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PS-GMAT prep [#permalink] New post 23 Feb 2006, 15:25
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D
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Hi
This is a tricky one...

1.Alices take home pay last year was the same each month, and she saved the same fraction of her take home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month?

a.1/2
b.1/3
c.1/4
d.1/5
e.1/6

Is there a shortcut to doing this one? I figured a slightly longish way

2.What is the greatest prime factor of 4^17-4^28

a.2
b.3
c.5
d.7
e.11

Thanks
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 [#permalink] New post 24 Feb 2006, 11:45
1. I got 1/5
2. Joe, how did you get 7? Can you please explain?
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GMAT Tests User
 [#permalink] New post 24 Feb 2006, 17:29
I got it all wrong.
1. 3/4 (its not in the answer choices)
2. 2047 (I dont believe it has any factors. Am I missing something? I could not factor it any less. And no answer choice divides this figure)
Any help is greatly appreciated.
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Re: PS-GMAT prep [#permalink] New post 25 Feb 2006, 00:02
girl17 wrote:
Hi
This is a tricky one...

1.Alices take home pay last year was the same each month, and she saved the same fraction of her take home pay each month.The total amount of money that she had saved at the end of the year was 3 times the amount of that portion of her monthly take home pay that she did not save.If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month?

a.1/2
b.1/3
c.1/4
d.1/5
e.1/6

Is there a shortcut to doing this one? I figured a slightly longish way

2.What is the greatest prime factor of 4^17-4^28

a.2
b.3
c.5
d.7
e.11

Thanks


1) i misread the q's
x=pay each month
y=save each month
x-y=amount she didnt save

12y=3(x-y)

y=1/5x

2) i simplified it to 2^34 *(-1)(2^22-1)=4194304-1=4194303

I think it is 3.
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 [#permalink] New post 26 Feb 2006, 17:05
The question is incorrectly stated, the correct question is "What is the greatest prime factor of 4^17-2^28"
A. 2
B. 2
C. 5
D. 7
E. 11
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 [#permalink] New post 01 Mar 2006, 07:01
x = amount not saved
y = amount saved per month
P= total monthly pay

3x = 12y
x = 4y
x/4 = y

P = x+y
P = 4x/4 + x/4
P = 5x/4

therefore, the portion of her take home pay that she saved each month is:

y/P = (1/4)/(5/4) = 0.25/1.25 = 1/5
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"To hell with circumstances; I create opportunities." - Bruce Lee

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 [#permalink] New post 01 Mar 2006, 10:07
1) Ans: 1/5

2) 4^17-4^28
=> 2^34 (1-2^22)
=> -2^34 (2^10 * 2^10 * 2^2 - 1)
need to do (1024 * 1024 * 4 - 1)

hence, must be experimental question ;)

Me too think, the question is stated in wrong way

If I take,
4^17-2^28
=> 2^34 - 2^28
=> 2^28 (2^6 - 1)
=> 2^28 (63)
=> 2^28 (3*3*7)

Ans: 7

What's the OA girl17?
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 [#permalink] New post 09 Mar 2006, 12:07
Hi
sorry for replying so late the OA for 1 is D

and OA for 2 is also D i.e 7


thanks....
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GMAT Tests User
 [#permalink] New post 09 Mar 2006, 20:19
can someone correct me pls? thanks

let x be the take home pay of Alice

and 1/y be the fraction that she saves

which means she has saved 12 * x/y for the year

and her actual take home pay was x-x/y i.e., 12 * (x-x/y) for the year



3*(12 * x/y) = 12 *(x-x/y)

=> 36x/y = (12xy-12x)/y
=> 36x = 12xy-12x
=> 48x = 12xy
=> 1/y = 1/4
Senior Manager
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 [#permalink] New post 10 Mar 2006, 10:09
D. 1/5


Lets say the monthly income is 100, save 20 (that is 1/5)

at the end of the year total saved is 20*12 =240

Monthly NOT saved is 80, which is 3 times the annual saving.
  [#permalink] 10 Mar 2006, 10:09
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