Hi All,

This question is based heavily on Number Properties involved in division. If you recognize those Number Properties, then you can solve this question in under 30 seconds without performing any lengthy calculations.

We're told that 8103/X is a NON-terminating decimal, meaning that the decimal will NOT end. We're asked which of the following COULD be a value of X?

When dividing an integer by 2 or by 5, the result will either be another integer or a number that has just one decimal point, so neither of these can be the value of X.

Dividing an integer by 9 almost always leads to a repeating decimal, unless the larger number is a multiple of 9. When dividing by 9, there is a great shortcut called 'the rule of 9': if the DIGITS of the larger number sum to a total that is divisible by 9, then the larger number is evenly divisible by 9.

For example:

279 is divisible by 9 because 2+7+9 = 18. Since 18 is divisible by 9, 279 is evenly divisible by 9

17 is NOT divisible by 9 because 1+7 = 8. Since 8 is NOT divisible by 9, 17 is NOT evenly divisible by 9.

Here, we're dealing with 8103. 8+1+0+3 = 12. since 12 is NOT divisible by 9, 8103 is NOT evenly divisible by 9 and thus is a non-terminating decimal.

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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# Rich Cohen

Co-Founder & GMAT Assassin

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