GMAT Problem Solving, GMAT Quantitative
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GMAT Quant Skills – Tackling Word Problems

One of the big reasons why the those who have good language skills do well on the GMAT is that even the Quantitative section has a lot of English comprehension.

The Quantitative section of the GMAT has quite a few Word Problems or problems involving barely any symbols and lots of language in both the Problem Solving and the Data Sufficiency formats.

This is especially challenging for non-native speakers of English who take the test since they tend to put English and Math or Verbal and Quantitative skills into separate compartments. Asian test-takers, especially those from India, are used to thinking of Math problems in terms of notational or algebraic language rather than English.

So the skill to convert English into either Logic or Algebra is something that test-takers have to master if they aim to score a 50 or more on the Quant section. This post will deal the steps involved in mastering this skill and solving these seemingly lengthy problems faster.


Don’t convert the words into an equation as you read from left to right

The natural reaction of those comfortable with writing equations to start converting a sentence into and equation as they are moving from left to right. Let us look at the statement below.

There are three times as many boys as there are girls

Test-takers who used to going into equation mode as are reading a problem, tend to straight away represent this as 3B = G since the terms three, boys and girls appear form left to right in that order.

This is an understandable mistake but you must also understand that this is not, to use tennis parlance, an unforced error but a forced error. The test-setters want you to make this mistake.

The first step is to resist this temptation and if you want to frame an equation, do so only after understanding the logic of the statement.

Are there more boys or girls? Boys.

Hence the statement has to be written as B = 3G


Don’t start framing equations till you reach the end of the problem

Another default reaction of test-takers is to start converting every sentence in a word problem, as they are reading it, into an equation if it is possible to do the same.

This is possibly the biggest mistake any test-taker can make on the Math section any aptitude test.

You are assuming that the information is being given in a linear format and building a structure to solve based on that premise. Questions, the moderate to tougher ones, do not present information sequentially.

After four lines of information the question might say, in how many days will the job be completed if B leaves after the fourth day.

You cannot not and should not start solving the problem until you reach the end of the problem. You will be create a structure to solve the problem without knowing what is asked and what final twists are yet to be revealed.

You will end up

  • either creating a more complex equation than what is required
  • or creating an equation with the wrong variables

So lesson number two is to leave the framing of the equations till you reach the end of the problem.


Write equations using the variable you need to determine, not the first variable you encounter

One of the advantages of reading the whole problem before starting to write is that you will exactly know what needs to be done and you will also know what the big reveal is

Even after they have figured this out most test-takers tend to write equations using the variables mentioned early on in the problem.

Let us look at a few problems to understand this better.

Alice’s take home pay was the same each month and she saved the same fraction each month. The total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save. If all the money that she saved last year was from her take home pay, what fraction of her take home pay did she save each month?

Most test-takers will start solving the problem by trying to write an equation for this statement – the total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save

They usually end up writing an equation using variables X for salary and Y for savings.

But what is the problem asking for?

The fraction that Linda saved, so it makes most sense to write the equation using the fraction as the variable.

If we take the fraction as F and the Salary as S, the equation becomes

12FS = 3 (1-F) S or F = 1/5

One advantage of this method is that the variable you solve for will be what the question is asking for.

If you write the equation using variables,other than the one you need to determine, there are very good chances that you will rush to mark the answer option as soon as you calculate the variable. GMAT test-setters will have cleverly included the value of that variable among the answer options as well.

To avoid this, it always makes sense, whether you are solving a word problem or a normal problem, to take what the question is asking you to determine as X and express everything else in terms of X.

Another way is to directly conver the words into logic instead of variables.

The seocnd sentence — the total amount she saved at the end of the year was 3 times the amount of that portion of her monthly take home that she did not save —  can be processed as — twelve times her monthly savings is equal to three times her monthly expenditure.

In other words, her monthly expenditure is 4 times her monthly savings, which means her monthly salary is 5 times her monthly savings.


The entire essence of this post can be summed up using the best way to solve this problem.

S is a set of 21 numbers. n is a part of this set of 25 numbers and is equal to four times the average of the remaining 20 numbers. Find the ratio of n to the sum of all the numbers in the set.

The usual tendency of test-takers is to write an equation using the variables mentioned in the second statement.

But the problem is asking for the ratio of n to the sum of all the numbers.

It is best to express the second sentence using n and S, sum of all numbers.

n = 4 ( S – n ) / 20, 6n = S or n / S = 1 / 6

We will take up more GMAT Quant Skills in the forthcomin posts.

 

 

 

 

 

 

 

 

 

 

 

 

 

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1 Comment

  1. Grishma Kajbaje says

    Thank you Sir for the valuable information..It will be great if you explain shortcuts to solve weighted average and ratio problems.

    Like

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