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# If a and b are positive and ab/x = a, then x/b =

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
If a and b are positive and ab/x = a, then x/b =  [#permalink]

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05 Feb 2019, 02:43
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:56) correct 26% (01:48) wrong based on 23 sessions

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If a and b are positive and $$\frac{ab}{x} = \sqrt{a}$$, then $$\frac{x}{\sqrt{b}} =$$

A. $$\sqrt{a}$$

B. $$\sqrt{ab}$$

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

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

E. a^2

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Re: If a and b are positive and ab/x = a, then x/b =  [#permalink]

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05 Feb 2019, 03:21
Bunuel wrote:
If a and b are positive and $$\frac{ab}{x} = \sqrt{a}$$, then $$\frac{x}{\sqrt{b}} =$$

A. $$\sqrt{a}$$

B. $$\sqrt{ab}$$

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

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

E. a^2

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

sqrt a*b=x

so
$$\frac{x}{\sqrt{b}} =$$
sqrt a * b/ sqrt b = sqrt a*b
IMO B
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SVP
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WE: Marketing (Energy and Utilities)
Re: If a and b are positive and ab/x = a, then x/b =  [#permalink]

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07 Feb 2019, 08:58
Bunuel wrote:
If a and b are positive and $$\frac{ab}{x} = \sqrt{a}$$, then $$\frac{x}{\sqrt{b}} =$$

A. $$\sqrt{a}$$

B. $$\sqrt{ab}$$

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

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

E. a^2

Solution attached

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Re: If a and b are positive and ab/x = a, then x/b =  [#permalink]

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10 Feb 2019, 07:37
Bunuel wrote:
If a and b are positive and $$\frac{ab}{x} = \sqrt{a}$$, then $$\frac{x}{\sqrt{b}} =$$

A. $$\sqrt{a}$$

B. $$\sqrt{ab}$$

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

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

E. a^2

Simplifying we have:

ab = x√a

a/√a = x/b

√a = x/b

Since b = √b * √b, we have:

√a = x/(√b *√b)

√a * √b = x/√b

√(ab) = x/√b

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Re: If a and b are positive and ab/x = a, then x/b =   [#permalink] 10 Feb 2019, 07:37
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