# Quant Boosters - Kamal Lohia - Set 8

• Q14) I bought 5 pens, 7 pencils and 4 erasers. Rajan bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what I paid. What percent of the total paid by me was for pens? [CAT1996]
a. 37.5%
b. 62.5%
c. 50%
d. None of these

• Q15) Given the equation (5/2)x - b = (8/5)x + 142, find the smallest positive integer b such that the solution x is a positive integer.

• Q16) Solve for x if (x - a - b)/c + (x - b - c)/a + (x - c - a)/b = 3 and ab + bc + ca ≠ 0.

• Q17) Find the condition for 'a' such that equation |ax - 2y - 3| + |5x + 9| = 0 has the solution (x, y) where x, y have same sign

• Q18) Find the number of positive integer solutions of the equation 123x + 57y = 531.

• Q19) Find all x which satisfy the equation x^4 - 12x^3 + 47x^2 - 60x = 0.

• Q20) Given |x - 2| < 3, solve the equation |x + 1| + |x - 3| + |x - 5| = 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%

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• @kamal_lohia
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