Problems of the quantitative section are among the trickiest questions asked in the GMAT exam. There are 31 questions of varying difficulty to be solved in 62 minutes. These problems range from time and work, basic algebra, percentages, powers and roots to probability and statistics based questions. They come in all shapes and forms including complex and puzzling word problems. Ratio and proportion problems are where the question-makers like to play with the candidate’s mind. Preparation and practicing of ratio and proportion problems help in arriving at solutions quickly and accurately. It solidifies prior quantitative knowledge and makes the candidate find quick solutions, in turn, saving time during the actual test.
Ratio and Proportion Problems: The Difference in the Terms
Ratio and proportion, often named in that order, are different in one important respect, here is a brief analysis of the two terms:
Ratios are essentially fractions and a measure for comparison. Basically, a portion of one quantity in relation to a portion of another quantity. For instance, the “ratio of men to women is 4 is to 5” or “ratio of sugar to milk is 2:5”. Colons, fractions and ‘is to’ are primarily used to express ratios.
Convert ratios into equations and you get proportions. In the above example, M/W = 4/5 is a proportion formed from the sentence “ratio of men to women is 4 is to 5”. Usually, GMAT problems list three quantities in a ratio and ask you to find the remaining quantity.
Examples to Explain Ratio and Proportion
The following examples will let you know the nature of ratio and proportion problems for GMAT:
Example 1: Ratio and Proportion problems for GMAT
Ratios always denote a part of something.
If P:Q appears in proportion of 4:7, there are 4 parts of P for every 7 parts of Q. Similarly when P:Q:R appear in 4:7:10, there are 4 parts of P for every 7 parts of Q and every 10 parts of R.
Furthermore, adding up all the parts gives the total number of parts or the whole. Here, 4+7=11 and 4+7+11= 22.
Do not take the ratio figure as actual figures. They are merely indicative of what size of the whole, a certain quantity is.
Also, suppose 5/7 is the given ratio of tomatoes on a tomato and onion pizza. Deductively ratio of onions on the pizza will be 2/7.
Example 2: Ratio and Proportion problems for GMAT
Let’s start off with a simple and easy-to-do example before solving a difficult problem.
A stretch of highway road is 350 kilometres. Alongside the road, 70 lamposts have been constructed. Calculate how many lamp posts were constructed on a stretch of 140 kilometres.
Here, we take a different approach. We will solve this with the help of equations.
Let x be the number of lamposts to be constructed.
So with the help of the information, ratio of kilometres of highway to number of lamp posts is 350:70. It is easy to construct the equation 350/70=140/x.
This equation can be reduced to 5=140/x which can be further reduced to x=140/5 or 28
So 28 lamp posts were constructed on a stretch of 1400 kilometres.
Example 3: Ratio and Proportion problems for GMAT
Here is a difficult problem. A commercial electric car runs three hundred kilometers per one round of charging and Raj pays Rs. 40 for every full charge. Find out how many kilometres the car can run with Rs. 800 worth of charging?
First, do not get confused between words. There are three quantities. Kilometres, rounds of charging and price of every full charge.
Converting the above quantities into ratios we get, 300km/charge and Rs. 40/charge.
Dividing 800 rupees by 40 rupees, we come to 800/40 rounds or 20 rounds of charging.
Now we have to calculate 300 kms per one round of charge multiplied by 20 rounds of charging. Numerically, 30 km/1 round of charge * 20 rounds of charge equals 6000 kms. Here rounds cancel out we arrive at our solution.
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Suggestions for Solving Ratio and Proportion Problems:
There are certain things that you must keep in mind while solving ratio and proportion problems, here is a list of a few things that you should consider:
- Try to construct equations wherever possible. Equations break down problems into small simpler bits. This, in turn, makes it easier to solve it.
- Reducing large numbers into smaller ones and canceling out operations help in the quick calculation.
- Word problems tend to have redundant information. Always look for figures that are final, not intermediate.
- Read the word problems at least twice before attempting. Many have interrelated relationships like being directly or inversely related.
Ratio and proportion problems can be perfected only through proper guidance and a well-planned approach towards tackling the quantitative section of the GMAT. With the help of the experts Leverage Edu you can come up with a plan to ace the exams and find your way into the hallways of your dream college.