4 2 3 NO (2) INSUFFICIENT

1/4

1/2

1/3

NO

(2) INSUFFICIENT: If we test values here we find two sets of

possible x and y values that yield conflicting answers to the

question.

x

x

³

y

Is x > y?

2

8

1

YES

-1/2 -1/8 -1/4

NO

(1) AND (2) SUFFICIENT: Let’s start with statement 1 and add the

constraints of statement 2. From statement 1, we see that x has to

be positive since we are taking the square root of x. There is no

point in testing negative values for y since a positive value for x

against a negative y will always yield a yes to the question. Lastly,

we should consider x values between 0 and 1 and greater than 1

because proper fractions behave different than integers with regard

to exponents. When we try to come up with x and y values that fit

both conditions, we must adjust the two variables so that x is

always greater than y.

2 1.4

8

1

YES