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Does ab= a^2

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Joined: 27 Feb 2012
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18 Dec 2012, 22:51
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Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3
[Reveal] Spoiler: OA
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18 Dec 2012, 23:02
jsphcal wrote:
Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3

1) a = + or - b. If a = +b. Answer is yes. If a = -b. Answer is no. Insufficient.

2)a = b. Sufficient.

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18 Dec 2012, 23:15
MacFauz wrote:
jsphcal wrote:
Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3

1) a = + or - b. If a = +b. Answer is yes. If a = -b. Answer is no. Insufficient.

2)a = b. Sufficient.

MacFauz

thanks for the reply, could you please elaborate more on the algebra use to solve?

(1) and why if a= + or -b or if a = +b stmt 1 suff, and if a = -b then insuff

did you pick numbers to test stmt 1 and 2?
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18 Dec 2012, 23:27
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jsphcal wrote:
Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3

$$ab=a^2 ab-a^2=0 a(b-a)=0$$

So we need a=0 or b=a

(1) doesnt help coz
$$a^2= b^2$$
$$a^2$$ is + or - a
$$b^2$$ is + or - b
We cant determine is it +ve or -ve
INSUFF

(2) helps
$$a^3= b^3$$
which means a=b or -a=-b
either way a=b
SUFF

Hence (B)
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18 Dec 2012, 23:27
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jsphcal wrote:
MacFauz wrote:
jsphcal wrote:
Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3

1) a = + or - b. If a = +b. Answer is yes. If a = -b. Answer is no. Insufficient.

2)a = b. Sufficient.

MacFauz

thanks for the reply, could you please elaborate more on the algebra use to solve?

(1) and why if a= + or -b or if a = +b stmt 1 suff, and if a = -b then insuff

did you pick numbers to test stmt 1 and 2?

1. We do not need to pick numbers.

1) $$a^2 = b^2$$
This means + or - a = + or - b. So we are basically given that a can be equal to b or a can be equal to -b.

If a = b, LHS of given equation becomes a^2 and hence is equal to RHS
If a = -b, LHS of given equation becomes -a^2 and hence may not be equal to RHS.

Since we are getting two different answers, this statement is insufficient.

2) $$a^3 = b^3$$
This means a = b and nothing else.

So, LHS of given equation can only be a^2 and hence is equal to RHS. Sufficient.
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19 Dec 2012, 02:47
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Does ab = a^2

Does $$ab = a^2$$? --> does $$a(a-b)=0$$? does $$a=0$$ or $$a=b$$?

(1) a^2 = b ^2 --> $$a=b$$ or $$a=-b$$. Not sufficient.

(2) a^3 = b ^3 --> $$a=b$$. Sufficient.

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29 Jan 2016, 04:54
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Re: Does ab= a^2   [#permalink] 29 Jan 2016, 04:54
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