please help me by solving these problems:part-1

[ahad]

1.A group of 4 pumps are filling a tank. Each of the 3 smaller pumps works at 2/3rd the rate of the largest pump. If all 4 pumps work at the same time, they should fill the tank in what fraction of the time.... that it would have taken the largest pump if it operated alone?

2. If xy < 36.
col A: (x+1)(y+1) col B: 49

3.A square was given and another square was formed by joining mid points of the square.

Perimeter of larger square was given X.

Col a: perimeter of smaller square Col b: X/2

4.There are five persons A, B, C, D, E. What are the possible combinations they are seated ,provided C and D always sit nearby?

5.If the volume of a cube is 1 cubic centimeter, then the distance from any vertex to the center point inside the cube is
A) 1/2 B) 1/sqrt2 C) sqrt2 D) sqrt3/2

6.If x and x+2 are both factors of y then which one is greater?
Col a: x(x+2)
Col b: y

7.Given an series 1, 2, 2, 3, 3, 3, 4, 4, 4, 4..... if this continues then what will be the value of the 100th term ?

8. 100 < a < b < 1000
Col A: 1/a - 1/b Col B: 1/100 - 1/1000

[econ_phd_2009]

1. 1/3

2. D

3. col B

[chestnut.cc]

1. 1/3... Let x be the rate of the biggest pump... therefore the rate of all pump together is 3*(2x/3) + 1/3 = 3x... ie 1/3rd the time taken by the biggest pump

2. D... both +ve a<b... both -ve a <b... both... then D

3. A... let the perimeter of the square be 16... therefore the side of the inscribed square is 2root2... therefore its perimeter is 8root2... ie (16*root2/2)... ie x/root2...

4. 2*4!

5. D

6. D

7. guess 14... (1...1) (2....2) (3... 5) (4...10) (5...15) (6... 21) (7... 28) (8... 36) (9... 45) (10... 55) (11... 66) (12... 78) (13... 91) (14... 105)

8. B... 100 <a... ie 1/100 > 1/a... similarly... b <1000... ie 1/b > 1/1000...

ie... small term - larger term < larger term - smaller term