GMAT Question of the Day – DS – Exponents

GMAT Question of the Day

GMAT Question of the Day – Data Sufficiency – Exponents/Number Properties

If k is not equal to 1, is 1+{{k}^{3}}+{{k}^{6}}+{{k}^{9}}<\frac{1}{1-k}?

(1) k > 0

(2) k < 1


GMAT Question of the Day Solution

This GMAT question of the day comes down to picking some good numbers. This is another example of a question that feels very infinite but by thinking in terms of big numbers and small numbers you can shrink it down. It’s tough to simplify the given information so you’ll have to go to the statements. Think of the extremes for Statement (1). What if k = 1/2? What if k = 1,000,000? In the first case the left is smaller. In the second case the left side is bigger. Insufficient. How did I think of those numbers? Special numbers for Data Sufficiency: 1, 0, -, +, integers, decimals

Again, use numbers for Statement (2). For k = 0 the sides are equal so the answer would be no. We could also try k = -1,000,000. Now the left hand side will be much smaller than the right hand side. So this statement leaves conflicting options. Insufficient.

Putting statement (1) and (2) together we are guaranteed positive so the negative and 0 examples will not work. We are also guaranteed NOT to be a positive integer so that example won’t work either. We are trapped in the positive fraction range in which the right hand side is always bigger. Sufficient.