Practice GMAT Problem Solving Question
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For which of the following values of x is the fraction below an integer:
Correct Answer: C
There are two ways to solve this problem.

Solve the equation algebraically.
 Start with the original fraction and simplify:
 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.
 Simplified version of original question: is ^{50}/_{x} an integer?
 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.
 Start with the original fraction and simplify:

Solve the equation using Backsolving.
 Simply plug in the answer choices and see what answer works.
 Since only C provides an integer, it is the correct answer
 Although this method provides the correct answer, it is considerably longer and should be used only as a last resort.
 Simply plug in the answer choices and see what answer works.
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