GRE Quant Backsolving Trick with Sample Questions

Some people dislike solving quantitative aptitude questions more than the others. But, the best part about Discrete Quant questions asked in the GRE is that only five options are provided to the candidates. These options play a huge role in simplifying the job of candidates, as you can simply check whether your answer is correct or not. This method of coming to an answer using the provided options is called backsolving. This method of solving a question is like reviewing someone’s work. All you have to do is imagine somebody told you the right answer and then you can simply check whether their answer is right or wrong.

In order to apply the backsolving trick, there are some conditions that need to be met. Only then, this method can work properly and provide you the right result. These conditions are:

  • Only applicable to the MCQs
  • The answer choices have to be in the form of numbers. This technique will not work on answer choices that are in the form of percentages, inequalities or variables.
  • The answer choices need to functional. Here the functionality of the answer choice will be determined by its usefulness in the better understanding of the problem.

If these three conditions are met then you can go ahead and use backsolving to get the right answer! Let’s look at some examples to develop a better understanding of this trick.

1. If 200 were incremented by 20% and then decremented by x%, then the result comes out as 144. What is the value of x?

  1. 20
  2. 40
  3. 55
  4. 72
  5. 90

Let’s assume, 55 is the right answer. Now, we must check if it is actually the correct choice. In order to check, first you will increase the value of 200 by 20%, then decrease it by 55%. If the result comes out as 144, then it is the right option, otherwise it is not!

200, incremented by 20%, is 240.

240, decremented by 55%, is 132.

The answer is not 144, so the assumption was wrong.

This means we have eliminated one option, leaving us with four possible answer choices. Now, should we pick an option that is higher or lower than 55?

We should pick a somewhat lower percentage, to receive 144 as the final value. In this case, we have only one answer choice that is slightly lesser than 55. Let’s find out if 40 gives us the desired output.

200, increased by 20%, is 240.

240, decreased by 40%, is 144.

40% is the right answer!

Let’s have a look at another simple problem.

2. A bottle that was 75% full of water was emptied into a 5-liter vessel. If the water filled 30% of the vessel’s volume, then what would be the total capacity of the bottle?

  1. 1.5
  2. 2
  3. 3
  4. 5
  5. 4.5

Let’s assume, 3 is the right answer. Now, we must check if it is actually the correct choice. In order to check, first we will take 75% of 3 and then check if its equal to 30% of 5. If they are equal, then 3 is the right option, otherwise it’s not the right choice!

75% of 3, is 2.25

30% of 5, is 1.5

The two values are not equal. Therefore, the assumption is wrong! But, we have eliminated one option. Now, the question is which option we should try next?

Since 75% of 3 is giving us a higher value then we want. We should take the next smaller value, which is 2. Let’s check and see if 2 gives us the desired output!

75% of 2, is 1.5

30% of 5, is 1.5

Therefore, 2 is the right answer!

This method can be quite effective in increasing your efficiency, as you can get the result much faster as compared to using the conventional methods for solving these problems. Keep on practicing easy to medium level questions so as to develop a better understanding of this trick. BYJU’S will be glad to help you in yourGRE preparation journey. You can ask for any assistance related to GRE from us by just giving a missed call at +918884544444, or you can drop an SMS. You can write to us at gre@byjus.com.