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abc > 0

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abc > 0 [#permalink]  24 Sep 2018, 03:35
Expert's post
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Question Stats:

87% (00:44) correct 12% (00:23) wrong based on 31 sessions
$$abc > 0$$

 Quantity A Quantity B c(a + b) abc

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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Intern
Joined: 07 Jan 2019
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Kudos [?]: 20 [1] , given: 11

Re: abc > 0 [#permalink]  11 Jan 2019, 23:51
1
KUDOS
Given:
abc > 0 which implies that,
Out of a,b,c either two of the variables can be negative or all of the three variables can be positive.
Suppose a=1, b=2 and c=3.
We get, A > B ( A=9 and B=6)
Suppose a= -1, b=-2 and c=3
We get, B > A ( A=-9 and B=3)
Please rectify if the process is wrong.

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Re: abc > 0 [#permalink]  12 Jan 2019, 04:36
Expert's post
Carcass wrote:
$$abc > 0$$

 Quantity A Quantity B c(a + b) abc

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.

A very straight forward solution, even if we take all as positive..
(1) Let $$a=b=c=3$$
A=(c(a + b))=$$3(3+3)=18$$
B=(abc)=$$3*3*3=27$$
so B>A
(2) Let $$a=b=c=1$$
A=(c(a + b))=$$1(1+1)=2$$
B=(abc)=$$1*1*1=1$$
so A>B

D
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: abc > 0   [#permalink] 12 Jan 2019, 04:36
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