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If abc = b3 , which of the following must be true?

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by Night reader » Sun Feb 20, 2011 7:42 am
does the problem specify b3 and not 3*b which is not possible with answer A (but still) may be b(+-)3, also division should be eliminated for answer A.
nikhilsrl wrote:If abc = b3 , which of the following must be true?

I. ac = b2
II. b = 0
III. ac = 1

A) None
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.

OA is A
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by stormier » Sun Feb 20, 2011 9:05 am
nikhilsrl wrote:If abc = b3 , which of the following must be true?

I. ac = b2
II. b = 0
III. ac = 1

A) None
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.

OA is A
abc = b^3

This is possible if either

b=0; or
ac = b^2

But none of the above individually must be true. Answer A
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by nikhilsrl » Mon Feb 21, 2011 5:22 am
Night reader it abc = b^3 and ac = b^2
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by GMATGuruNY » Mon Feb 21, 2011 6:08 am
nikhilsrl 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

This is from Kaplan CAT. I am not quite sure how they arrived at the answer.

OA is A
Try to show that the answers don't have to be true.

Let a = 2, b = 0, c = 2. This works, because 2*0*2 = 0^3.

I. ac = b^2
2*2 = 0^2.
Not true. Eliminate B and D, each of which includes I.

II. b = 0
True so far. Hold onto II.

III. ac = 1
2*2 = 1.
Not true. Eliminate E, which includes III.

Let a = 1, b = 1, c = 1, so that 1*1*1 = 1^3.

II. b = 0
Not true. Eliminate C.

The correct answer is A.
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