GMAT – Best 5 Problem Solving strategies
Problem Solving is the most scoring section of the Quantitative section of the GMAT. The GMAT problem solving questions, though tricky at times, are not as much as the ones asked under the Data Sufficiency category. One point to remember is that simply memorizing formulae won’t help much. One needs to develop a smart approach to solving the questions. Keeping a few points, as presented below, in mind, would definitely help one to clear the PS questions with ease.
- Sharpen the axe and hit repeatedly
GMAT is an adaptive test and you want to get all the easier ones correct so that you have a chance of maximizing your score. The first few questions would be simple and your basic concepts would be enough to get you through those. Since the first few questions are on the easier side, they should be done faster, leaving you with sufficient time to attempt the tougher ones that are to follow. Remember that there is a huge penalty for not attempting all the questions in any section. However, you don’t want to rush and get the easier ones wrong.
- Apply brain, traps ahead
If you find that a particular question seems too obvious, spare a moment to rethink! In the GMAT, it might be a trap question. Let us take a simple problem to elucidate the point.
“A 30-liter mixture contains 20% alcohol and the rest water. How much mixture should be removed and replaced with water to reduce it to 10% concentration?”
One may be tempted to work as follows:
Initial quantity of alcohol = 20% of 30 = 6 liters
Final quantity of alcohol = 10% of 30 = 3 liters.
So, quantity removed is 3 liters (You think – See! I got the answer so fast!).
However, the above reasoning is flawed, since the 3 liters is only alcohol component which is 20% of the total volume you removed (since the volume you removed has 20% alcohol). Thus, the volume to be removed = (3 x 100)/20 = 15 liters (adding water does not change the quantity of alcohol).
- There is always a smarter way
Do calculations faster. The numbers that are used in GMAT problem solving questions are chosen in such a way that the answers can be obtained with minimal calculation. It is better to have a few short-cut calculation tricks up your sleeve.
For example: 28 x 125 can be simply done by multiplying and dividing by 8:
(28 x 125 x 8)/8 = (28/8) x (125 x 8) = 3.5 x 1000 = 3500
Similarly, 28/25 can also be simply done by multiplying and dividing by 4:
(28 x 4)/(25 x 4) = 112/100 = 1.12
Try to learn up the multiplication tables till 20, squares till 20 and cubes till 10. Also, try and remember the reciprocals till 20. So, the next time you see a fraction 1/13, you can easily put it as 7.7 percent.
A useful method of multiplication is shown below.
Say, we need to multiply 56 x 24: 56 x 24 = 50 x 24 + 6 x 24 = (100/2) x 24 + 144 = 1344. The above process can be done mentally with a little practice, and would be faster than doing the normal approach.
- The bottom five are your friends
Use the options to solve. Some of the questions, especially the ones having the options in terms of variables, can be solved by plugging in values of the variables in the problem, working out the calculation and then, plugging in the same values of the variables in the options to determine the option giving the same result. Sometimes, more than one option may seem correct. In such an event, try out with another set of values and only check those options which gave the same result previously. In this approach, it is suggested that one should not use easy or obvious values like 0, 1, 2, 3 etc. for the variables. Rather, choose some odd values like 4, 7, etc.
Also, for number theory based GMAT problem solving questions, it is best to plug in numbers to observe any pattern in the result. Remember the four major regions are: Numbers from 0 to 1, Numbers greater than 1, Numbers from 0 to – 1, and Numbers less than – 1.
- Believe me the bottom five are close friends
In some GMAT problem solving questions, you can plug in the values from the options is the one which seems too complicated to analyze or solve. For example, an apparently simple problem on time-speed-distance can easily lead to a quadratic equation in the variable whose value has to be determined. In such cases, one can simply plug in the values given in the options and determine the one which satisfies the conditions in the problem. While putting in the options, one should follow this hierarchy (Let us assume the options are in ascending order of magnitude, as is usually the case):
You first try with option C. If it fails, observe whether the result obtained is greater or lower than the required value. Next, you try option B. If this too fails, again observe whether the result obtained is greater or lower than the required value. If for both B and C, the results obtained are greater than the required value but B is relatively closer to the required value, the answer must be A. However, if C is relatively closer, the answer must be either D or E. Now, you try with option D. If it too fails, the answer must be E. Thus, we need to verify a maximum of three options to get the answer.
Remember that GMAT – PS is not about only solving mathematics problems.
Many of the problems in this section can be solved with a little bit of logic. Applying the steps mentioned above can help in cutting down on the time taken to attempt the questions so that you do not have a feeling of having to rush through the questions towards the end. A fast-and-steady approach is what is needed to crack the PS questions.
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