Gella
Is y between -2 and 1 on the number line?
(1) y is to the right of -1 on the number line.
(2) y is to the left of 2 on the number line.
The question is asking whether y is between -2 and 1 and the statements should be able to answer "yes" or "no". Hence combining both statements we get that y is between -1 and 2 and this answers the question that y is not between -2 and 1. Isn't it?
There are two types of data sufficiency questions:
1. YES/NO DS Questions:
In Yes/No Data Sufficiency questions, a statement is sufficient if the answer is always "yes" or "no", whereas a statement is insufficient if the answer can be "sometimes yes" and "sometimes no".
2. VALUE DS QUESTIONS:
When a DS question asks about the value of some variable, then the statement is sufficient ONLY if you can obtain a single numerical value for this variable.
The question at hand belongs to the first category. For a statement to be sufficient, we should get a definite YES or a definite NO answer to the question, which asks "is -2 < y < 1?" When combining the statements, we get that -1 < y < 2. Now, y is a specific number, so if y = 0, then the answer is YES, y IS between -2 and 1 on the number line. However, if y = 1.5, then the answer is NO, y is NOT between -2 and 1 on the number line. Thus, we don't have a definite answer to the question, which means that the statements are insufficient and the answer is E.
To represent this visually, the question asks whether y falls within the green zone shown below:
----(-2)--(-1)-----1--2----Upon combining the statements, we deduce that y falls somewhere within the blue zone shown below:
----(-2)--(-1)-----1--2----As you can observe, y might or might not fall within the green zone, which indicates that the statements, when taken together, are insufficient.
Hope it's clear.