Practice GMAT Problem Solving Question

There are two ways to solve this problem.

1. Solve the equation algebraically.
   1. Start with the original fraction and simplify:
      
   2. Since the question simply asks what value of x will make the equation an integer, the equation can be simplified to ⁵⁰/_x. This is true because, if ⁵⁰/_x is an integer, adding 1 to that value will not change whether it is an integer. Likewise, if ⁵⁰/_x is not an integer, adding 1 to that value will not make it an integer.
   3. Simplified version of original question: is ⁵⁰/_x an integer?
   4. Use the divisibility rules to quickly evaluate this question:
      A: x = 0 --> Not an integer. You cannot divide by 0
      B: x = 4 --> Not an integer. You cannot divide 50 by 2 twice, so 50/4 is not an integer.
      C: x = 5 --> An integer; 50/5 = 10
      At this point, you could stop. However, just to be safe, it does not hurt to keep checking.
      D: x = 6 --> Not an integer. You cannot divide 50 by both 2 and 3, so 50/6 is not an integer. (Remember that for a number to be divisible by 3, its digits must sum to a number divisible by 3. The sum of the digits of 50 is 5, which is not divisible by 3).
      E: x = 7 --> Not an integer. No quick rule for divisibility by 7. However, since 7*7 is 49, there is no way 50 will be divisible by 7.
2. Solve the equation using Backsolving.
   1. Simply plug in the answer choices and see what answer works.
      
   2. Since only C provides an integer, it is the correct answer
   3. Although this method provides the correct answer, it is considerably longer and should be used only as a last resort.