# Quant Boosters - Kamal Lohia - Set 8

• Q21) Find real x such that x|x| - 3|x| - 4 = 0

• Q22) For how many integers (m, n) whose absolute value is less than 7, the system of equations 3x + my - 5 = 0 and x + ny - 4 = 0 has no solution?

• Q23) Assume the equation 2x² + x + a = 0 has the solution set A, and the equation 2x² + bx + 2 = 0 has the solution set B, and A ⋂ B = {1/2}, find A ⋃ B

• Q24) Find real valued solutions (x, y, z) for the equation √(x) + √(y - 1) + √(z - 2) = (x + y + z)/2.

• Q25) Solve the equation (x + 1)/(x + 4) - (x + 4)/(x + 1) + (x + 1)/(x - 2) - (x - 2)/(x + 1) = 2/3.

• Q26) If the equation x² - 2x - 4y = 5 has real valued solutions, find the maximum value of x - 2y.

• Q27) Find the sum of all solutions of |3x - |1 - 2x|| = 2.

• Q28) For what value/s of k, the quadratic equation (k² - 1)x² - 6(3k - 1)x + 72 = 0 with variable x has two distinct positive integer roots.

• Q29) Solve system of equations; logₓ8 + log₂y = 2 and logₓ2 + log₈y² = 1.

• Q30) A colony of 15000 ants increased by 50% after being fed. A fter, 4 weeks without food, the number of ants dropped by 60%. What percentage decline did the original population undergo?
a. 90%
b. 55%
c. 50%
d. 40%
e. 10%

• @kamal_lohia D)40% first you will find the increase in percentage which will be 22500.
after 4 weeks without food ,the drop was 60%
so the final count will be 9000
:- (15000-9000/15000)*100=40%

• .....................

• @kamal_lohia
C..........................

• @kamal_lohia
8/10 * 12/16 * mf = 12/10

3/5 * mf = 6/5

mf = 6/3 => 100%

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