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Problem Solving for 780+ Aspirants

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Problem Solving for 780+ Aspirants [#permalink] New post 21 Mar 2009, 07:25
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67% (02:19) correct 33% (00:00) wrong based on 4 sessions
Folks, with over 6 yrs of experience as a GMAT Mentor and Content Developer I hope I can make a difference in your GMAT preparation through this thread.As I manage similar threads in other forums you many find these questions on other websites as well of course you will find the same avatar in all those places

I request the users to adhere to the following rules to avoid confusion in the thread

1. Do not post your questions here. Please post them in the relevant thread on this forum

2. Every question posted here will have an unique number and please use this in your PMs.

3. Instead of simply giving your answer try to support your answer with some explanation

Let's start...and here is the first question.

There are 1001 red marbles and 1001 black marbles in a box. Let Ps be the probability that two marbles drawn at random from the box are the same color, and let Pd be the probability that they are different colors. Find |Ps − Pd|.

(A) 0

(B) \frac{1}{2002}

(C) \frac{1}{2001}

(D) \frac{2}{2001}

(E) \frac{1}{1000}
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 23 Mar 2009, 15:01
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Because of symmetry (1001 red = 1001 black) it doesn't matter what marble we take first. For second marble:
\frac{1000}{2001} - the same color

\frac{1001}{2001} - the different color

|Ps - Pd| = |\frac{1000}{2001} - \frac{1001}{2001}| = \frac{1}{2001}
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 27 Mar 2009, 00:17
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Since the number of black marbles = number of red marbles, we need not consider the first ball in the calculation.

So, the probability of getting different balls = probability of picking up the second ball from the lot other than from which the first ball is picked= \frac{1001}{2001}

Similarly the probability of getting same colored ball=probability of picking up the second ball from the same lot from which the first ball is picked =\frac{1000}{2001}

Hence |{P_s - P_d}|= \frac{1}{2001}
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 01 Apr 2009, 03:16
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Here is the next one...

N, the set of natural numbers is portioned into subsets
S1={1}
S2={2,3}
S3={4,5,6}
S4={7,8,9,10} and so on.

The sum of the numbers in subset S50 is


(A) 61,250
(B) 65,525
(C) 42,455
(D) 62,525
(E) None of these

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Re: Problem Solving for 780+ Aspirants [#permalink] New post 01 Apr 2009, 10:31
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With the same logic
S50 = 50*49/2 + 1 = 1226

SUM = 1226+1227....(1226+49)
= 1226*50 + (1+2...49)
= 61250 + 49*50/2
D
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 16 Apr 2009, 21:32
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cicerone wrote:
Here is the next one.....

If x,yare positive integers such that 5 \times x^3 = 6 \times y^4, find the minimum possible value of x+y.


A. 1240
B. 1260
C. 1060
D. 1080
E. None of these


Given that: x and y are +ve integers and
5x^3 = 6y^4
5x^3 = 2x3 y^4
y = (5x^3/6)^(1/4)

x = 5x6x6x6 = 6x180= 1080

y = [5 (5x6x6x6)^3 /6)]^(1/4)
y = [5^4 (6)^8)]^(1/4)
y = 5x6x6=180

x+y = 1260


Guess I encountered such question earlier too. :roll:
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 18 Apr 2009, 15:32
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nightwing79 wrote:
GMAT TIGER wrote:
nightwing79 wrote:
so I had exactly the same working as you did except

"x = 5x6x6x6 = 6x180= 1080"

how did you get that? hmmmm


Just get y's value in integer. To do that, x has to be 5*6*6*6. Since y = 4sqrt(5x^3 / 6) has one 5, one 6 in denominator, and three x, make the value of (5x^3 / 6) a squre of a square. To do that, x requires 5^3 to make 5^4 and 6^9 to make 6^8 after cancealing a 6. Hence 4th sqrt power of (5x^3 / 6) is a minimum integer vale.



Good stuff!

However - why does it have to be 6^9 why not 6^5 to make 6^4 hence square root of would still be an integer value.

The key is root to the power of 4 - have to remember that and then looking to understand what a min integer value would look like - good learning.

look forward to your correspondence.

che
dg


How do you get that? If you can, then thats the answer. But again, how?:roll:
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 05 May 2009, 22:26
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cicerone wrote:
Here is the next one.....

If x,yare positive integers such that 5 \times x^3 = 6 \times y^4, find the minimum possible value of x+y.

A. 1240

B. 1260

C. 1060

D. 1080

E. None of these


Folks, nice to see a good discussion on this question and also our friends have come up with some quick and lucid solutions.

I just thought to put forward another lucid way ....

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Re: Problem Solving for 780+ Aspirants [#permalink] New post 04 Nov 2013, 08:25
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walker wrote:
Because of symmetry (1001 red = 1001 black) it doesn't matter what marble we take first. For second marble:
\frac{1000}{2001} - the same color

\frac{1001}{2001} - the different color

|Ps - Pd| = |\frac{1000}{2001} - \frac{1001}{2001}| = \frac{1}{2001}



Walker...i think we should multiply it by 2 for same color and different color individually because we might get 2 blacks or 2 reds. So prob will be 2(1000/2001) and 2(1001/2001)

And the final answer would be 2/2001
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 23 Mar 2009, 02:28
This will be my first post here, sorry for my bad spelling (iam not a native english speaker).

First to support the chanse to have two red(r) marbles or two black(b) marbles (Ps).

P( (b*b) + (r*r) )

first marble P1(b) = 1001/2002
second marble p2(b) = 1000/2001 (1 less black marble and 1 less overall marbels)
The same calculation for the red marbles.

((1001/2002)*(1000/2001)) = ((1/2)*(1000/2001)) = 1000/4002 (b*b)
so:
P( (1000/4002) + (1000/4002) ) = 2000/4002 (This makes Ps)

Now for Pd:
The following combinations (r*b) and (b*r)
P( (r*b) + (b*r) )

P( b*r ) = (1001/2002) * (1001/2001) = ((1/2)*(1001/2002))= 1001/4002
Again the same goes for r*b

P( (1001/4002) + (1001/4002) ) = 2002/4002 (this makes Pd)

Now to answer the question:
|Ps - Pd|

(2000/4002) - (2002/4002) = (2/4002) = (1/2001)

So i think it would be answer C.
Than again, its my first post so comments plz :lol:
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 23 Mar 2009, 02:40
Sjorsl wrote:
This will be my first post here, sorry for my bad spelling (iam not a native english speaker).

First to support the chanse to have two red(r) marbles or two black(b) marbles (Ps).

P( (b*b) + (r*r) )

first marble P1(b) = 1001/2002
second marble p2(b) = 1000/2001 (1 less black marble and 1 less overall marbels)
The same calculation for the red marbles.

((1001/2002)*(1000/2001)) = ((1/2)*(1000/2001)) = 1000/4002 (b*b)
so:
P( (1000/4002) + (1000/4002) ) = 2000/4002 (This makes Ps)

Now for Pd:
The following combinations (r*b) and (b*r)
P( (r*b) + (b*r) )

P( b*r ) = (1001/2002) * (1001/2001) = ((1/2)*(1001/2002))= 1001/4002
Again the same goes for r*b

P( (1001/4002) + (1001/4002) ) = 2002/4002 (this makes Pd)

Now to answer the question:
|Ps - Pd|

(2000/4002) - (2002/4002) = (2/4002) = (1/2001)

So i think it would be answer C.
Than again, its my first post so comments plz :lol:


Welcome dude...A very good attempt...Why don't you cut down the calculation part? Think of it....
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 23 Mar 2009, 14:49
im getting 0 as my answer. is that right ? ill explain my logic if it is.
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 23 Mar 2009, 21:54
Agree with walker..

|2002/2002*1000/2001 - 2002/2002*1001/2001| = 1/2001
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 24 Mar 2009, 01:20
walker wrote:
Because of symmetry (1001 red = 1001 black) it doesn't matter what marble we take first. For second marble:
\frac{1000}{2001} - the same color

\frac{1001}{2001} - the different color

|Ps - Pd| = |\frac{1000}{2001} - \frac{1001}{2001}| = \frac{1}{2001}


:o once you see it its so obvious!
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 25 Mar 2009, 05:36
Sjorsl I concur

Quite simple actually!
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 27 Mar 2009, 21:32
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Folks, here comes the next one..This is from Geometry....

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Re: Problem Solving for 780+ Aspirants [#permalink] New post 27 Mar 2009, 23:07
cicerone wrote:
Folks, here comes the next one..This is from Geometry....

Image


IMO A.


the distance from small circle center to the origin point of XY plane is = root2 r.

16 = r + r Root 2)

r = 16(root 2 -1)
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 01 Apr 2009, 02:49
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Re: Problem Solving for 780+ Aspirants [#permalink] New post 11 Apr 2009, 03:17
Folks, sorry for the delay.(I was on a vacation)...

Here is the next one.....
There are some boys and some girls. If each child sits on one chair, one boy will have no chair to sit. If two boys sit on one chair and one girl occupies one chair, then three chairs are unoccupied. How many boys are there?

A. 4

B. 6

C. 8

D. 10

E. Cannot be determined

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Re: Problem Solving for 780+ Aspirants [#permalink] New post 11 Apr 2009, 19:03
cicerone wrote:
Folks, sorry for the delay.(I was on a vacation)...

Here is the next one.....
There are some boys and some girls. If each child sits on one chair, one boy will have no chair to sit. If two boys sit on one chair and one girl occupies one chair, then three chairs are unoccupied. How many boys are there?

A. 4

B. 6

C. 8

D. 10

E. Cannot be determined


b + g = c + 1
b/2 + g = c - 3

b = 8
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Re: Problem Solving for 780+ Aspirants   [#permalink] 11 Apr 2009, 19:03
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