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# PS-GMAT prep

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Intern
Joined: 09 Jan 2006
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PS-GMAT prep [#permalink]  23 Feb 2006, 15:25
00:00

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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
Manager
Joined: 14 Jun 2005
Posts: 100
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Kudos [?]: 5 [0], given: 0

1. I got 1/5
2. Joe, how did you get 7? Can you please explain?
Manager
Joined: 20 Feb 2006
Posts: 213
Followers: 1

Kudos [?]: 5 [0], given: 0

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.
Director
Joined: 17 Oct 2005
Posts: 940
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Kudos [?]: 62 [0], given: 0

Re: PS-GMAT prep [#permalink]  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

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.
Manager
Joined: 28 Dec 2005
Posts: 117
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Kudos [?]: 1 [0], given: 0

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
Manager
Joined: 04 Sep 2005
Posts: 142
Location: Fringes of the Boreal, Canada
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Kudos [?]: 4 [0], given: 0

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
_________________

"To hell with circumstances; I create opportunities." - Bruce Lee

SVP
Joined: 14 Dec 2004
Posts: 1707
Followers: 1

Kudos [?]: 50 [0], given: 0

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?
Intern
Joined: 09 Jan 2006
Posts: 14
Location: USA
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Hi
sorry for replying so late the OA for 1 is D

and OA for 2 is also D i.e 7

thanks....
Intern
Joined: 06 Mar 2006
Posts: 37
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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
Joined: 11 Nov 2005
Posts: 332
Location: London
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Kudos [?]: 8 [0], given: 0

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.
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