# Practice GMAT Problem Solving Question

Return to the list of practice GMAT problem solving questions.

x is a positive integer divisible by 4; as x increases from 1824 to 1896, which of the following must decrease?
I. 4x2 - 4x + 4
II. -10 - 1/x2
III. 4/x2
 A) I only B) II only C) III only D) II and III only E) None
Correct Answer: C
1. Although this question can be solved using algebra, it is significantly easier to solve by picking small numbers and observing the changes.
2. Although x is defined as a positive integer divisible by 4 from 1824 to 1896, there is no reason you cannot seek to determine whether the equations increase by using x = 2 and x = 4. The equations will behave the same for x = 2 and x = 1824. To be safe and convince yourself that the patterns between 2 and 4 will hold, you could also check x = 6, although this is not necessary and will consume extra time.
 Equation f(2) f(4) f(6) f(x) = 4x2 – 4x + 4 12 52 124 f(x) = -10 – 1/x2 -10 – 1/4 -10 – 1/16 -10 – 1/36 f(x) = 4/x2 1 1/4 1/9
3. Evaluate equation I. As x increases, equation I must increase. Any answer choice that includes I is wrong.
4. Evaluate equation II. The pattern that emerges is that as x increases, a smaller number is subtracted from a negative number. Subtracting a smaller number from a negative number actually makes the overall value increase (e.g., -10 – 20 = -30, which is less than -10 – 15 = -25). Consequently, as x increases, equation II must increase. Any answer choice that includes II is wrong.
5. Evaluate equation III. Both by looking at the equation and by observing the values, it is clear that as x increases, the value of equation III decreases since four is being divided by a larger number.

Return to the list of practice GMAT problem solving questions.