# 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. 4x

II. -10 - 1/x

III. 4/x

I. 4x

^{2}- 4x + 4II. -10 - 1/x

^{2}III. 4/x

^{2}Correct Answer:

**C**- Although this question can be solved using algebra, it is significantly easier to solve by picking small numbers and observing the changes.
- 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) = 4x ^{2}– 4x + 412 52 124 f(x) = -10 – 1/x ^{2}-10 – 1/4 -10 – 1/16 -10 – 1/36 f(x) = 4/x ^{2}1 1/4 1/9 - Evaluate equation I. As x increases, equation I must increase. Any answer choice that includes I is wrong.
- 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.
- 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.