This video explains Ratios in GMAT Test and tricks to do well on the GMAT Math Secion.
Ratios in the GMAT [Video Transcript]
In this lesson, we will take an introductory look at ratios. To begin, a ratio is a comparison of two or more quantities. For example, we might say that at a certain school, the ratio of girls to boys is 2 to 5. Here we are comparing the number of boys to the number of girls. Now, it’s important to note that the 2 to 5 ratio here does not imply that there are exactly 2 boys and exactly 5 girls at the school. Ratios tell us nothing about actual quantities. They only tell us about proportions. So here, the 2 to 5 ratio means at the school there are 2 boys for every 5 girls. Also, note that the order of the numbers is very important. For example, if we were to say that the ratio of boys to girls is 5 to 2, then that would mean there are 5 boys for every 2 girls.
Now, there are three different types of notation we can use to express ratios. We can express the ratio as 2 to 5. Or, we can express it using a colon to separate the terms. Or we can express the ratio as a fraction. Now, in general, if we are given information that can be re-worded in the form ‘for every something there is something else’, we are typically dealing with a ratio question. So be sure to keep this in mind. Now most ratio questions fall into 2 categories: equivalent ratio questions & portioning questions. Let’s look at equivalent ratio questions first.
Now to begin, we should recognize that the ratio 1 to 2 is equivalent to the ratio 3 to 6. For example, saying there is 1 girl for every 2 boys at a school is the same as saying there are 3 girls for every 6 boys at a school. Both ratios express the same proportions. So we say that 1 to 2 and 3 to 6 are equivalent ratios. Now we can create equivalent ratios by multiplying or diving both terms by the same value. So for example, if we take the ratio 2 to 7, and multiply both terms by 2, we get the equivalent ratio 4 to 14. Similarly, if we take the ratio 3 to 4 and multiply both terms by 5, we get the equivalent ratio 15 to 20. Now a common question type relate to equivalent ratios is one where we are told that two ratios are equal and we need to solve for some unknown value. To solve this type of question, we first re-write the equivalent ratios using fraction notation and then we apply the following rule. So when we apply this rule and cross-multiply, we get the following equation.. And when we simplify the right hand side we get X equals 18. So the ratio 1 to 2 is equal to 9 to 18.
Okay, let’s try another question. Once again, we will first re-write the ratios using fraction notation. And then we apply the following rule to get the following equation. From here, when we simplify the right-hand side and divide both sides by 5, we get X equals 77 over 5, which we can also re-write as 15.4. So the ratio 7 to 5 is equal to the ratio 15.4 to 11. Alright, now let’s tackle a word question involving equivalent ratios. Here we are told that at a certain zoo, the ratio of reptiles to birds is 7 to 2. There are 28 birds and we must find the number of reptiles. Now this question happens to feature the word ratio. So we know it’s a ratio question. However we also know it’s a ratio question because we can rephrase the information to read for every 7 reptiles, there are two birds.
Now the question tells us that the ratio of the number of reptiles to the number of birds is 7 to 2. So we can write this as the number of reptiles to the number of birds is equal to 7 to 2. The question also tells us that there are 28 birds. So we can replace the number of birds here with 28. Now we don’t know the number of reptiles. In fact, the question asked us to find this number. So let’s let ‘r’ represent the number of reptiles at the zoo and then replace the number of reptiles in our ratio with R. Now this ratio we are told is equal to 7 to 2. We now have an equation we can solve for R. To solve this equation we can apply the following rules & cross-multiply and then simplify the right-hand side and then divide both sides by 2 to get R equals 98. This means there are 98 reptiles at the zoo.
Now the other question type involving ratios requires us to portion quantities into certain ratios. For example, in this question, Bruce has a total of 15 cookies and he plans to distribute them to Kendra and Patty in a 2 to 1 ratio. In other words, for every two cookies Kendra receives, Patty receives one cookie. Our goal here is to calculate how many cookies each person receives. To do this, we first add the terms in the ratio. So for this question, we add 2 and 1 to get 3. This tells us that for every 3 cookies, Kendra receives 2 cookies and Patty receives 1 cookie. Now here comes the most important part. If we had 3 bags of cookies with equal amounts of cookies in each bag, then we would achieve the 2 to 1 ratio by giving Kendra 2 bags and giving Patty 1 bag.
So given this, let’s divide all 15 cookies evenly into three bags. This means we will put 5 cookies in each bag. Now that we have 3 bags of cookies, we can divide the bags into a 2 to 1 ratio. This means Kendra gets 2 bags and Patty gets 1 bag. When we do this, we see that Kendra gets 10 cookies and Patti gets 5 cookies. Also, notice that the ratio of 10 to 5 is equal to the target ratio of 2 to 1. Okay, let’s try one more question and then we will generalize the results. In this question, we have a certain nut mix where the ratio of peanuts to walnuts to cashews is 5 to 2 to 1. Our task is to determine how many pounds of walnuts there are in 48 pounds of nut mix. Now notice that our ratio has 3 terms. This is no different from ratios with 2 terms. This ratio tells us that for every 5 pounds of peanuts, there are 2 pounds of walnuts, and 1 pound of cashews. To solve this question we first add the terms in the ratio to get a sum of 8. This tells us that for every 8 pounds of nut mix, there are 5 pounds of peanuts, 2 pounds of walnuts, and 1 pound of cashews. At this point let’s divide 48 pounds of nut mix into 8 equal parts. When we do this we get 6 pounds of nuts in each part. At this point, we divide the 8 parts into the target ratio of 5 to 2 to 1. Once we do this we can assign 5 parts to peanuts, 2 parts to walnuts, and the last remaining part to cashews. This means that in 48 pounds of nut mix, there are 30 pounds of peanuts in the mix, 12 pounds of walnuts, and 6 pounds of cashews.
Alright, let’s summarize. In this lesson we learn that if a question can be written in the format ‘for every X there are Y’, then it is a ratio question. We learned how to solve equivalent ratio questions and we learned how to solve portioning questions. Now to solve portioning questions we add the terms in the ratio to get a sum of T. Then we divide the total quantity into T equal parts. And then we divide the T equal parts into the target ratio.