How can I using algebra, solve for this, thank you

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skyjuice: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Tue Nov 14, 2006 11:09 am

by skyjuice » Mon Nov 05, 2007 5:34 pm

If (2^x)(3^y)=288 where x and ya are positive intergers then (2^x-1)(3^y-2)= ?

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Source: Beat The GMAT — Problem Solving | Mon Nov 05, 2007 5:34 pm

camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Mon Nov 05, 2007 8:46 pm

Skyjuice, we can write -
(2^x)(3^y)=288 in (2^x)(3^y)=2^5 * 3^2
So x = 5 and y =2
And the rest thing we can calculate, right!

Correct me If I am wrong

Regards,

Amitava

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samirpandeyit62: Master | Next Rank: 500 Posts; Posts: 460; Joined: Sun Mar 25, 2007 7:42 am; Thanked: 27 times

by samirpandeyit62 » Mon Nov 05, 2007 8:50 pm

If (2^x)(3^y)=288 where x and ya are positive intergers then (2^x-1)(3^y-2)= ?

(2^x)(3^y)=288

now (2^x-1)(3^y-2)= (2^x)(3^y)/2*9 = 288/18 =16

Regards
Samir

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moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

by moneyman » Mon Nov 05, 2007 9:44 pm

Samir can u explain this step pls

(2^x-1)(3^y-2)= (2^x)(3^y)/2*9 = 288/18 =16

How did u get 2*9??

Maxx

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camitava: Legendary Member; Posts: 645; Joined: Wed Sep 05, 2007 4:37 amFollowed by: 5 members; Location: India; Thanked: 34 times

by camitava » Mon Nov 05, 2007 9:51 pm

Moneyman, Samir has taken -

(2^x-1)(3^y-2)= (2^x)(3^y)/2*9 = 288/18 =16

by this what he tried to mean that 2^x - 1 = 2^(x - 1) and same for the rest.
I am still confused what skyjuice wanted to mean it - is it 2^x - 1 or 2^(x - 1). Got my point, moneyman!

Correct me If I am wrong

Regards,

Amitava

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samirpandeyit62: Master | Next Rank: 500 Posts; Posts: 460; Joined: Sun Mar 25, 2007 7:42 am; Thanked: 27 times

by samirpandeyit62 » Mon Nov 05, 2007 9:51 pm

(2^x-1)(3^y-2)= (2^x)(3^y)/2*9 = 288/18 =16

(2^x-1) = 2^x /2

(3^y-2)= 3^y / 3^2

Regards
Samir

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moneyman: Master | Next Rank: 500 Posts; Posts: 468; Joined: Sat Mar 03, 2007 10:17 pm; Thanked: 5 times

by moneyman » Mon Nov 05, 2007 9:58 pm

I think I have got the logic here

(2^x-1) = 2^x/2 because lets assume x=3 then 2^x=2^3=8 and (2^x-1)=2(3-1)=2^2=4 or 2^3/2.

Thanks a lot Samir!!

Maxx

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