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505-555 (Easy)|   Algebra|      
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If b is an integer greater than 1, ab=? 18 Jul 2016, 09:29
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75% (00:56) correct 25% (01:07) wrong based on 389 sessions

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If b is an integer greater than 1, ab=?
1) b^a=1
2) b=2

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If b is an integer greater than 1, ab=? 18 Jul 2016, 10:36
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MathRevolution
If b is an integer greater than 1, ab=?
1) b^a=1
2) b=2

*An answer will be posted in 2 days
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If b is an integer greater than 1, we can say b=2,3,4.. any positive integral value.

Now, Statement 1 : (b)^a=1 will be true only if either b=1 or a=0; but we know b<>1 => a=0; hence ab = 0*b=0; -- Sufficient

Statement 2 : b=2 doesn't tell us anything about a. -- Not Sufficient.

Ans -- A
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If b is an integer greater than 1, ab=? 19 Jul 2016, 01:35
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As for statement 1:
if b^a=1, we can have log(b)1=a
therefore, a=0 => ab=0

Could I get the conclusion as above? ( using the function of log)
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If b is an integer greater than 1, ab=? 19 Jul 2016, 01:45
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As for statement 1:
if b^a=1, we can have log(b)1=a
therefore, a=0 => ab=0

Could I get the conclusion as above? ( using the function of log)
Show more

Yes, using log could be another way to solve this question.

And for statement 2, you can say that since the value of 'a' is unknown, you cannot find 'ab'. Thus, B would be insufficient in that case.
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If b is an integer greater than 1, ab=? 20 Jul 2016, 04:11
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abhimahna
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As for statement 1:
if b^a=1, we can have log(b)1=a
therefore, a=0 => ab=0

Could I get the conclusion as above? ( using the function of log)

Yes, using log could be another way to solve this question.

And for statement 2, you can say that since the value of 'a' is unknown, you cannot find 'ab'. Thus, B would be insufficient in that case.
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I got it. Thanks for making it clear!
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If b is an integer greater than 1, ab=? 20 Jul 2016, 07:17
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MathRevolution
If b is an integer greater than 1, then ab=?

1) b^a = 1
2) b = 2

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Target question: What is the value of ab?

Given: b is an integer greater than 1

Statement 1: b^a = 1
There are 3 possible cases to consider:
case a: b = 1 and a is any number
case b: b = -1 and a is an even integer
case c: b = any number and a = 0

Since we're told that b is an integer greater than 1, we can rule out cases a and b, which means it MUST be the case that a = 0, in which case ab = 0
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: b = 2
Since we have no information about the value of a, we cannot determine the value of ab
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer =
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A

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If b is an integer greater than 1, ab=? 25 Jul 2016, 05:44
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Since there are 2 variables in the original condition, there is a high chance that C is the correct answer. However, we have to apply the common mistake type 4(A) since it is an integer question, one of key questions. In case of con 1), since we have a=0, we get ab=0. The answer is unique and the condition is sufficient. Hence, the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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If b is an integer greater than 1, ab=? 25 Jul 2016, 06:10
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tinalongmao
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As for statement 1:
if b^a=1, we can have log(b)1=a
therefore, a=0 => ab=0

Could I get the conclusion as above? ( using the function of log)

Yes, using log could be another way to solve this question.

And for statement 2, you can say that since the value of 'a' is unknown, you cannot find 'ab'. Thus, B would be insufficient in that case.
I got it. Thanks for making it clear!
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Another way to thank is to HIT KUDOS. :lol:
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If b is an integer greater than 1, ab=? 25 Dec 2023, 01:31
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