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Is ab < a?

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Is ab < a?

by raj44 » Fri Aug 29, 2014 7:12 am
Is ab < a?

1.a = 0

2.b = 0

I want to confirm my approach-whether it's right or incorrect:

->a(b-1)<0
so either a<0 or b<1...if any of these conditions is proved, then we have a definite answer.

1. a=0..since a is 0 a CANNOT be less than 0, therefore from the question stem we have b<1..and hence SUFFICIENT
2. provides no information about a..also b=0 does not help since we still have the possibility maintained- a<0 or b<1...INSUFFICIENT

OA is A

Please assist.

Thanks
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Source: — Data Sufficiency |
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by GMATGuruNY » Fri Aug 29, 2014 7:19 am
raj44 wrote:Is ab < a?

1.a = 0

2.b = 0
Statement 1: a=0
If a=0, then ab=a.
Thus, it is NOT possible that ab<a.
SUFFICIENT.

Statement 2: b=0
If a=0 and b=0, then ab=a.
If a=1 and b=0, then ab<a.
INSUFFICIENT.

The correct answer is A.
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by GMATGuruNY » Fri Aug 29, 2014 7:32 am
raj44 wrote:Is ab < a?

->a(b-1)<0
so either a<0 or b<1...if any of these conditions is proved, then we have a definite answer.
This line of reasoning is not quite correct.
If a(b-1)<0, then a and b-1 must be DIFFERENT SIGNS.

Case 1: a>0 and b-1<0, implying that b<1.
Thus, if a>0 AND b<1, then ab < a.

Case 2: a<0 and b-1>0, implying that b>1
Thus, if a<0 and b>1, then ab < a.

Question stem rephrased: Is either Case 1 or Case 2 possible?

Statement 1: a=0
Since neither Case 1 nor Case 2 is possible, SUFFICIENT.

Statement 2: b=0
If a>0 and b=0, then Case 1 is possible.
If a≤0 and b=0, then neither Case 1 nor Case 2 is possible.
INSUFFICIENT.

The correct answer is A.

Here, algebra seems to make the problem harder.
Testing values seems easier and faster.
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by raj44 » Fri Aug 29, 2014 8:06 am
Thanks a lot Mitch..I thought that testing values will consume more time..
GMATGuruNY wrote:
raj44 wrote:Is ab < a?

->a(b-1)<0
so either a<0 or b<1...if any of these conditions is proved, then we have a definite answer.
This line of reasoning is not quite correct.
If a(b-1)<0, then a and b-1 must be DIFFERENT SIGNS.

Case 1: a>0 and b-1<0, implying that b<1.
Thus, if a>0 AND b<1, then ab < a.

Case 2: a<0 and b-1>0, implying that b>1
Thus, if a<0 and b>1, then ab < a.

Question stem rephrased: Is either Case 1 or Case 2 possible?

Statement 1: a=0
Since neither Case 1 nor Case 2 is possible, SUFFICIENT.

Statement 2: b=0
If a>0 and b=0, then Case 1 is possible.
If a≤0 and b=0, then neither Case 1 nor Case 2 is possible.
INSUFFICIENT.

The correct answer is A.

Here, algebra seems to make the problem harder.
Testing values seems easier and faster.
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by GMATinsight » Sat Aug 30, 2014 3:29 am
raj44 wrote:Is ab < a?

1.a = 0

2.b = 0

I want to confirm my approach-whether it's right or incorrect:

->a(b-1)<0
so either a<0 or b<1...if any of these conditions is proved, then we have a definite answer.

1. a=0..since a is 0 a CANNOT be less than 0, therefore from the question stem we have b<1..and hence SUFFICIENT
2. provides no information about a..also b=0 does not help since we still have the possibility maintained- a<0 or b<1...INSUFFICIENT

OA is A

Please assist.

Thanks
Simplification is a fine process however we should restrict the simplification to the extent where it makes it easier to understand. therefore, I would not like to simplify it further beyond understanding from the question than
ab<a i.e. a(b-1) < 0

Statement 1) a = 0
i.e. a(b-1) = 0 and hence we can answer the question as NO
SUFFICIENT

Statement 2) b = 0
i.e. a(b-1) = -a which may or may not be less than 0 therefore
INSUFFICIENT

Answer: Option A
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