198 questions : Please can some one help me with following

[ashforgmat]

Please can some one help with the following questions :-

Please post the complete solution with the method.

Thanks,
Ash.


23) Alice's take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month.
a. 1�2
b. 1�3
c. 1�4
d. 1�5
e. 1�6



40) Some water was removed from each of 6 tanks. If standard deviation of the volumes of water at the beginning was 10 gallons, what was the standard deviation of the volumes at the end?
a. For each tank, 30% of water at the beginning was removed
b. The average volume of water in the tanks at the end was 63 gallons




64) Each employee is either a director or a manager. What % of the employees are directors?
a. The average salary of managers is $5000 less than the average of all employees
b. The average salary of directors is $15000 greater than the average of all employees


68) A thin piece of 40 m wire is cut in two. One piece is a circle with radius of r. Other is a square. No wire is left over. Which represents total area of circle and square in terms of r?
a. Πr2
b. Πr2 + 10
c. Πr2 + ¼ π2r2
d. Πr2 + (40 - 2πr)2
e. Πr2 + (10 - ½ Πr)2



70) If x4 + y4 = 100, 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



73) In xy plane, what is y-intercept of l?
a. Slope of l is 3 times the y intercept
b. x-intercept of l is (-1/3)

[shashank.ism]

70) If x4 + y4 = 100, 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



since x^4 + y^4 = 100 and y^4 is always +ve so for greatest value of x , take y =0
so x^4 = 100 --> x^2 = 10 hence the greatest value of x lies between[spoiler] 3 & 6 Ans B[/spoiler]

[Rahul@gurome]

(23) Let Alice's take home pay = $x and she saved $y each month.
Amount she saved at the end of year = $12y.
Amount not saved every month = $(x - y)
So, 12y = 3(x -y) implies 5y = x or y = x/5

The correct answer is (D).

68) Circumference of circle = 2*pi*r
Left over wire = 40 - 2*pi*r = Perimeter of square
So, length of each side of square = (40 - 2*pi*r)/4 = 10 - pi*r/2
Area of circle = pi*r^2
Area of square = (10 - pi*r/2)^2
Therefore, total area of circle and square = pi*r^2 + (10 - pi*r/2)^2

The correct answer is (E).

70) x will be maximum when y is minimum.
Minimum value of y can be 0
So, x^4 = 100 implies 3^4 = 81 and 4^4 = 256, which means x should be greater than 3 and less than 4. So, (B) is the best choice.

The correct answer is (B).

[shashank.ism]

23) Alice's take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month.
a. 1�2
b. 1�3
c. 1�4
d. 1�5
e. 1�6

let the fraction she saved for each month was f
and the fraction she did not saved each month = 1-f
total amount saved at the end of year = 12x(f)A where A is the total amount she used to receive as payment.
12fA = 3 (1-f) A --> 4f= 1-f --> f= 1/5
so [spoiler]she used to save 1/5 of her take home money each month. Ans D [/spoiler]

[shashank.ism]

64) Each employee is either a director or a manager. What % of the employees are directors?
a. The average salary of managers is $5000 less than the average of all employees
b. The average salary of directors is $15000 greater than the average of all employees

Let X be the percentage of directors and 100-X be the percentage of managers.
Let D be the salary of directors and M be the salary of managers
av (directors)= D, Av. (Managers) = M, Av.(all Employees) = [DX + M(100-X)]/100
Statement A. M - [DX + M(100-X)]/100 = 5000 --> (M-D)X = 5000x100...........(i) not sufficient
Statement B. [DX + M(100-X)]/100 - D = 15000 --> (D-M)X/100 + M-D = 15000........(ii) not sufficient

combined: -5000 + M-D =15000 --> M-D = 20000
from X = 5000x100/20000 = [spoiler]25 % Ans C[/spoiler]

[ashforgmat]

Thanks for all the answers and solutions guys !!

Please can someone throw light on the SD question No. 40 and intercept question No. 73 .


Thanks....