Integers

irock wrote:Is the range of the integers 6, 3, y, 4, 5, and x greater than 9 ?

(1) y > 3x
(2) y > x > 3

OA C

Before looking at the statements, REPHRASE the question stem.

First, put the known values in order: 3, 4, 5, 6. The range of the values that we know is 6 - 3 = 3. We would know that we had a range greater than 9 if one of our variables was less than -3 (6 - -3 = 9) or greater than 12 (12 - 3 = 9).

Target question: is either x or y less than -3 or greater than 12?

(1) y > 3x
Test small values:
x = 0
y = 1
Answer to target question: no.

Test a large value:
x = 0
y = 100
Answer to target question: yes.
Insufficient.

(n.b. when testing cases with 2 variables, it's often helpful to keep 1 variable constant, and only change the other one).

(2) y > x > 3
Test small values:
x = 4
y = 5
Answer to target question: no.

Test a large value:
x = 4
y = 100
Answer to target question: yes.
Insufficient.

(1) & (2) together: y > 3x and y > x > 3
Test small values:
x = 4 (smallest possible value of x)
y = 13 (smallest possible integer greater than 3x)
Answer to target question: yes.

Test a large value... we don't have to. The larger x gets, the larger y gets, and we'll definitely have a value greater than 12. Sufficient.

The answer is C.