some hard OGs

[ss1]

1)X^4 + y^4=100, then the greatest possible value of x is between:
a)0 and 3 B) 3 and 6 c) 6 and 9 d) 9 and 12 e)12 and 15
OA: B



2)In the xy plane, what is the y-intercept of line l?
1) The slope of line l is 3 times its y intercept
2) The x-intercept of line l is -1/3
M=3c, so the equation would be: y=mx+c, so y=3c.x +c
2)when y=0, x=-1/3. So here we have: 0=3c(-1/3)+c. which comes to:-c+c=0. What am I doing wrong here? Shouldn’t the answer be C?OA:E
Also, does the xy plane mean quadrant 1?


3) six machines, each working at the same constant rate, together can complete a certain job in 12 days. how many additional machines, each working at the same constant rate will be needed to finish the job in 8 days?
a)2 b)3 c)4 d)6 e)8
OA: B


4)a certain city with a population of 132,000 is to be divided into 11 voting districts. and no district is to have a population that is 10% greater than the population of any other district. what is the minimum possible population that the least populated district could have?
a)10,700 b)10,800 c)10,900 d)11,000 e)11,100
OA: D

[ss1]

comeon guys, anyone?

[ace_gre]

Q3.

6 m/c can complete a job in 12 days.
1 m/c can complete the same job in 72 days.

To complete the same job in 8 days, 9 m/cs are needed.
Additional number of machines = 9-6=3.

thanks!

[ace_gre]

Q4.

Minimum population in one voting district is achieved when the rest of the 10 voting districts have max population.

Say minimum population district has x no. of people.
Other 10 districts can have 1.1x.

Total population = x+ 10*(1.1x)= 132000
x+11x=12x=132000

Minimum population x=11,000

[ss1]

thank you ace_gre. any help on the other two?

[ace_gre]

Here is my approach to Q1 and Q2 (though I still have doubts!!)

Q1. greatest possible value of x is possible when y has the least value. y==0.
then x^4= 100.So x is between 3 and 4. 3^4=81 and 4^4=216.
From all the choices, only B is in the valid range. Hence B

Q2. If I am interpreting the question correctly,(knowing that the OA is E) , we need to find the numerical value of c. I would approach the same way as you did. But it is not possible to find the value of c.
-c +c =0 is true for any value of c. Hence E??
x-y plane refers to all of x-y plane and includes all four quadrants..

Does this make sense?