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# PS-Prep, time killer

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Senior Manager
Joined: 29 Nov 2006
Posts: 318
Location: Orange County, CA
PS-Prep, time killer [#permalink]

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28 Jun 2007, 09:19
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Any suggestions for a quicker answer?

I was taking too long determining sign changes and adding / subtracting between each item (1-10) and ended up just guessing in order to move onto the next problem.

Looking for ways to cut down time on easy questions like this.
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VP
Joined: 08 Jun 2005
Posts: 1145

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28 Jun 2007, 10:38
using Geometric Progression formula is shorter but easy to make mistakes:

Sn = a(1-R^n)/(1-R)

n = 10
a = 1/2

F(1) = 1/2
F(2) = -1/4
F(3) = 1/8

hence R = -1/2

solve GP

Sn = 1/2*(1-(-1/2^10))/(1-(-1/2))

Sn = (1025/2048)/(3/2)

Sn = 2050/2048/3

Sn = ~1/3

the answer is (D)

CIO
Joined: 09 Mar 2003
Posts: 463
Re: PS-Prep, time killer [#permalink]

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28 Jun 2007, 12:06
misterJJ2u wrote:
Any suggestions for a quicker answer?

I was taking too long determining sign changes and adding / subtracting between each item (1-10) and ended up just guessing in order to move onto the next problem.

Looking for ways to cut down time on easy questions like this.

Also D. 1 minute.

1. Find pattern. There has to be one, otherwise it wouldn't be a GMAT question. Very quickly see that this thing is just alternating positive and negative powers of 1/2:
1/2, -1/4, 1/8, -1/16....

2. Every change is smaller than the previous one. Classic GMAT game. I drew a number line:

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2

Numbers start at 1/2, then down 1/4, then up 1/8, then down 1/16. You basically bounce back and fourth, but you NEVER cross 1/4, and you never cross 1/2.

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2
...................................................... Start
............................ {---------------------- ....(Back 1/4)
............................. ------------} ...............(forward 1/8)
......................................{----- ................(back 1/16)
.......................................---} .................(forward 1/32)
....................................... {- .................. (back 1/64)

Etc, etc. It's a lot here to type out, on paper, really simple. Either way, you can see the range you're in pretty clearly.
VP
Joined: 08 Jun 2005
Posts: 1145
Re: PS-Prep, time killer [#permalink]

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28 Jun 2007, 12:25
ian7777 wrote:
misterJJ2u wrote:
Any suggestions for a quicker answer?

I was taking too long determining sign changes and adding / subtracting between each item (1-10) and ended up just guessing in order to move onto the next problem.

Looking for ways to cut down time on easy questions like this.

Also D. 1 minute.

1. Find pattern. There has to be one, otherwise it wouldn't be a GMAT question. Very quickly see that this thing is just alternating positive and negative powers of 1/2:
1/2, -1/4, 1/8, -1/16....

2. Every change is smaller than the previous one. Classic GMAT game. I drew a number line:

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2

Numbers start at 1/2, then down 1/4, then up 1/8, then down 1/16. You basically bounce back and fourth, but you NEVER cross 1/4, and you never cross 1/2.

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2
...................................................... Start
............................ {---------------------- ....(Back 1/4)
............................. ------------} ...............(forward 1/8)
......................................{----- ................(back 1/16)
.......................................---} .................(forward 1/32)
....................................... {- .................. (back 1/64)

Etc, etc. It's a lot here to type out, on paper, really simple. Either way, you can see the range you're in pretty clearly.

Nice ! - Thanks for your help - I'm guessing its a lot of work to write it all down. A true and elegant solution.

Director
Joined: 26 Feb 2006
Posts: 899
Re: PS-Prep, time killer [#permalink]

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28 Jun 2007, 12:33
ian7777 wrote:
misterJJ2u wrote:
Any suggestions for a quicker answer?

I was taking too long determining sign changes and adding / subtracting between each item (1-10) and ended up just guessing in order to move onto the next problem.

Looking for ways to cut down time on easy questions like this.

Also D. 1 minute.

1. Find pattern. There has to be one, otherwise it wouldn't be a GMAT question. Very quickly see that this thing is just alternating positive and negative powers of 1/2:
1/2, -1/4, 1/8, -1/16....

2. Every change is smaller than the previous one. Classic GMAT game. I drew a number line:

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2

Numbers start at 1/2, then down 1/4, then up 1/8, then down 1/16. You basically bounce back and fourth, but you NEVER cross 1/4, and you never cross 1/2.

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2
...................................................... Start
............................ {---------------------- ....(Back 1/4)
............................. ------------} ...............(forward 1/8)
......................................{----- ................(back 1/16)
.......................................---} .................(forward 1/32)
....................................... {- .................. (back 1/64)

Etc, etc. It's a lot here to type out, on paper, really simple. Either way, you can see the range you're in pretty clearly.

wonderful approach..

btw, i got 341/1024 using my lengthy approach..
Senior Manager
Joined: 29 Nov 2006
Posts: 318
Location: Orange County, CA

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28 Jun 2007, 12:55
Quote:

Also D. 1 minute.

1. Find pattern. There has to be one, otherwise it wouldn't be a GMAT question. Very quickly see that this thing is just alternating positive and negative powers of 1/2:
1/2, -1/4, 1/8, -1/16....

2. Every change is smaller than the previous one. Classic GMAT game. I drew a number line:

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2

Numbers start at 1/2, then down 1/4, then up 1/8, then down 1/16. You basically bounce back and fourth, but you NEVER cross 1/4, and you never cross 1/2.

-|---------------------|----------------------|
0 ....................... 1/4 ..................... 1/2
...................................................... Start
............................ {---------------------- ....(Back 1/4)
............................. ------------} ...............(forward 1/8)
......................................{----- ................(back 1/16)
.......................................---} .................(forward 1/32)
....................................... {- .................. (back 1/64)

Etc, etc. It's a lot here to type out, on paper, really simple. Either way, you can see the range you're in pretty clearly.

Thanks Ian. That's exactly what I was looking for. I figured there was some easier way. Now I just have to be able to find it and apply it on test day!
Manager
Joined: 14 Mar 2007
Posts: 235

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28 Jun 2007, 13:25
my aproach to this question:

first try 3 consecutive numbers

for k =1 : 0.5
for k=2 : -0.25
for k=3 : 0.125

so we have a geometric progression with ratio 1/-2....with this you can get your answer in less than 1minut
28 Jun 2007, 13:25
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# PS-Prep, time killer

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