Is William taller than Jane? (1) William is taller than Anna. (2) Anna

Need to find whether W>J

1. W>A --- Not sufficient
2. A<=J --- Not Sufficient

Combining both - Still not sufficient ---- Ans E

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No. This question asks whether William is taller than Jane.

Given information from the question stem: The question asks whether William is taller than Jane. If you can show that William is DEFINITELY taller than Jane or that William is DEFINITELY NOT taller than Jane, the statement (or statements) is sufficient.

Statement 1: You can write this as W > A (William taller than Anna). This is not sufficient because we do not know anything yet about Jane. Choices A and D are eliminated.

Statement 2: You can write this as A < J (Anna is not as tall as Jane). This is not sufficient because it provides no information about William. Choice B is eliminated.

Together: Taken together, you can write the statements as:
W > A, and J > A

Note that it’s important to get the inequalities pointed in the same direction (Statement 2 was given as A < J, but that also means that J > A). This helps you to notice that both William and Jane are taller than Anna, but that is all you can conclude. You still have no way to establish the relationship between William and Jane. Because you do not have enough information even taken together, the answer is E.

W > J ?

I: W >A Insufficient
II: J > A Insufficient

I + II:
Both statements indicates that William and Jane both are taller than Anna. But there is not cue, who is more taller among William or Jane.

Insufficient

E is correct answer.

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 William taller than Jane?

(1) William is taller than Anna.
(2) Anna is not as tall as Jane.

In the original condition, there are 2 variables(w,j) and in overall 3 variables(w,j,a), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. In 1) & 2), they become w>a and j>=a, but j and w cannot be compared, which is not sufficient. Therefore, 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.

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