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 [#permalink] New post 05 Oct 2006, 00:40
Hey kevin, paddyboy, yezz, govinam,icedtea, GMATT73 where r u?
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 [#permalink] New post 05 Oct 2006, 20:11
Here is my solution


triangle bad is similar to triangle bca.
ba/bc=ad/ac=bd/ab
bc=ab^2/bd=9 thus dc=5

trianle abc is similar triangle aeb
thus
ab/ae=bc/eb=ac/ab
ae=36/5
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 [#permalink] New post 06 Oct 2006, 02:32
yogeshsheth wrote:
Here is my solution


triangle bad is similar to triangle bca.
ba/bc=ad/ac=bd/ab
bc=ab^2/bd=9 thus dc=5

trianle abc is similar triangle aeb
thus
ab/ae=bc/eb=ac/ab
ae=36/5


Congrats yogesh,......................
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 [#permalink] New post 06 Oct 2006, 02:44
Here comes our next question.......

3. Fresh Grapes contain 90% water and 10% grape pulp whereas Dry Grapes
contain 20% water and 80% grape pulp. How many kgs of Dry Grapes can
be obtained from 20 kgs of Fresh Grapes?
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 [#permalink] New post 06 Oct 2006, 06:55
Amount of grape pulp will remain same.
80Z/100 =10/100*20
z=2.5

Answer is 2.5 kgs
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 [#permalink] New post 06 Oct 2006, 13:25
yogeshsheth wrote:
Amount of grape pulp will remain same.
80Z/100 =10/100*20
z=2.5

Answer is 2.5 kgs


As simple as that....................

Here comes our next question

4. A group of men can complete a work in certain number of days. After they
worked for 12 days 1/4 of them left. To complete the remaining work the
remaining men have taken as many days as the initial number of men
would have taken to complete the entire work. In how many days is the
work completed?
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 [#permalink] New post 06 Oct 2006, 14:55
I got DC = 5 and CE = 11/5. Also used similarity of triangles by a side and two adjacent angles.

EDIT: whooops, missed the second page :) Sorry, this was for question 2.

EDIT2: here goes number 4...

S = total job
v = total speed of all men
t = original time

S = v*t
S = 12*v + 0.75v*t

vt = 12v + 0.75vt
0.25t = 12
t = 48

ANSWER: the work will be done in (48 + 12) = 60 days.
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 [#permalink] New post 08 Oct 2006, 04:54
That's the right answer......

Any other approaches.........
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 [#permalink] New post 08 Oct 2006, 12:02
Here comes our next question.........

5. When a clock indicates completion of 24 hours it actually loses one hour. How much time does it loose in 5 days?
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 [#permalink] New post 09 Oct 2006, 08:16
I get 5 hrs .. I know it is not that simple but that's what I can see.

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 [#permalink] New post 09 Oct 2006, 10:30
A little less than that I would say. How about 4.8 hours? (It loses 1 hour every 25 hours, if I understand correctly).
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 [#permalink] New post 10 Oct 2006, 10:38
Yed Honghu, that's the right answer
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 [#permalink] New post 10 Oct 2006, 21:31
Folks, it's time again to get into some fight............

Here comes our next question.........

6.

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 [#permalink] New post 10 Oct 2006, 22:54
very tough quest indeed
I find that the radius of the bigger circle is 5
I think this is not a kind of GMAT quest (easy math prob but take too much time and paper also)
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 [#permalink] New post 10 Oct 2006, 23:45
I got 5 as well ;) It's true that it's not a usual GMAT question ;)

I worked it out using an XY plan.

The figure is symetrical. So, we can have the same kind of rectangle at the bottom left of the square (1 vertex on C and the other on the circle).

By defining the origin 0(0,0) = C(0,0), the equation of the circle is:
(1) (x-r)^2 + (y-r)^2 = r^2 with r the radius of the circle.

As the vertex of the rectangle on the circle has the coordinates (2,1), we can plug the values of x & y in (1).

(2-r)^2 + (1-r)^2 = r^2
<=> 4 - 4*r + r^2 + 1 - 2*r + r^2 = r^2
<=> r^2 - 6*r + 5 = 0

We can use the "reduiced" Delta = 3^2 - 5*1 = 4 = 2^2

Thus, we have 2 possibilies :
o r= (3+2)/1 = 5
o r= (3-2)/1 = 1

For the latter radius, the vertex lying on the circle is represented by a point on the "other side" of the circle. In the case of this picture, the radius is 5.
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 [#permalink] New post 11 Oct 2006, 06:31
Hi Fig,

I m not clear how you can take the cordinates of vertex as (2 , 1) since 2 and 1 are the length of the rectangle and you are taking the center of the circle as the origin. Even by Visual observation I am not able to understand the login.. Can you please explain ..?


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 [#permalink] New post 11 Oct 2006, 06:32
sorry c as the Origin
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 [#permalink] New post 11 Oct 2006, 06:37
Amit05 wrote:
Hi Fig,

I m not clear how you can take the cordinates of vertex as (2 , 1) since 2 and 1 are the length of the rectangle and you are taking the center of the circle as the origin. Even by Visual observation I am not able to understand the login.. Can you please explain ..?


Regards,
Amit


I take the origine O(0,0) at the point C : the vertex of the scare at the bottom left :)

Since this origine definied,
o the vertex of a silimar little rectangle from C and on the circle has the coordinates (2,1) (lenght, width).
o the center of the cicle Z is at (r,r)

Hope this help :)
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 [#permalink] New post 11 Oct 2006, 07:04
Amit05 wrote:
sorry c as the Origin


Ok ;)
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 [#permalink] New post 11 Oct 2006, 13:07
Quote:
A group of men can complete a work in certain number of days. After they
worked for 12 days 1/4 of them left. To complete the remaining work the
remaining men have taken as many days as the initial number of men
would have taken to complete the entire work. In how many days is the
work completed?


I tried like this:

r (12) = w
.75r (t - 12) = w ---> .75rt - 9r = 12r ---> rt = 28r ---> t = 28

t = 28 + 12 = 40

I see this is the wrong answer. Should I not have set the two equations equal to one another? Can someone suggest how to correct this
  [#permalink] 11 Oct 2006, 13:07
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