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0 < a < b < c [#permalink]
Expert's post 00:00

Question Stats: 83% (00:39) correct 16% (00:35) wrong based on 80 sessions
$$0 < a < b < c$$

 Quantity A Quantity B $$\frac{b}{a}$$ $$\frac{c}{b}$$

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.

Kudos for R.A.E
[Reveal] Spoiler: OA

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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. VP Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: 0 < a < b < c [#permalink]
1
KUDOS
Carcass wrote:
$$0 < a < b < c$$

 Quantity A Quantity B $$\frac{b}{a}$$ $$\frac{c}{b}$$

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.

Kudos for R.A.E

Here no information apart from positive nos. is given for a, b and c
SO they can be integer or fraction

Taking integer value

a = 1 ; b = 2 ; c = 3

Then QTY A = 2/1 = 2

QTY B = 3/2 = 1.5

Therefore QTY A > QTY B

Taking fraction

a = 1/2 ; b = 1 ; c = 2

Then QTY A = 2

QTY B = 3/1 = 3

So QTY B > QTY A

Hence option D
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Re: 0 < a < b < c [#permalink]
1
KUDOS
Expert's post
Carcass wrote:
$$0 < a < b < c$$

 Quantity A Quantity B $$\frac{b}{a}$$ $$\frac{c}{b}$$

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.

Kudos for R.A.E

Pranab01's solution (above) is probably the fastest, but we can also solve this question using matching operations

Given:
Quantity A: $$\frac{b}{a}$$
Quantity B: $$\frac{c}{b}$$

Since a is POSITIVE, we can safely multiply both sides by a to get:
Quantity A: $$b$$
Quantity B: $$\frac{ca}{b}$$

Since b is POSITIVE, we can safely multiply both sides by b to get:
Quantity A: $$b^2$$
Quantity B: $$ca$$

At this point, we can see that, if a = 1, b = 2, and c = 4, then the two quantities are equal
Conversely, if a = 1, b = 2, and c = 3, then Quantity A is greater

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If you enjoy my solutions, you'll like my GRE prep course.  Re: 0 < a < b < c   [#permalink] 07 Jun 2019, 06:30
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