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Bunuel
If the ratio of 2a to b is 8 times the ratio of b to a, then \(\frac{b}{a}\) could be which of the following?

I. \(-2\)

II. \(-\frac{1}{2}\)

III. \(\frac{1}{2}\)

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

Let's set up our equation :dazed

\(2*\frac{a}{b} = 8*\frac{b}{a}\)

Now let's plug in the answers!

\(\text{I. } \frac{b}{a} = -2 \therefore \frac{a}{b} = -\frac{1}{2}\)

\(2*-\frac{1}{2} = 8*-2\)
\(-1 = -16\) ?
FALSE

\(\text{II. } \frac{b}{a} = -\frac{1}{2} \therefore \frac{a}{b} = -2\)

\(2*-2 = 8*-\frac{1}{2}\)
\(-4 = -4\) ?
TRUE

\(\text{III. } \frac{b}{a} = \frac{1}{2} \therefore \frac{a}{b} = 2\)

\(2*2 = 8*\frac{1}{2}\)
\(4 = 4\) ?
TRUE

E is the correct answer.
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Asked: If the ratio of 2a to b is 8 times the ratio of b to a, then \(\frac{b}{a}\) could be which of the following?

(2a/b) = 8 * (b/a)
2a/b - 8b/a = 0
(2a^2 - 8b^2)/ab = 0
(a-2b)(a+2b)/ab = 0
Either a= 2b; b/a = 1/2
Or a = -2b ; b/a = -1/2

I. \(-2\)

II. \(-\frac{1}{2}\)

III. \(\frac{1}{2}\)

A. I only
B. II only
C. III only
D. II and III only
E. I, II and III

IMO D
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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