prime factors

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sat Mar 19, 2011 3:56 am

a^1/3*(sqroot(b))^6= 500

What can a+ b=?

I got 69

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Source: Beat The GMAT — Problem Solving | Sat Mar 19, 2011 3:56 am

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Sat Mar 19, 2011 5:34 am

Is the ^6 applicable only to b?

Vineesh,
Just telling you what I know and think. I am not the expert.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Mar 19, 2011 9:47 am

yellowho wrote:a^1/3*(sqroot(b))^6= 500

What can a+ b=?

There may be various possible results as there is no declaration about whether a and b are integers or not. But if we assume they are integers, then,

[a^(1/3)]*[b^(1/2)]^6 = [a^(1/3)]*[b^3] = 500 = 4*125 = (2^2)*(5^3)

Comparing the terms, a^(1/3) = 4 => a = 64 and b = 5 => (a + b) = 69

But if they are not integers, then other possible solution is,

a^(1/3) = 125 and b^3 = 4
And accordingly we need to find (a + b)

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