Well what better to practice than to get an actual question from the test writers.
Today's question is [I hope that CollegeBoard does not get mad at me for showing this question - but heck, I tell everyone to read their stuff & buy their book. So, I think that they should be happy with me - I make them money]:
A woman drove to work at an average speed of 40 miles per hour and returned along the same route at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?
-
30 - 30
- 34
- 35
- 40
Hard questions also have hard answers. So if the numbers in the problem appear in the answer choice, like A & E, they are usually wrong.
Also if you can find an answer choice with one easy math step, like D. 35 which is the average of 40 and 30, it will most likely be wrong as well.
Think about it: How could this be a hard problem if the math was short and easy?
So here we are having eliminated A, D & E - leaving us with a 50/50. NOW is the time to make a good guess.
B. smells fishy, it looks too close to 30. The answer has to be somewhere around the middle of the two numbers but less than the average (because 30 is slower than 40, it hogs more time).
C. fits the bill. It looks just right, being an "ugly" answer that is around the average.
It is the correct answer.
Less than 40% of 50,000 people answered correctly - yet it is one of the easiest "Hard" questions to guess the correct answer!
On guessing: if you have absolutely NO clue, then do NOT guess. It will hurt you. But if you can eliminate 2 or 3 answer choices, then I say: GO FOR IT!
1 comment:
Great question! I agree that it's pretty obvious to rule out A, D, and E right away:
A would mean traveling the WHOLE way at 30, which you didn't do, so it must be larger than 30
D would mean you travelled the same amount of time at each speed, which you didn't do (since the drive TO work would have taken less time at a faster speed), so it must be less than 35
E would mean traveling the whole way at 40, which you didn't do, so it must be smaller than 40.
When it came time to choose between B or C, though, I also would be tempted to choose B simply because it's easily divisible by 2 (making a one way trip 17 and 1/7).
Chances are if you do sit down and solve this problem algebraically, you'll end up solving for the one-way distance, but then you'll have to double your answer for the round trip. (Of course this isn't foolproof, since a one-way trip could have been a distance over 14, but we're talking about hedging our bets here.)
So, not only is B "sufficiently ugly" to be the right answer to a HARD question, but it's also "sufficiently nice" to be the result of something doubled.
Thanks for the question!
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