HKD1710 wrote:
A, B, and C each drove 100-mile legs of a 300-mile course at speeds of 40, 50, and 60 miles per hour, respectively. What fraction of the total time did A drive?
(A) 15/74
(B) 4/15
(C) 15/37
(D) 3/5
(E) 5/4
This is a great example of how quant questions can be tackled in a number of different ways, and the best approach for each student depends on your strengths, weaknesses, pacing, and degree to which you're able to be nimble with numbers.
Three ways. First is quantitative REASONING. Third is QUANTITATIVE reasoning. Second is somewhere in between.
First, ballparking. This is how I would do it on a real test. Faster, easier, almost no chance of making a silly calculation error, and eliminating four answer choices makes this NOT a guess.
A is the slowest, so must account for more than 1/3 of the time.
Look at the answer choices. A and B are greater than 1/3, so they are out.
A can't account for more than the full time. E is out.
We are down to C and D. All three speeds were within 20% of the median. A can't have driven for 60% of the time, right? D is out.
Answer choice C.
Second, math using something other than 300 miles for the trip. Yeah, they told us that the total distance is 300 miles, but the question just asks us for a ratio and the ratios will apply regardless of the distances, so we can use whatever we want for the total distance to make our lives easier. I refer to this as a "Hidden Plug In" since there's no explicit variable but there's something we can make up that gives us a clear path to the solution. How about each person drives 600 miles instead of 100 miles?
A drives for 15 hours.
B drives for 12 hours.
C drives for 10 hours.
A drives for 15 of the 37 hours. 15/37.
Answer choice C.
Third, math (plus a tiny bit of ballparking) using the numbers they gave us.
A drives 100 miles at 40mph, so 2.5 hours.
B drives 100 miles at 50mph, so 2 hours.
C drives 100 miles at 60 mph, so 1.66667 hours. Let's just call this 1.7 and see if we get close enough.
Total time is 6.2 hours. A drove for 2.5.
\(\frac{2.5}{6.2}\) That's less than 1/2 but more than 1/3.
Answer choice C.
ThatDudeKnowsBallparking
ThatDudeKnowsHiddenPlugIn