Carcass wrote:
If abc = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1
A. None
B. I only
C. II only
D. I and III
E. II and III
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math BookLet's answer this question by Process Of Elimination.
I. ac = b²
Must this be true? No.
Consider the case where a = 1, b = 0 and c = 1
This set of values satisfies the given equation (abc = b³),
HOWEVER it is
not the case that ac = b²
Plug in the values to get (1)(1) = 0² - NOT TRUE
II. b = 0
Must this be true? No.
Consider the case where a = 1, b = 1 and c = 1
This set of values satisfies the given equation (abc = b³),
HOWEVER it is
not the case that b = 0
NOTE: At this point, we need not examine statement III, because none of the answer choices state that
only statement III must be true.
However, let's examine statement III for "fun"
III. ac = 1
Must this be true? No.
Consider the case where a = 0, b = 0 and c = 0
This set of values satisfies the given equation (abc = b³),
HOWEVER it is
not the case that ac = 1
Answer: A
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Brent Hanneson - founder of Greenlight Test Prep