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01 Apr 2016, 03:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (01:19) correct
38%
(01:08)
wrong
based on 556
sessions
History
Date
Time
Result
Not Attempted Yet
01 Apr 2016, 03:50
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Is a = b?
St1: x^a = x^b
If x = 1 then 1^2 = 1^3 --> Is a = b? No
If x > 1; 2^2 = 2^2 --> Is a = b? Yes
Not Sufficient
St2: x = x^2 --> Provides information that x = 0 or x = 1. No information about a and b. Not Sufficient
Combining St1 and St2;
1^2 = 1^2 --> Is a = b? Yes
1^2 = 1^3 --> Is a = b? No
Not sufficient.
Answer: E
St1: x^a = x^b
If x = 1 then 1^2 = 1^3 --> Is a = b? No
If x > 1; 2^2 = 2^2 --> Is a = b? Yes
Not Sufficient
St2: x = x^2 --> Provides information that x = 0 or x = 1. No information about a and b. Not Sufficient
Combining St1 and St2;
1^2 = 1^2 --> Is a = b? Yes
1^2 = 1^3 --> Is a = b? No
Not sufficient.
Answer: E
03 Apr 2016, 04:28
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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.
If ab ≠ 0, does a = b?
(1) x^a = x^b
(2) x = x^2
In the original condition, there are 3 variables(x,a,b), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, and 1 more equation is needed, which is likely to make E the answer.
When 1) & 2), if x=1, a=b=1 -> yes. If x=1, a=1, b=2, it is no and not sufficient.
Thus, the answer is E.
For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
If ab ≠ 0, does a = b?
(1) x^a = x^b
(2) x = x^2
In the original condition, there are 3 variables(x,a,b), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, and 1 more equation is needed, which is likely to make E the answer.
When 1) & 2), if x=1, a=b=1 -> yes. If x=1, a=1, b=2, it is no and not sufficient.
Thus, the answer is E.
For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.
