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# a/b=3/4

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Founder
Joined: 18 Apr 2015
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a/b=3/4 [#permalink]  25 Dec 2018, 15:19
Expert's post
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Question Stats:

72% (01:06) correct 28% (01:02) wrong based on 25 sessions
$$\frac{a}{b}=\frac{3}{4}$$

 Quantity A Quantity B $$\frac{2a-b}{b}$$ $$\frac{a}{a+b}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Founder
Joined: 18 Apr 2015
Posts: 10110
Followers: 209

Kudos [?]: 2504 [0], given: 9501

Re: a/b=3/4 [#permalink]  25 Mar 2020, 15:48
Expert's post
For the two terms: on the LHS and on the RHS for being equal they must be an integer.

We can cross multiply

$$4a=3b$$

This means that a is a multiple of 3 and b is a multiple of 4. The two quantities must balance

As such, $$b = 4$$ and $$a =3$$.

Then $$\frac{2a-b}{b}=\frac{a}{a+b}$$

Substitute

$$\frac{6-4}{4}=\frac{3}{4+3}$$

$$\frac{2}{4}=\frac{3}{7}$$

$$\frac{2}{4} > \frac{3}{7 }$$

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Re: a/b=3/4   [#permalink] 25 Mar 2020, 15:48
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