Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
Before jumping into this problem using the numbers provided, we must analyze what is really being tested here. We are really being asked, what happens when we increase a positive integer by a value of 1. Whether we use 165 and 166 does not matter. So to make the calculations easier, we will use the smaller numbers 2 and 3. We can now rephrase the question:
As x increases from 2 to 3, which of the following must increase?
Let’s test out the new numbers for each Roman numeral.
I. 2x – 5
When x = 2:
2(2) – 5 = -1
When x = 3:
2(3) – 5 = 1
This DOES increase. Roman numeral I is correct.
II. 1 – 1/x
When x = 2:
1 – 1/2 = 1/2
When x = 3:
1 – 1/3 = 2/3
This DOES increase. Roman numeral II is also correct.
III. 1/(x^2 – x)
When x = 2:
1/(2^2 – 2)
1/(4 – 2) = 1/2
When x = 3:
1/(3^2 – 3)
1/(9 – 3) = 1/6
This DOES NOT increase. Roman numeral III is not correct.
Thus, only I and II are correct.
Answer: C
