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If the ratio of 2a to b is 8 times the ratio of b to a, then b/a could

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If the ratio of 2a to b is 8 times the ratio of b to a, then b/a could  [#permalink]

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New post 05 Jun 2019, 00:28
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (01:37) correct 44% (01:34) wrong based on 48 sessions

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If the ratio of 2a to b is 8 times the ratio of b to a, then b/a could  [#permalink]

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New post Updated on: 05 Jun 2019, 00:37
Bunuel wrote:
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


given
2a/b=8*b/a
solve
a^2=4*b^2
square
a=2b
b/a= +/-1/2
IMOD
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Originally posted by Archit3110 on 05 Jun 2019, 00:31.
Last edited by Archit3110 on 05 Jun 2019, 00:37, edited 2 times in total.
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Re: If the ratio of 2a to b is 8 times the ratio of b to a, then b/a could  [#permalink]

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New post 05 Jun 2019, 00:36
Bunuel wrote:
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


IMO D.

solving the equation-

2a/b = 8b/a we get (b/a)^2 = 1/4

So, b/a = +- 1/2
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Re: If the ratio of 2a to b is 8 times the ratio of b to a, then b/a could  [#permalink]

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New post 06 Jun 2019, 21:37
Bunuel wrote:
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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Re: If the ratio of 2a to b is 8 times the ratio of b to a, then b/a could   [#permalink] 06 Jun 2019, 21:37
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