Problem Solving

Hi RiyaR,

This question is a real "pattern-matcher's" question. You don't have to do a lot of math to solve it, but you do have to think about how fractions can be equal to one another….

We're told that B and C are positive.

We're also told that 1/B = B/C = C/8

Let's start with that last fraction….C/8. We're told that the other two fractions are also equal to C/8 so they both need to have denominators that are either FACTORS of 8 or MULTIPLES of 8. Since the answer choices are relatively small, we're probably going to be dealing with FACTORS of 8….

So, what divides evenly into 8? 1, 2, 4, 8…..

B/C = C/8

If C = 8, then B = 8, but then 1/B would not equal the other two fractions, so C CANNOT = 8
If C = 4, then B = 2…..and we have 1/2 = 2/4 = 4/8. This is exactly what we're looking for.

The question asks us for B+C…..2+4 = 6

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

RiyaR wrote:If b and c are positive numbers and 1/b = b/c = c/8 , then b + c =
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

Here's an algebraic solution.

Begin with 1/b = b/c = c/8
The lowest common denominator of b, c and 8 is 8bc.
So, multiply all three sides by 8bc to get: 8c = 8b² = bc²

Let's focus on 8c = 8b²
Divide both sides by 8 to get: c = b²

Now, let's focus on 8c = bc²
Divide both sides by c to get: 8 = bc

So, we have the following system:
c = b²
8 = bc

Take the red equation, and replace c with b² to get: 8 = b(b² )
Simplify: 8 = b³
Solve: b = 2

Now that we know that b = 2, we can use the fact that 1/b = c/8 to get 1/2 = c/8
This means that c = 4

So, b + c = 2 + 4 = [spoiler]6 = B[/spoiler]

Cheers,
Brent

RiyaR wrote: ↑

Fri Sep 19, 2014 10:15 am

17. If b and c are positive numbers and 1/b=b/c=c/8 , then b + c =
(A) 4
(B) 6
(C) 7
(D) 8
(E) 9

We see that the equation can be re-expressed as three separate equations: 1/b = b/c, b/c = c/8, and 1/b = c/8.

Using the first equation, we have:

1/b = b/c

b^2 = c

Using the third equation, we have:

1/b = c/8

bc = 8

Since c = b^2, we have:

b(b^2) = 8

b^3 = 8

b = 2

So c = 2^2 = 4, and therefore, b + c = 2 + 4 = 6.

Answer: B