This video explains GMAT Math Word Problems and how to tackle them on the GMAT Test.
GMAT Math Word Problems [Video Transcript]
In this lesson, we will examine questions where we are given information about people’s ages in the past and/or in the future. In this question, we are given information about the present ages of Sue and Marco, and we are given information about their ages four years in the future. To solve this question, we will create a table with both time periods as columns. Let’s begin with the information concerning their ages at present. Here we’re told that Sue is eight years older than Marco. So let’s assign a variable to the smaller value which is Marco’s age. Let’s let “M” represent Marco’s current age. Since Sue is eight years older than Marco, her age will be M plus eight. Now please note that we could also assign a different variable to Sue’s age, however the given information here does not appear complex enough to warrant this. Having said that, this question can also be solved using two variables. And in our next example, we will use two variables to solve a different question.
Okay, back to our question. Once we have assigned variables to Marco’s current age and Sue’s current age, a common mistake is to then move on to the information about their ages four years in the future. The important point here is that if we know the present ages of Marco and Sue, then we can easily determine their ages four years in the future. To find Marco’s age four years from now, we simply take his current age M, and add four to it. Similarly, to find Sue’s age four years from now, we take her current age, M plus eight, and add four to it. At this point we can examine the information about their ages four years in the future.
Now from our table, we can see that in four years Marco’s age will be M plus four, and Sue’s age will be M plus eight plus four. Our goal at this point will be to create an equation. So can we say that these two quantities are equal? The answer is no, since the question tells us that in four years Sue’s age will be twice that of Marco’s age. So if we want to make these two quantities equal, we can take Marco’s age and multiply it by two, in which case the two quantities are now equal, and we have an equation we can solve for M. From here we can expand the left hand side, and simplify the right hand side. Then if we subtract M from both sides, and then subtract eight from both sides, we get M equals four. Now that we know that M equals four, do not make the mistake of choosing answer choice A. Keep in mind that the question asks us to find Sue’s current age, and earlier we said that her age is equal to M plus eight. So, if M equals four, we can replace M with four to see that Sue is 12 years old. And the answer her is C.
Okay, now let’s try another age question. In this question, we are given information about the present ages of Abbie and Iris. And we are given information about their ages 11 years in the past. So let’s create a table with both time periods as columns. We will begin with the information about their ages at present. Here we are told that the sum of their ages is 42. So one option is to assign a variable to one age, and let the other age be 42 minus that variable. Another option here is to use two variables. Let’s try that. We will let “A” represent Abbie’s present age, and let “I” represent Iris’ present age. Since we’re using two variables, we will need to create two equations so that we can solve for A and I. Well, since their ages presently add to 42, we can say that A plus I equals 42. All right, now let’s complete our table. If Abbie’s present age is A, then her age 11 years ago was A minus 11. Similarly, if Iris’ present age is I, then her age 11 years ago was I minus 11.
Now let’s work with the information we have about their ages 11 years ago. Here is Abbie’s age 11 years ago, and here’s Iris’ age 11 years ago. These ages are not equal since the question tells us that Abbie’s age is three times that of Iris’ age. So if we take Iris’ age and multiply it by three, these two values will be equal. From here we can take this equation and expand the right hand side, then subtract three I from both sides, and then add 11 to both sides to get another equation with two variables. At this point we can take the two equations and solve this system. To do this, we will first take the top equation and multiply both sides by three, and we will leave the bottom equation as is. From here if we add the two equations, we get 4A equals 104. And when we divide both sides by four, we see that A is equal to 26. Now don’t forget that A is equal to Abbie’s present age, and the question asks us to find her age two years from now. So her age in two years will be 28, which means the answer is E.
All right, let’s summarize. In this lesson, we learn to solve questions involving past and future ages by first creating a table with the given time periods. Then we create two or more equations to solve, and finally we recheck the question to ensure that we have obtained the required information.