The infinite sequence a1, a2, …, an, … is such that a1=2 The sum of the repeating sequence comes from simply figuring out how often the sequence repeats–in this case every 4 terms–and then adding this however many times the sequence itself fits into, in this case, 97. So that’s four terms sum to 3, … Read More
If n is a positive integer, which of the following could be equal to ((n+1)^3)−((n^3)+1)? A. 7^3(6^3−1) B. 7^3(6^3+1) C. 2∗26∗27 D. 3∗31∗32 E. 0 You can do this step-by-step by hand, but it will be a hell of a lot easier if you have the cubic expansion for a binomal handy: (a+b)^3 = a^3 … Read More
This looks like something where we ought to be able to square the second equation as it stands–but that will give you a polynomial with a root in the middle. Bad. However, if you look at the left equation as a difference of squares (where the right equation is one of the two brackets), then … Read More
Solomon’s truck gets 24 mpg GMAT In this case, you need to look at the units as mpg/lbs or mpg/mph, then multiply these values by lbs or mph, respectively. It’s awkward, but slow down the video to see more. Solomon’s truck gets 24 mpg (miles per gallon) when driven at a speed of 40 mph … Read More
Last year Comfort Airlines had twice as many delayed flights GMAT In an explain the apparent contradiction question, you need to consider what we’re measuring. The discrepancy appears between the number of delays and the number of complaints. Could there be an issue somehow with the quality of the delays–that is, have the delays become … Read More
