Keep getting the wrong answer!!!! Again what do you think?

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Kaunteya: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jan 28, 2008 4:12 pm; Location: Montreal, Canada; Thanked: 2 times

by Kaunteya » Thu Feb 28, 2008 4:26 pm

(8/10)^-5 / (4/10)^-4=

(A) 3/32
(B) 5/64
(C) 1/2
(D) 1
(E) 2

I keep getting C but the OA is B?
Why?

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Source: Beat The GMAT — Problem Solving | Thu Feb 28, 2008 4:26 pm

keerthivivek: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Mon Jan 07, 2008 6:31 pm; Thanked: 1 times

simplification

by keerthivivek » Thu Feb 28, 2008 4:52 pm

num = (8/10) ^ -5 = (10/8 ) ^ 5

den = (4/10) ^ -5 = ( 10/4 ) ^ 5

so, num/den= (10/8) ^ 5 * (4/10) ^5

= 10/(2^5)

= 5/64

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smushkas: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jul 01, 2007 5:56 pm; Thanked: 3 times

by smushkas » Thu Feb 28, 2008 5:23 pm

N => (8 / 10)^-5 ==> (10 / 8)^5
D => (4 / 10)^-4 ==> (10 / 4)^4
Then you can write ==> [ 10^5 / 8^5 ] * [ 4^4 / 10^4 ] ==> 10^4 cancel out in both fractions,
leaving you with [10 * (2^2)^4 ] / [ (2^3)^5 ] = [ 10 * 2^8 ] / [ 2^15 ]
here you can cancel out 2^8 from both N & D that leaves 10 / 2^7 = 10 / 128 = 5 / 64
Perhaps there are some other quicker ways or tricks to deal with this kinda problems....

Hope this helps!

keerthivivek;
You have a typo in the denominator, it is power of [-4]

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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 » Fri Feb 29, 2008 5:59 am

Try this ..

By properties, n^-1=1/n^1 so

(8/10)^-5=(8^-5)/(10^-5)=(1/8^5)/(1/10^5)=(10^5/8^5)

The same way (4/10)-4=(10^4/4^4)

Therefore, (8/10)^-5/(4/10^-4)=(10^5/8^5)/(10^4/4^4)

which will be =(10^5/8^5)*(4^4/10^4) (by the rule of division)

by cross multiplying we get, (10/8^5)*(4^4)=(10/2^15)*(2^8)

which will be equal to 10/2^7 = 10/128=5/64

Hope it helps!!

Maxx

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