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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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Joined: 02 Sep 2009
Posts: 60687
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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05 Jun 2019, 00:28
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Difficulty:

45% (medium)

Question Stats:

58% (01:30) correct 42% (01:33) wrong based on 57 sessions

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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

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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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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

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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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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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

$$2*\frac{a}{b} = 8*\frac{b}{a}$$

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

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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