BTGmoderatorDC 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
Source: Official Guide
Excluding x and y, the range of the list 6, 3, y, 4, 5, and x is 6 - 3 = 3. We have to determine whether the range of the list is greater than 9.
Let's take each statement one by one.
(1) y > 3x
Case 1: Say x = 0, and y = 1, the range = 6 - 0 = 6 < 9. The answer is No.
Case 2: Say x = 0, and y = 20, the range = 20 - 0 = 20 > 9. The answer is Yes.
No unique answer.
(2) y > x > 3
Case 1: Say x = 4, and y = 4, the range = 6 - 3 = 3 < 9. The answer is No.
Case 2: Say x = 4, and y = 20, the range = 20 - 3 = 17 > 9. The answer is Yes.
No unique answer.
(1) and (2) together
Case 1: Say x = 4, then since y > 3x, we must have y ≥ 13. The minimum value of y = 13. The range = 13 - 3 = 10 > 9. The answer is Yes.
There is no need to check other cases since the minimum value of the list would be 3 and y would be greater than 13, making range > 10.
The correct answer:
C
Hope this helps!
-Jay
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