Quant Quiz - II

Directions—(Q. 1-5)-  In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer if :
(1) x >  y
(2) x ≥  y
(3) x  < y
(4) x ≤  y
(5) x = y or the relationship cannot be established

1.
I. x^2 -√ (1296)^(1/2) = 58
II. (y)^(7/3) × (y)^(2/3) - 262 = 250


2.
I. 2x + 3y = 19
II. 7x- 4y = 23

3.
I.  x^2 + 12 = 7x
II. y^2 + 30 = 11y

4.
I. √16 + √(x + 18 ) = √121
II. y^2 - 640 = 321

5.
I. x^2 – (11) ^ (5/2)/(√x) = 0
II. 18/(√y) - √y = 7/(√y)
+
6.
I. x^2 – 4 = 0
II. y^2 + 5y + 6 = 0

7.
I. x^2 – 9x + 18 = 0
II. y^2 – 13y + 42 = 0

8.
I. x^3 – 62 = 63
II. y^3 – 123 = 93

9.
I. 7x + y = 22
II. 5x - 2y = 13

10.
I. 2x^2 + 11x + 12 = 0
II. 5y^2 + 27y + 10 = 0



ANSWER

1. (4)
I. x^2 – 6 = 58
X = +8,-8

II. y^3= 512
Y = 8, `
X ≤ y

2. (1)
I. 2x + 3y = 19
II. 7x – 4y = 23
So x = 5 and y= 3
X > y

3. (3)
I. factors are (x- 3 )(x - 4) = 0
X = 3, 4

II. factors are (y - 5)(y - 6) = 0
Y = 5, 6
X <  y

4. (2)
I. √16 + √((x) + 18) = √121
4 + √(x+18)=11
So, x = 72 - 18 = 31
II. y^2 – 640 = 321
Y^2 = 961 , so y = ∓31
Hence x ≥y

5. (5)
I.  x^(5/2) = (11)^(5/2)
So, x = 11

II. 18/√y - √y = 7/√y
So 18/√y - 7/√y = √y
So y = 11
And x = y 

6. (2)
x = 2, -2  and   y = -3, -2

7. (4)
x = 3, 6   and   y = 6, 7

8. (3)
x = 5   and   y = 6

9. (1)
x = 3  and   y = 1

10. (5)
x = -4, -3/2   and   y = -5, -2/5