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If a/b=-2/3, then (b-a)/a=?

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If a/b=-2/3, then (b-a)/a=?

by swerve » Fri Nov 24, 2017 11:28 am
$$If\ \frac{a}{b}=-\frac{2}{3},\ then\ \frac{b-a}{a}=?$$

$$(A)\ −5/2$$
$$(B)\ −5/3$$
$$(C)\ −1/3$$
$$(D)\ 0$$
$$(E)\ 7$$

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
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by EconomistGMATTutor » Sat Nov 25, 2017 7:53 am
$$If\ \frac{a}{b}=-\frac{2}{3},\ then\ \frac{b-a}{a}=?$$

$$(A)\ -5/2$$
$$(B)\ -5/3$$
$$(C)\ -1/3$$
$$(D)\ 0$$
$$(E)\ 7$$

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
Hi swerve,
Let's take a look at your question.
We are given with:
$$\frac{a}{b}=-\frac{2}{3}$$
$$a=-\frac{2b}{3}$$

We need to find the value of,
$$\frac{b-a}{a}$$

Plugin the value of a in the expression.

$$=\frac{b-\left(-\frac{2b}{3}\right)}{-\frac{2b}{3}}$$
$$=\frac{b+\frac{2b}{3}}{-\frac{2b}{3}}$$
$$=\frac{\frac{3b+2b}{3}}{-\frac{2b}{3}}$$
$$=\frac{\frac{5b}{3}}{-\frac{2b}{3}}$$
$$=\frac{5b\times3}{3\times\left(-2b\right)}$$
$$=\frac{5b}{\left(-2b\right)}$$
$$=-\frac{5}{2}$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.
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by [email protected] » Sat Nov 25, 2017 12:09 pm
Hi swerve,

We're told that A/B = -2/3. We're asked for the value of (B-A)/A. This question can be solved by TESTing VALUES.

IF....
A = -2 and B = 3
(B-A)/A = (3 - (-2))/-2 = 5/-2 = -5/2

Final Answer: A

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by Brent@GMATPrepNow » Sat Nov 25, 2017 1:28 pm
swerve wrote:$$If\ \frac{a}{b}=-\frac{2}{3},\ then\ \frac{b-a}{a}=?$$

$$(A)\ −5/2$$
$$(B)\ −5/3$$
$$(C)\ −1/3$$
$$(D)\ 0$$
$$(E)\ 7$$

Here's one more approach.

The GMAT seems to love the following identify: (x - y)/z = x/z - y/z

Let's see how we can apply that identity here.

First recognize that, if a/b = -2/3, then b/a = -3/2

So, we get: (b - a)/a = b/a - a/a (from the above identity)
= b/a - 1
= -3/2 - 1
= -3/2 - 2/2
= -5/2

Answer: A

Cheers,
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by Brent@GMATPrepNow » Sat Nov 25, 2017 1:31 pm
swerve wrote:$$If\ \frac{a}{b}=-\frac{2}{3},\ then\ \frac{b-a}{a}=?$$

$$(A)\ −5/2$$
$$(B)\ −5/3$$
$$(C)\ −1/3$$
$$(D)\ 0$$
$$(E)\ 7$$
By the way, I would have solved the question using the same approach that Rich used.
I just want to demonstrate that the approach works for ANY values of a and b such that a/b = -2/3
Rich successfully used a = -2 and b = 3

So, let's try a = 4 and b = -6
Notice that a/b = 4/(-6) = -2/3 (perfect!)

So, (b-a)/a = (-6 - 4)/4
= -10/4
= -5/2
= A

Cheers,
Brent
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Re: If a/b=-2/3, then (b-a)/a=?

by Scott@TargetTestPrep » Tue Jan 21, 2020 8:35 am
swerve wrote: ↑
Fri Nov 24, 2017 11:28 am
 $$If\ \frac{a}{b}=-\frac{2}{3},\ then\ \frac{b-a}{a}=?$$

$$(A)\ −5/2$$
$$(B)\ −5/3$$
$$(C)\ −1/3$$
$$(D)\ 0$$
$$(E)\ 7$$

The OA is A.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
We can let a = -2, and b = 3, and we have:

(3 - (-2))/(-2) = -5/2

Alternate Solution:

a/b = -⅔

Cross-multiplying gives us:

-3a = 2b

(-3a) / 2 = b

Now, substitute (-3a) / 2 for b in the expression (b - a) / a:

(b - a) / a = { [(-3a) / 2] - a} / a = (-3a - 2a) / 2a = -5a / 2a = -5/2

Answer: A

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