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ps can anyone help?

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ps can anyone help? [#permalink]

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New post 14 Apr 2010, 16:18
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#1 Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much as Mark, how many more hours did Mark charge to the project than Kate?

#2 What is the greatest prime factor of 4^17 - 2^28
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Re: ps can anyone help? [#permalink]

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New post 14 Apr 2010, 16:57
Ques 1
X+2X+6X = 162
X= 18

5X =90

Ques2

4^17 and 2^28 = 2^34 + 2^28
greates Prime factor = 2
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Re: ps can anyone help? [#permalink]

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New post 14 Apr 2010, 22:04
Socker121314 wrote:
Ques 1
X+2X+6X = 162
X= 18

5X =90

Ques2

4^17 and 2^28 = 2^34 + 2^28
greates Prime factor = 2


The question is 4^17 - 2^28 not 4^17 + 2^28.
4^17 - 2^28 = 2^34 - 2^28
= 2^28(2^6-1)
=2^28 (63)
=2^28*3^2*7
Greatest prime factor should be 7
Even 4^17 + 2^28 = 2^28(2^6+1)
=2^28*13*5 . So greatest prime factor should be 13
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Re: ps can anyone help? [#permalink]

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New post 14 Apr 2010, 22:34
CC2HBS wrote:
#1 Pat, Kate and Mark charged a total of 162 hours to a certain project. If Pat charged twice as much time to the project as Kate and 1/3 as much as Mark, how many more hours did Mark charge to the project than Kate?
____________

let the hours charged by pat = p hours
let the hours charged by kate = k hours
let the hours charged by mark = m hours
given that,
p = 2k => k = p/2
p = m/3 => m = 3p
p+k+m = 162
so, p + p/2 + 3p = 162
solving for p we get p = 36
m = 3*36 = 108, k = 36/2 = 18
and m-k = 90
hope it is correct.
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Re: ps can anyone help? [#permalink]

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New post 15 Apr 2010, 08:04
2nd question

Isnt it 4^17 - 2^28

why every1 is adding both instead of subtracting

heres my solution -
2^28 (2^6 - 1) => 2^28 (63) => 2^28 (3*3*7)
Greatest prime factor is 7
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Re: ps can anyone help?   [#permalink] 15 Apr 2010, 08:04
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