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Word Problem (Overlapping Set and Volume)

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by Cedagmat » Mon Nov 15, 2010 2:56 pm
Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
(A) 25 % (B) 30 % (C) 32.5 % (D) 37.5 % (E) 45 %
[spoiler]Answer: B[/spoiler]

I can't seem to breakdown this question. It doesn't seem to have enough information.

The length, width, and height of a rectangular solid are in the ratio of 3 to 2 to 2. If the volume of the solid is V, what is the height, in terms of V?
(A) sqrt(V/3)
(B) cube rt(V/3)
(C) sqrt(2V/3)
(D) cube rt(2V/3)
(E) cube rt(4V/3)

[spoiler]Answer: D[/spoiler]
V=lwh=3*2*2
h=V/lm=V/6

What are we suppose to gather from the answer choices?
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by diebeatsthegmat » Mon Nov 15, 2010 5:54 pm
Cedagmat wrote:Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
(A) 25 % (B) 30 % (C) 32.5 % (D) 37.5 % (E) 45 %
[spoiler]Answer: B[/spoiler]

I can't seem to breakdown this question. It doesn't seem to have enough information.

The length, width, and height of a rectangular solid are in the ratio of 3 to 2 to 2. If the volume of the solid is V, what is the height, in terms of V?
(A) sqrt(V/3)
(B) cube rt(V/3)
(C) sqrt(2V/3)
(D) cube rt(2V/3)
(E) cube rt(4V/3)

[spoiler]Answer: D[/spoiler]
V=lwh=3*2*2
h=V/lm=V/6

What are we suppose to gather from the answer choices?
there is something wrong with the question1, can you recheck? whats the solve?
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by Cedagmat » Mon Nov 15, 2010 7:17 pm
Sorry I do not have the solution to the problem only the answer. I was pretty stumped on this question because it seems to missing a piece of information.
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by goyalsau » Mon Nov 15, 2010 9:06 pm
Cedagmat wrote:Of the employees in a company, 30 % are female who have a master degree. If 20 % of the female employees do not have a master degree, what percent of the employees in the company are female?
(A) 25 % (B) 30 % (C) 32.5 % (D) 37.5 % (E) 45 %
[spoiler]Answer: B[/spoiler]
I just don't understand How the answer is B,

Just look at this example,

if there are 200 employees in a company then there are 60 female with master degree
then this 30 % female employees with master degree are 80 % of all female employees because the rest 20% of female employees do not have a master degree
which means there are 75 female employees 75/200 is 37.5%
Saurabh Goyal
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by Rahul@gurome » Mon Nov 15, 2010 10:06 pm
Cedagmat wrote:The length, width, and height of a rectangular solid are in the ratio of 3 to 2 to 2. If the volume of the solid is V, what is the height, in terms of V?
(A) sqrt(V/3)
(B) cube rt(V/3)
(C) sqrt(2V/3)
(D) cube rt(2V/3)
(E) cube rt(4V/3)
The ratio of the length, width, and height is given. If we take them as their values, the solution becomes more conceptual. The general process to solve these kind of problems is:

Say, Length = 3x => Width = Height = 2x
Therefore, volume = (3x)*(2x)*(2x) = 12*x³

So, 12*x³ = V
= > x³ = V/12
=> x = cube rt (V/12)

Therefore, Height = 2x = 2*cube rt (V/12) = cube rt(8V/12) = cube rt(2V/3)

The correct answer is D.



Now, if we take length = 3, width = 2, and height = 2, Volume = 12

Given that, volume is V and we have to find the height. We can solve this by making V = 12 in the answer choices. The option that results in height = 2 is the correct one.
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by Rezinka » Mon Nov 15, 2010 10:33 pm
1)
The answer id definitely D.
I found it using the table method.
No doubts there.

2)
ANS : D
This solution might look time consuming but it took me 1 minute 24 sec so I guess it is good enough.
l : w : h = 3 : 2 : 2 = 3x : 2x : 2x
Now, V = l*w*h = (3x)*(2x)*(2x) = 12(x^3)
h = v/(l*w)
= 12(x^3) / (3x*2x)
= 2x
Now we try plugging in using V=12(x^3).
We know that sqrt is the wrong option as sqrt(x^3) will not give us x and we need the ans to be 2x..
Eliminate A and C.
Lets start with the last option (cause thats what I did)
E)
cube rt(4V/3)
= cube rt(4*12(x^3/3))
= x*cube rt(16)................................. INCORRECT
D)
cube rt(2V/3)
= cube rt (2*12(x^3)/3)
= cube rt (8*(x^3))
= 2x................................................ CORRECT
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