This week's GMAT Question of the Day relates to question #343 from the Official Guide for GMAT Review, 2017. It is a typical AD/BCE, YES/NO Question.
A little content knowledge:
- Decimal expansions of (reduced) fractions depend on the denominator, not the numerator
- The decimal expansion of a (reduced) fraction will terminate if the prime factorization of the denominator contains only 2’s and 5’s.
The first of these should be pretty common sense, but the second takes some thinking. When we convert a fraction to a decimal we’re dividing the numerator by the denominator. To make this work we add zeros to the dividend (the numerator) and continue dividing until the process terminates or we find a repeating pattern. Because we’re adding zeros, our dividend is a multiple of a power of ten. If an integer doesn’t divide any power of ten it won’t divide a multiple of a power of ten unless it is a factor of that multiple – in that case the fraction wasn’t reduced:
That’s pretty abstract, but worth knowing because it will solve this problem for you right away. However, a totally common-sense straightforward approach will work:
(1) SUFFICIENT: This is a lot easier to work with than it looks – there are a finite number of factors of 100 (9 in fact: 1, 2, 4, 5, 10, 20, 25, 50, and 100) and we know decimal equivalents for all of them. Multiplying those decimal equivalents by an integer r isn’t going to change the fact that they all terminate.
(2) INSUFFICIENT: Pick a factor of 100, like 5. That’s r. If s = 2 the answer is YES. If s = 7 the answer is NO.
The correct answer is A.
- In a YES/NO question, if you’re given a statement that results in a finite number of cases that you can produce quickly, just check them.