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Does ab= a^2

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jsphcal
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Does ab= a^2 [#permalink] New post   18 Dec 2012, 22:51
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Does ab = a^2

(1) a^2 = b ^2

(2) a^3 = b ^3
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B
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shanmugamgsn
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Re: Does ab= a^2 [#permalink] New post   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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Re: Does ab= a^2 [#permalink] New post   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.

Answer is B.



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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Re: Does ab= a^2 [#permalink] New post   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.

Answer: B.
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Re: Does ab= a^2? [#permalink] New post   17 Sep 2013, 02:09
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Does ab= a^2?

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

(1) a^2 = b^2 --> |a| = |b|. Not sufficient. (Consider a=b=1 for an YES answer and a=1 and b=-1 for a NO answer.)

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

Answer: B.
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Re: Does ab= a^2 [#permalink] New post   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.

Answer is B.
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Re: Does ab= a^2 [#permalink] New post   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.

Answer is B.



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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Does ab= a^2? [#permalink] New post   Updated on: 17 Sep 2013, 02:16
Does \(ab= a^2\)?

(1) \(a^2 = b^2\)
(2) \(a^3 = b^3\)

Originally posted by fozzzy on 17 Sep 2013, 02:04.
Last edited by fozzzy on 17 Sep 2013, 02:16, edited 1 time in total.
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Re: Does ab= a^2 [#permalink] New post   29 Nov 2022, 01:08
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Re: Does ab= a^2 [#permalink]
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