With DS problems, I always ask myself the following three questions:
What do I want?
What do I have?
What do I need?
The goal is not to solve but only to determine whether the statement gives you sufficient information to solve. In other words: Is the statement giving me what I need?
In this case:
What do I want? To know whether (4^x)[(1/3)^y] < 1
What do I have? Before I look at the two statements, what information have I been given? In this case, that x and y have to be positive integers.
What do I need? In this case, more information about x and y.
Since the answer to the question "Is (4^x)[(1/3)^y] < 1?" can be yes or no, I need to do the following:
Try different kinds of numbers in order to see whether the answer to the question stays consistently YES or NO or could go either way.
As I try out different kinds of numbers:
If the answer to the question stays consistently YES, the statement is SUFFICIENT.
If the answer to the question stays consistently NO, the statement is SUFFICIENT.
If the answer to the question can be YES or NO, the statement is INSUFFICIENT.
Important: I have no stake in whether the answer is yes or no, as long as it stays consistent; if the answer is always YES or always NO, the statement is SUFFICIENT.
Statement 1:
If x = 1, y = 2. Is (4^x)[(1/3)^y] < 1? Yes, because (4^1)[(1/3)^2] = 4/9, and 4/9 < 1.
If x = 2, y = 4. Is (4^x)[(1/3)^y] < 1? Yes, because (4^2)[(1/3)^4] = 16/81, and 16/81 < 1.
If x = 10, y = 20. Is (4^x)[(1/3)^y] < 1? Yes, because (4^10)[(1/3)^20] = a messy fraction, so (4^10)[(1/3)^20] < 1.
Since the answer stays consistently YES, the statement is SUFFICIENT.
Statement 2:
Tells us only that y = 4, but nothing about x.
If x = 2 and y = 4, is (4^x)[(1/3)^y] < 1? Yes, because (4^2)[(1/3)^4] = 16/81, and 16/81 < 1.
If x = 4 and y = 4, is (4^x)[(1/3)^y] < 1? No, because (4^4)[(1/3)^4] = 256/81, and 256/81 > 1.
Since the answer can be YES or NO, the statement is INSUFFICIENT.
The correct answer is A.
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