Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Is x > 10^10 ? (1) x > 2^34 (2) x = 2^35
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30 Dec 2015, 23:26
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.
Is x > 10^10 ?
(1) x > 2^34
(2) x = 2^35
In case of inequality questions, it is important to note that the conditions are sufficient if the range of the question includes the range of the conditions.
There is 1 variable (x) in the original condition. In order to match the number of variables and the number of equations, we need 1 equation. Since the condition 1) and 2) each has 1 equation, there is high chance D is going to be the answer.
In the case of the condition 1), if we do the calculation, we get 10^10<10*(10^3)^3=10*(1000)^3<16*(1024)^3=(2^4)(2^10)^3=2^34. Since the range of the question includes the range of the conditions, the condition 1) is sufficient.
In the case of the condition 2), if x=2^35, the answer can always be either ‘yes’ or ‘no’. Therefore, the condition is sufficient, and the correct answer is D.
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.