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Data-Sufficiency
There is another type of Data-Sufficiency Question which asks you to determine whether the given question can be answered as YES or NO.
2. If x-y = 40, is x = 60?
(1) x = 3y
(2) y = 20
Note that the question does not ask you to find out the value of x, but asks you to state whether it has specific value?
The equation x-y = 40 will be true for an infinite set of values for ( x, y) such as (-10,-50), (40, 0), (55, 15) etc…
If no other information is given, we can not assertively confirm that x = 60.
With the information given in statement (1) alone, the given equation becomes as follows:
If x = 3y, then the equation {x - y = 40} becomes as 3y - y = 40.
That means 2y = 40.
So, y = 20.
If y = 20, then as per the given equation x - y =40,
x - 20 = 40
x = 40 + 20
x = 60.
So, the question can be answered as YES from the Statement (1) alone.
With the information given in statement (2) alone{ y = 20}, the given equations becomes
x - y = 40
x - 20 = 40
x = 40 + 20
x = 60.
So, the statement (2) alone is enough to answer the question.
Since both the statements are individually enough to answer the question,
The answer is (D).
The answer to this type of question need not always be YES.
Even if a statement leads to the unambiguous answer NO, you should conclude that it helps you to answer the question unambiguously.
