Converting Word Problems into Mathematical Statements
INSTRUCTOR: Sowmya Subramaniam, Quant Expert at Galvanize Test Prep
M.Sc Mathematics  IIT Madras, M.S. Mathematics, San Jose State University
Word problems are one of the most common types of questions in the GRE Quant section. Hence, they certainly demand the attention of the GRE aspirants. Solving word problems requires effective time management skills and mastery of various topics in math, including (though not limited to) percentages, ratios and algebra.
The image below shows the proportion of word problems in the GRE Quant section compared to the other question types.)
While they present the greatest opportunity to score points in the GRE Quants, word problems are also a challenge to the test takers.
Test takers face several problems while dealing with the Quant section: Difficulty in framing the mathematical equations, proceeding without knowing whether the equations are right, not understanding the required value and, of course, the inevitable careless mistake or two.
To pick up some helpful tips on how to solve word problems confidently, watch the following recording of our webinar on âConverting Word Problems into Mathematical Statementsâ.
In this webinar, Mrs. Sowmya Subramaniam (M.Sc Mathematics, San Jose State University) explained the methodology to deal with word problems and also addressed various problems faced by GRE aspirants with respect to word problems.
Below is the transcript of the Q& A session handled during the webinar.
Q1: How can I ensure that the mathematical equations that I have framed are correct?
A1:  It would be effective if you can retrace the steps, i.e., take the  answer that you got and fit into the question, ideally working backwards .Look at the following example to understand this.
Problem Statement:
The ratio of the mother and sonâs age is 3:1. 10 years ago, the ratio was 5:1 .What is the present age of the mother?
Solution: In this question, the two equations are x=3y and x-10 = 5y-50 and solving this gives the values of x and y as 60 and 20 respectively.
There are two things that need to be checked here: the solution and the equations.
To check the solution alone (assuming the equations are correct and that you might have made a calculation error), substitute these values back into the two equations and verify if LHS=RHS (i.e., the equation is balanced)
To check if the equations are correct:
Motherâs age = 60, Sonâs age = 20.
Check the following
i) Logic: Logically the answer is correct since mother's age is more than the son's age and you have not got a negative result.
ii) Analytics:
The ratio should be 3:1.
60:20 = 3:1, so the first part of the question is satisfied by these values of x and y >
The ratio 10 years ago should be 5:1
10 years ago --Mother would have been 60-10=50 years old and the son would have been 20-10 = 10 years old. So the ratio of their ages = 50 : 10=5:1. So the second statement is also satisfied by these values .
Satisfying both checks would imply that your equations are correct.
Q2: What are the topics that have to be covered to make solving word problems easier? E.g., Percentages and Ratios.
A2: Apart from percentages and ratios, there are several other topics like rates, mixtures & allegations, distance & time and profit & loss that are tested in word problems in the GRE Quant section. Practising problems extensively in these topics while applying the correct strategies can ease the task of word problem solving.
Q3: How to solve questions in a shorter period of time?
A3: Drawing a table or a diagram and converting the data given into visual representation is the best way to save time while solving word problems. Merely reading and rereading the question will not help much in understanding or solving the problem. You need to read with an eye for detail, collect information, connect the data and represent them in the form of a table or diagram. Follow the mnemonic âPIESâ (P-Picture or diagram , I-Information , E-Equation and S-Solve) to remember the steps to solve any word problem.
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