Quant Boosters  Kamal Lohia  Set 8

Q11) A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
a. Rs. 375
b. Rs. 400
c. Rs. 600
d. Rs. 800

Q12) The rate of inflation was 1000%. Then what will be the cost of an article, which cots 6 units of currency now, two years from now? [CAT1995]
a. 666
b. 660
c. 720
d. 726

Q13) A student took five papers in an examination, where the full marks were same for each paper. His marks in these papers were in the proportion of 6:7:8:9:10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is [CAT2001]
a. 2
b. 3
c. 4
d. 5

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 xx  3x  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%