Explanation

If this question, or any GMAT question, strikes you as impossible when you first encounter it, do not despair. The GMAT is not all about tricks - they are probably better described as puzzles - but they are like magic tricks in a way: if you don't know the trick, it can seem magical and mysterious, but when you understand the trick, it's simple. Through practice, the appearance of magic will disappear and you will be the one waving the wand.

Whenever we have a fraction that we need to convert into a decimal, if the conversion is not obvious or we don't know a shortcut, we can always try long division. A fraction represents division, so represents 3 divided by 11, and we can actually perform this division by hand through long division.



We can actually pause here, because there is a pattern that will repeat. The digits 2 and 7 will alternate, so . This result makes sense, since has a slightly larger denominator than , so it should be slightly smaller than 0.3.

We can determine the 30th number to the right of the decimal point from the pattern. The first digit to the right is a 2, the second digit to the right is a 7, and the third digit is a 2. Evidently, the odd places have a 2 and the even places have a 7. The 30th place is an even place, so the digit there will be a 7.

The correct answer is (E).