powers..

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ska7945: Master | Next Rank: 500 Posts; Posts: 200; Joined: Thu Aug 07, 2008 5:14 pm; Thanked: 1 times

by ska7945 » Mon Aug 11, 2008 5:51 pm

Which of the following is equal to (2^12-2^6)/(2^6-2^3)?

a) 2^6+2^3 b) 2^6-2^3 c)2^9 d)2^3 e)2

provide explanation please.
answer a

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Source: Beat The GMAT — Problem Solving | Mon Aug 11, 2008 5:51 pm

Sunny22uk: Master | Next Rank: 500 Posts; Posts: 144; Joined: Thu Apr 17, 2008 3:33 pm; Thanked: 8 times

Re: powers..

by Sunny22uk » Mon Aug 11, 2008 6:45 pm

ska7945 wrote:Which of the following is equal to (2^12-2^6)/(2^6-2^3)?

a) 2^6+2^3 b) 2^6-2^3 c)2^9 d)2^3 e)2

provide explanation please.
answer a

Solution:-
1) Equation is (2^12-2^6)/(2^6-2^3)
2) Take 2^6 common for numerator and 2^3 common for denominator
i.e. 2^6(2^6-1)/2^3(2^3-1) which is 2^3(2^6-1)/(2^3-1)
3) 2^3(2^6-1)/(2^3-1) can be rewritten as 2^3(2^3-1)(2^3+1)/(2^3-1)
4) The equation becomes 2^3(2^3+1) i.e. 2^6+2^3
5) Hence A

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