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GMAT "Tricks" Part 2: Backsolving Revisited
Posted by ian on Sun 21 Sep 08 at 4:05pm
We discussed in Part 1 why backsolving isn't often a good option on the GMAT. Still, if you are going to backsolve, there are a few things to know. On some questions, particularly word problems, if you test one of the wrong answers, you may be able to tell whether the correct answer is smaller or larger than the wrong answer you've tested. For example:
Al earns $12 per hour at his day job, and $18 per hour at his night job. Each week he works three times more hours at his day job than at his night job. If he earns a total of $810 each week, how many hours does he work per week at his day job?
A) 30
B) 36
C) 40
D) 45
E) 60
Doing this question algebraically is not especially challenging, but let's say we choose to backsolve. If we begin with answer C, and assume he works 40 hours on the day job, then he works 40/3 hours on the night job. He would then make:
40*12 + (40/3)*18 = 480 + 240 = 720 dollars.
The answer we get is too low: he must have worked more hours. So the correct answer must be larger than 40. Notice that we've ruled out answers A, B and C now. We only need to do one more test. We can do that test if we need to the correct answer is D.
In questions like this, answer choices are usually written in increasing order on the GMAT. If you're backsolving, is it best to start with answer choice C? While you'll often read on GMAT forums and in some GMAT books that it's best to start with C  and as you can see from the above, you rule out three answers immediately if C is wrong which isn't bad  in fact, you can do better. The best place to start in this kind of question is with answer B or answer D. Why?
If we start with answer choice C, we might get lucky (one time out of five) and find that C is the right answer. Otherwise we'll have two remaining possible answers, and we'll need to do another test. So, by starting with C, we do:
1 in 5 chance: you get the answer on the first test
4 in 5 chance: you get the answer on the second test
If we start with answer choice B, we might get lucky (one time out of five) and find that B is the right answer. But, if B is too high, we'll also know immediately that A is the right answer. We get the right answer after one test two times in five. If B is too low, we can test D, and from there we can work out which answer is correct D might be correct; if D is too high, C is correct; if D is too low, E is correct. So by starting with B or D, we do:
2 in 5 chance: you get the answer on the first test
3 in 5 chance: you get the answer on the second test
That's better than starting with C.
All of that said, there aren't many problems for which it's obvious whether the correct answer is higher or lower than the answer choice you've tested. So while it may be interesting to know what the optimal strategy is for backsolving these kinds of problems, in practice it isn't often helpful.
One final comment:
The GMAT test designers know very well what strategies are described in test prep books, and the purpose of the GMAT is not to test what testtaking strategies you've learned. It's quite easy to modify any problem to make backsolving difficult, and it's clear, if you read through many GMAT questions, that GMAT test writers often do this. The problem above, for example, could instead read:
Al earns $12 per hour at his day job, and $18 per hour at his night job. In Week A, he works three times as many hours at his day job than at his night job, and he earns a total of $810. In Week B he works twice as many hours at his night job and half as many hours at his day job than in Week A. What were Al's combined earnings from his day job and night job in Week B?
A) $540
B) $650
C) $720
D) $810
E) $900
Now backsolving becomes difficult. The question is designed in such a way that the test taker is forced to answer the question directly. The answer is $810, incidentally, as can be found using an algebraic approach in week B, Al's hours change in such a way that his total earnings remain the same.


