### Data-Sufficiency

Example-2

There is another type of Data-Sufficiency Question which asks you to determine whether the given question can be answered as YES or NO.

Question

2. If x-y = 40, is x = 60?

(1) x = 3y

(2) y = 20

Analysis

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,