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b and c are postive numbes and 1/b=b/c=c/8 What is b+c? For

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Manager
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b and c are postive numbes and 1/b=b/c=c/8 What is b+c? For [#permalink] New post 09 Nov 2003, 12:46
b and c are postive numbes and 1/b=b/c=c/8

What is b+c?

For b, I am getting 1/8 and c=1

The choices are

4
6
7
8
9
Manager
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 [#permalink] New post 09 Nov 2003, 16:45
I get 6.

...weird problem though!
Manager
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Hey [#permalink] New post 09 Nov 2003, 17:03
6 is the answer, how did you get it?
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 [#permalink] New post 10 Nov 2003, 23:48
{b^2=c
{c^2=8b

b and c are not zeroes

solve the system and get b=2 and c=4

2+4=6
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Re: Hey [#permalink] New post 11 Nov 2003, 12:27
ftoor wrote:
6 is the answer, how did you get it?

To try a quick way, I looked at only the first two parts, disregarding c/8, because they give me some information about relation between b and c.
1/b=b/c
b┬▓ = c

Here since you know c = b┬▓, you could use this information in the equation b + c.
b + c
= b + b┬▓
= b(b + 1)

This tells us that the answer should be the product of b and it's immediate follower: the only answer that satisfies this condition is 6. 2(2 + 1) = 2*3 = 6.

Of course, the drawback of this technique is that you have to go with an intuition that b is an integer, otherwise you end up back and top and start all over again. But that doesn't take too long... probably like 30-40 seconds.
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 [#permalink] New post 11 Nov 2003, 13:00
from 1/b=b/c=c/8
b^2=c & b*c=8

So,
b* (b^2)=8
b=2

b*c=8
2*c=8
c=4
  [#permalink] 11 Nov 2003, 13:00
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b and c are postive numbes and 1/b=b/c=c/8 What is b+c? For

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