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Does ab = a^2

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by Gmat_mission » Sat Apr 14, 2018 3:09 am

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Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3

[spoiler]OA=B[/spoiler].

Why is not sufficient the statement (1)? Can anyone give me a good explanation? I'd be thankful.
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Source: — Data Sufficiency |

by GMATGuruNY » Sat Apr 14, 2018 3:40 am
Gmat_mission wrote:Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3
ab = a²
0 = a² - ab
0 = a(a-b).
The resulting equation is valid only if a=0 or a=b.
Question stem, rephrased:
Does a=0 or a=b?

Statement 1:
If a=1 and b=1, then the answer to the rephrased question stem is YES.
If a=1 and b=-1, then the answer to the rephrased question stem is NO.
Since the answer is YES in the first case but NO in the second case, INSUFFICIENT.

Statement 2:
a³ = b³ implies that a=b.
Thus, the answer to the rephrased question stem is YES.
SUFFICIENT.

The correct answer is B.
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