As established in many of our previous posts, performing well on GMAT Quant is less about being able to solve math than it is about being able to strategically approach difficult problems. This ensures that you are able to get to the crux of the problem quickly and with expert precision. One of these strategies that is extremely useful is ‘Backsolving’.
Backsolving is just like Picking Numbers, except instead of coming up with the number ourselves, we’ll use the numbers in the answer choices. We’ll literally work backward through the problem, looking for the answer choice that agrees with the information in the question stem. Or in other words similar to the Picking Numbers strategy, Backsolving allows us to plug numbers into a problem containing variables. With Backsolving, we’ll use numbers from the answer choices, because we know that one of the answer choices has to be correct.
The most efficient way to Backsolve in most problems is to begin with either (B) or (D). This is because the answer choices are always listed in numerical order. If we can determine whether the answer choice we’ve plugged in is too large or too small, choosing (B) or (D) will allow us to adjust efficiently. For example, if we tried (B) and recognized that it’s too large, we can eliminate not only (B) but the larger answers as well and vice versa.
Let’s see this at work with a GMAT like Quantitative reasoning question:
A teacher grades students’ tests by subtracting twice the number of incorrect responses from the number of correct responses. If Student A answers each of the 100 questions on her test and receives a score of 73, how many questions did Student A answer correctly?
Here, we’re looking for the number of questions the students answered correctly.
So, if the student got a 73 as her score, and incorrect answers are subtracted from correct ones, we know that she had to get more than 73 questions correct. Right away we can eliminate answer choices (A), (B), and (C), and you know that Backsolving is going to be even more efficient.
All you have to do now is test (D) and we’ll have the right answer, right away. It will either be (D) or if (D) is too low, (E). Let’s plug (D) into the problem. If the student got 82 questions correct. Then, to calculate her score, we have to subtract 2 times the number of incorrect responses. Since there are 100 questions, that’s 100 minus 82 or 18 wrong. 82 minus 2 times 18 equal 46. That’s way too low.
So we know our answer must be (E). Even if we have great algebra skills, Backsolving is often the best way to get from the problem to solution quickly and efficiently.
Backsolving can save us a great deal of time. It is also an exceptional approach when we have no idea how to begin a problem. Backsolving can often mean the difference between getting lost in a problem and moving systematically through the problem to the correct answer, and that means points on Test Day
Want more GMAT test-day tips? Watch our GMAT strategy tip videos on youtube to understand the test from a test-maker’s perspective.