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Re: If A and B are integers and A^2-B^2=101, what is A?
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16 Apr 2016, 02:41
If A and B are integers and A 2 −B 2 =101 A2−B2=101 , what is A?
(1) A and B are consecutive integers.
(2) A>B
There are 2 variables in the original condition (A and B) and 1 equation (A^2-B^2=101) in the original condition. In order to match the number of variables to the number of equations, we need 1 more equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the answer.
In case of the condition 1), from (A-B)(A+B)=101, we get A+B=101 and A-B=1. Then we get A=51 and B=50. However, when A+B=-101 and A-B=-1, we get A=-51 and B=-50. The answers are not unique and the conditions are not sufficient.
In case of the condition 2), we get (A,B)=(51,50),(51,-50). However, since A=51, the answer is unique and the condition is sufficient. Therefore, the correct answer is B.
l For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.