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If b is an integer greater than 1, ab=?

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by Max@Math Revolution » Mon Jul 18, 2016 8:30 am
If b is an integer greater than 1, ab=?
1) b^a=1
2) b=2

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Jul 20, 2016 6:14 am
Max@Math Revolution wrote:If b is an integer greater than 1, then ab = ?

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

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Mon Jul 25, 2016 4:44 am
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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