silverprince
BrentGMATPrepNow, thanks for your solution to this problem. I have a question about
strategy. When would you choose to use "bottom-up" algebra (like you did here) compared to "top-down"
backsolving from the answer choices? The first time I solved this problem, I used backsolving, but I noticed that it was hugely inefficient and took twice as long as when you solve using algebra.
Would appreciate your insight. Thanks!
Backsolving (aka testing the answer choices) is often a valid approach. In fact, when students first encounter a word problem like this, they should automatically consider testing the answer choices. Then they should give themselves 15 to 20 seconds to find a different (and hopefully faster) approach. If they can't come up with some alternate approach, they should start testing the answer choices.
In some cases, testing the answer choices can be very time-consuming.
This is one of those cases.
For example let's test answer choice B ($2,070)
This means the total COST of the costumes worn by Group B = $2,070
Since the costumes worn by Group B cost $90 each, the total NUMBER of costumes = $2,070/90 = 23
So there are 23 dancers in Group B
50 - 23 = 27
So, there are 27 dancers in Group A
The costumes for group a dancer's cost $80 each, so the total costume COST for Group A = (27)($80) = $2160
So the total COST for both groups = $2,070 + $2,160 = $4230
No good. We need the total cost to be $4,270
So, answer choice B is incorrect.
Phew!!! Now we need to test ANOTHER answer choice!
Determining whether testing the answer choices will be too time-consuming can be difficult. You need to be able to quickly predict the number of steps it will take to test each answer choice before wasting a bunch of time.
Cheers,
Brent