Answer to GMAT Question #5

Here is the answer to GMAT Practice Question #5

Answer: C

Explanation:
There are two ways to solve this problem. The first way is to use your intuition about math and the second way is to use advanced mathematical techniques. We’ll explain both here.

Let’s start with the intuitive approach. Pay attention to this equation. Notice that it multiplies a negative number by a squared number. The squared number will always be positive, so the product of the two will always be negative. That number is then added to 30,000, but since it’s negative, we are really subtracting it from 30,000.

Now picture the rocket. 1 second into it, it should still be low. That is borne out by the formula. At 1 second, t = 1, so t – 20 = -19, and -19 to the second power is a big, positive number (you don’t need to know 192 by heart for the GMAT – but know that it’s slightly less than 202, or 400. You do need to know 202 by heart). Multiply by -52, and we’ll get a really small negative number. Add that to 30,000, and the number just isn’t so big.

As t climbs, t – 20 gets smaller, and so -52(t – 20) to the second power gets larger (gets closer to zero), and h gets bigger.

This should make sense, because the rocket is climbing.

When will the rocket hit its peak? When (t – 20) to the second power is as small as possible. That occurs when t = 20, because then (t – 20) to the second power is 0. At that point, h will be 30,000. Every number for t higher than 20 will cause (t – 20) to the second power to be larger than 0 and h will get smaller, that is, the rocket is coming back down to earth. So the rocket peaks at 20 seconds.

The question asks what the height is five seconds before the peak, which is t = 15. Just plug 15 in for t and do the math. h will equal 28,700 feet.

The other way to do this problem is to take the first derivative of the equation and set it equal to zero. That will show what t is at the maximum. In general, you don’t need to know calculus for the GMAT, but in some cases, finding the derivative can get you out of a jam:

See Figure 1

Thus, the maximum of the original equation occurs when t = 20.

The answer and explanation to GMAT Practice Question #5 was written by Integrated Learning, a company that provides professional and private one on one tutoring services.