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If 0<x<y, is x<4?

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by Max@Math Revolution » Wed Jul 06, 2016 4:00 pm
If 0<x<y, is x<4?
1) (1/x)+(1/y)=1/2
2) 1/x>1/4

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Source: — Data Sufficiency |
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by 800_or_bust » Thu Jul 07, 2016 6:22 am
Max@Math Revolution wrote:If 0<x<y, is x<4?
1) (1/x)+(1/y)=1/2
2) 1/x>1/4

*An answer will be posted in 2 days
(1) SUFFICIENT. x must be between 2 and 4, in order for this equation to be true and the given inequality to hold. If x were greater than or equal to 4, then we would be adding a number equal to or less than 50% of 1/2 to an even smaller number. Thus, the sum of 1/x + 1/y would be smaller than 1/2, and the equation could not hold.

(2) SUFFICIENT. x must be between 0 and 4. If x were greater than or equal to 4, 1/x would be less than 1/4.

Answer: D
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by Max@Math Revolution » Sun Jul 10, 2016 11:35 pm
Since there are 2 variables in the original condition, there is a high chance that C is the correct answer. Condition 2) becomes the answer too easily because from 1/x>1/4, we get 0<x<4. The condition is sufficient. However, the condition is rather too hard. If we apply the common mistake type 4(B), the answer becomes D.

- 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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