 3) = 0
(2Y +3)(2Y + 3) = 0
Y = 3/2, 3/2
So, Y>X is right.
10.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  X  12 = 0
2. Y² + 5Y + 6 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X â‰¥ Y 

Answer is: DSolve:
X²  X  12 = 0
X²  4X + 3X  12 = 0
X(X  4) + 3(X  4) = 0
(X  4)(X + 3) = 0
X = 4, 3
Again
Y² + 5Y + 6 = 0
Y² + 3Y + 2Y + 6 = 0
Y(Y + 3) + 2(Y + 3) = 0
(y + 3)(Y + 2) = 0
Y = 3, 2
So, X â‰¥ Y is right.
11.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  8X + 15 = 0
2. Y²  3Y + 2 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X â‰¥ Y 

Answer is: BSolve:
X²  8X + 15 = 0
X²  5X  3X + 15 = 0
X(X  5)  3(X  5) = 0
(X  5)(X  3) = 0
X = 5, 3
Again
Y²  3Y + 2 = 0
Y²  2Y  y + 2 = 0
Y(Y 2) 1(Y 2) = 0
(Y 2)(Y  1) = 0
Y= 2, 1
So, X is greater than Y.
12.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  32 = 112
2. Y²  âˆš169 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X = Y 

Answer is: ASolve:
X²  32 = 112
X² = 144
X = Â± 12
Again
Y²  âˆš169 = 0
Y² = âˆš169
Y = 13
So, Y > X is true.
13.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X  âˆš121 = 0
2. Y²  121 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X â‰¥ Y 

Answer is: DSolve:
X  âˆš121 = 0
X = 11
Again
Y²  121 = 0
Y = Â± 11
This statement X â‰¥ Y is true.
14.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. X²  16 = 0
2. Y²  9Y + 20 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X = Y 

Answer is: CSolve:
X²  16 = 0
X = Â± 4
Again
Y²  9Y + 20 = 0
Y²  5Y  4Y + 20 = 0
Y(Y  5)  4(Y  5) = 0
(Y  5)(Y  4) = 0
Y = 5, 4
So, X â‰¤ Y is true.
15.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. 5X²  18X + 9 = 0
2. 20Y²  13Y + 2 = 0  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X = Y 

Answer is: BSolve:
5X²  18X + 9 = 0
5X²  15X  3X + 9 = 0
5X(X  3)  3(X  3) = 0
(X  3)(5X  3) = 0
X = 3, 3/5
Again
20Y²  13Y + 2 = 0
20Y²  8Y  5Y + 2 = 0
4Y(5Y  2)  1(5Y  2) = 0
(4Y  1)(5Y  2) = 0
Y = 1/4, 2/5
So, X > Y is right.
16.  In each of the equations, two equations numbered 1 and 2 are given. You have to solve both the equations
1. XÂ³  878 = 453
2. YÂ²  82 = 39  (a)X < Y  (b)X > Y  (c)X â‰¤ Y  (d)X â‰¥ Y 

Answer is: DSolve:
XÂ³  878 = 453
XÂ³ = 453 + 878
XÂ³ = 1331
X = 11
Again
YÂ²  82 = 39
YÂ² = 39 + 82
YÂ² = 121
Y = Â± 11
X â‰¥ Y, this statement is right.
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