If abc = b^3 , which of the following must be true?
I. ac = b^2
II. b = 0
III. ac = 1
B. I only
C. II only
D. I and III
E. II and III
This is from Kaplan
CAT. I am not quite sure how they arrived at the answer.
Responding to a pm:
I think I won't be able to take 'Must be true' for another week on my blog (Std Dev still not over). Hence, explaining this question right here.
Given: abc = b^3abc - b^3 = 0b(ac - b^2) = 0
This tells us that either b = 0 OR ac = b^2
. At least one of these 2 'must be true'.
So can I say b must be equal to 0? No! It is possible but it is also possible that instead, ac = b^2
So can I say ac must be equal to b^2
? No! It is possible but it is also possible that instead, b = 0.
So can I say that b = 0 AND ac = b^2
? No! It is possible but it is also possible that only one of them is true.
So can I say that b = 0 OR ac = b^2
? Yes, I can! One of them must be true.
If one of the options were 'I or II', that would have been true.
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