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This is the type of question that can bait you into time-consuming calculations, whereas a shrewd test taker can gain valuable time by recognizing that this question is simply asking you to calculate a certain number by 60, and then multiplying it by 60 again (let’s do the time warp!). Even if a question asks you to change one unit into another, you can always do it step by step or all in one shot. There are many ways to solve this, but let’s begin with the detailed process so we make sure we don’t make any mistakes.
If the space shuttle orbits the earth at 8 kilometers per second (you can replace this word by miles if you’re more comfortable), then how many kilometers will it cover in one minute? We can simply multiply 8 by 60 to get 480 kilometers/minute. This is the number in answer choice A, but it is not the correct answer as we’ve only covered a single minute, or about 1.67% of the hour. (There’s still a lot of spinning to go!). If we take the 480 km/minute and multiply it by 60 minutes, we will get to the number of kilometers /hour. 480 x 60 is not obvious, but you ignore the 0’s so it boils down to 48 x 6. Doing this longhand, we can get to 288, and then add back in the two zeros for a total of 28,800. This is answer choice D and the correct answer to this question.
If you followed that strategy, you would get the right answer, but you would miss many opportunities for shortcuts. One of the most glaring shortcuts is to forgo the two-step process and simply multiply the initial speed of 8 km/second by 3,600. This is 60 x 60, and represents the number of seconds in an hour. Since 60 is a number that shows up so frequently on the GMAT, it’s worth knowing that the square of 60 is 3,600 as you may be asked to convert from hour to second and vice versa. Multiplying 8 by 3,600 will also get you to 28,800 in one operation instead of two.
Furthermore, it is possible to solve this question using zero calculations, using the power of order of magnitude. Very simply, if you recognize that there are 3,600 seconds in an hour, and you’re going a little less than 10 kilometers per second, then your answer should be a little under 36,000 kilometers/hour. Since answer choice E is bigger than this, and answer choice C is about five times too small, the answer must be answer choice D. This strategy may be difficult to use if the answer choices are close together, however it is undoubtedly the fastest way to get the correct answer when the answer choices are spread out as they are in this question.
There are also multiple other ways to get the right answer here. One hybrid solution that is pretty intuitive is to multiply 8 kilometers/second by 60 to get 480 kilometers/minute, as we did in the very first step. From there you know you need to multiply 480 by 60 to get the speed per hour, but your trap options are 480 x 10 and 480 x 100, both of which are clearly incorrect at a cursory glance. By order of magnitude, you can again determine that the correct choice must be D.
_________________
A space shuttle orbits the earth at about 8 kilometers per second. This speed is equal to how many kilometers per hour?
(A) 480 (B) 2,880 (C) 4,800 (D) 28,800 (E) 48,000
Kudos for a correct solution.
We can solve this using equivalent ratios
1 hour = 3600 seconds
So, let's use equivalent ratio to compare kilometers/seconds We get: 8/1 = x/3600 Cross multiply: (8)(3600) = (x)(1) Simplify: (8)(3600) = x Since (8)(4000) = 32,000, we can conclude that (8)(3600) is a little bit less than 32,000