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If a and b are positive and

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Carcass

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If a and b are positive and [#permalink]

Updated on: 25 Jul 2021, 21:41

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If a and b are positive and

$\frac{ab}{x}=\sqrt{a}$ then

$\frac{x}{b^2}=$

A.

$\sqrt{a}$

B.

$\frac{\sqrt{a}}{b}$

C.

$\frac{a}{b^2}$

D.

$\sqrt{ab}$

E.

$\sqrt{\frac{a}{b}}$

Kudos for the right answer and explanation

Official Answer

B

Originally posted by Carcass on 27 Jan 2020, 15:22.
Last edited by Ks1859 on 25 Jul 2021, 21:41, edited 1 time in total.

GreenlightTestPrep

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Re: If a and b are positive and [#permalink]

27 Jan 2020, 16:21

1

Carcass wrote:

If a and b are positive and

$\frac{ab}{x}=\sqrt{a}$ then

$\frac{x}{b^2}=$

A.

$\sqrt{a}$

B.

$\frac{\sqrt{a}}{b}$

C.

$\frac{a}{b^2}$

D.

$\sqrt{ab}$

E.

$\sqrt{\frac{a}{b}}$

Kudos for the right answer and explanation

Rather than attempt a lot of algebraic manipulations, we can simply find values of a, b and x that satisfy the given equation and then test the answer choices...

If

$\frac{ab}{x}=\sqrt{a}$ , then it COULD be the case that a = 4, b = 3 and x = 6, since these values satisfy the given equation.

The question asked us to find the value of

$\frac{x}{b^2}$

So, plug a = 4, b = 3 and x = 6 into the expression to get:

$\frac{x}{b^2}=\frac{6}{3^2}=\frac{6}{9}=\frac{2}{3}$

So, when a = 4, b = 3 and x = 6,

$\frac{x}{b^2}=\frac{2}{3}$

This means the correct answer will be the one that evaluates to equal 2/3 when we plug in a = 4, b = 3 and x = 6....

A.

$\sqrt{4}$ = 2. NO GOOD. We want the expression to evaluate to be 2/3

B.

$\frac{\sqrt{4}}{3}$ = 2/3. Perfect!

C.

$\frac{4}{3^2}$ = 4/9. NO GOOD. We want the expression to evaluate to be 2/3

D.

$\sqrt{(4)(3)}$ = √12. NO GOOD. We want the expression to evaluate to be 2/3

E.

$\sqrt{\frac{4}{3}}$ = 2/√3. NO GOOD. We want the expression to evaluate to be 2/3

Answer: B

Cheers,
Brent

GreenlightTestPrep

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Re: If a and b are positive and [#permalink]

27 Jan 2020, 16:36

1

Carcass wrote:

If a and b are positive and

$\frac{ab}{x}=\sqrt{a}$ then

$\frac{x}{b^2}=$

A.

$\sqrt{a}$

B.

$\frac{\sqrt{a}}{b}$

C.

$\frac{a}{b^2}$

D.

$\sqrt{ab}$

E.

$\sqrt{\frac{a}{b}}$

Kudos for the right answer and explanation

Alternate solution....

Given:

$\frac{ab}{x}=\sqrt{a}$

Square both sides to get:

$\frac{a^2b^2}{x^2}=a$

Divide both sides by

$a^2$ to get:

$\frac{b^2}{x^2}=\frac{a}{a^2}$

Simplified to get:

$\frac{b^2}{x^2}=\frac{1}{a}$

Multiply both sides by

$x$ to get:

$\frac{b^2}{x}=\frac{x}{a}$

Flip both fractions to get:

$\frac{x}{b^2}=\frac{a}{x}$

NOTE: Since none of the answer choices include the variable x, we still need to replace the x (on the right side of the equation) with an equivalent expression that equals x
So at this point we're going to solve the original equation for x.

Take:

$\frac{ab}{x}=\sqrt{a}$

Multiply both sides of the equation by x to get:

$ab=x\sqrt{a}$

Divide both sides of the equation by

$\sqrt{a}$ to get:

$\frac{ab}{\sqrt{a}}=x$

Simplify the left side of the equation to get:

$b\sqrt{a}=x$

Great! We've now found an expression that is equivalent to x

So, take:

$\frac{x}{b^2}=\frac{a}{x}$

And replace x with

$b\sqrt{a}$ to get:

$\frac{x}{b^2}=\frac{a}{b\sqrt{a}}$

Simplify to get:

$\frac{x}{b^2}=\frac{\sqrt{a}}{b}$

Answer: B

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Re: If a and b are positive and [#permalink]

28 Jan 2020, 04:25

Carcass wrote:

If a and b are positive and

$\frac{ab}{x}=\sqrt{a}$ then

$\frac{x}{b^2}=$

A.

$\sqrt{a}$

B.

$\frac{\sqrt{a}}{b}$

C.

$\frac{a}{b^2}$

D.

$\sqrt{ab}$

E.

$\sqrt{\frac{a}{b}}$

Kudos for the right answer and explanation

$ab/x = \sqrt{a}$ ... (i)

Squaring both sides (to get rid of the square-root):

$a^2 * b^2/x^2 = a$

Dividing by

$a$ on both sides:

$a * b^2 = x^2$

Dividing by

$b^2$ on both sides:

$a = x^2/b^2$

Dividing by

$x$ on both sides:

$a/x = x/b^2$

Thus, we have:

$x/b^2 = a/x$ ... (ii)

From (i):

$ab/x = \sqrt{a}$

Dividing by

$ab$ on both sides:

$1/x = \sqrt{a}/ab$

$=> x = ab/\sqrt{a}$

From (ii):

$x/b^2 = a/x$

$= a/(ab/\sqrt{a})$

$=> x/b^2 = \sqrt{a}/b$

Answer B

Ashgre

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Re: If a and b are positive and [#permalink]

28 Jan 2020, 07:02

Another approach is to simplify ab/x = √a, for x to get: x = b√a.

Then substitute x in x/b^2 = b√a/b^2 = √a/b.

Ezio23

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Re: If a and b are positive and [#permalink]

29 Jan 2020, 06:34

1

x/(a*b) = 1/ √a
3 step answer:
step1: x/b = a/ √a
step2: x/b^2 = a/(b*√a)
step3: x/b^2=√a/b

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Re: If a and b are positive and [#permalink]

09 Jul 2023, 17:49

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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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Re: If a and b are positive and [#permalink]

09 Jul 2023, 17:49

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