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Senior Manager
Joined: 29 Nov 2006
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PS-Prep, time killer [#permalink]
 28 Jun 2007, 09:19
Question Stats:
0% (00:00) correct
 0% (00:00) wrong based on 0 sessions
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
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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)
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CIO
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Re: PS-Prep, time killer [#permalink]
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.
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VP
Joined: 08 Jun 2005
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Re: PS-Prep, time killer [#permalink]
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.
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Director
Joined: 26 Feb 2006
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Re: PS-Prep, time killer [#permalink]
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..
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Senior Manager
Joined: 29 Nov 2006
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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!
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Manager
Joined: 14 Mar 2007
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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
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