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In our last post, we observed how competitive the GMAT test has become and looked at the format of the test. In this post, we will understand the problem-solving type questions of the quantitative section and suggest ways you can prepare and succeed with this question type.
The good news about the problem-solving type question of the GMAT is that it does not test advanced mathematical concepts, such as calculus, differentiation, or regression. The bad news is that it does include the basic mathematical concepts (arithmetic, algebra, geometry, percentages, fractions, elementary statistics, combinations, and permutations) and can appear to be quite difficult if you don’t have a quantitative background. Therefore, you need to spend time improving your knowledge of the quantitative concepts by revising your high school math books.
Problem-solving questions are typically straightforward in nature. The questions are presented like a mathematical puzzle and you are asked to select the best option from the five options given. Below you will find few questions and strategies to give you a sense of how to solve this question type.
We know the typical steps in solving a problem – read the question, find out the problem, perform the calculations and arrive at the answer. Almost half of the problem-solving questions are word problems (i.e. the problems are given in prose rather than in mathematical notations - “What does five minus three equal?” rather than “5 – 3 = ?”). In total, you will find about 22 problem-solving questions in the quantitative section. Let us go over few sample questions and discuss strategies to solve such questions:
1.What is the closest approximation of four billion divided by 198,567?
a.20.5
b.200
c.2500
d.20000
e.25000
Critical Success Factor: Avoid unnecessary calculation. Use approximation techniques.
Speed is critical for attaining a top 10% GMAT match score. Learn to approximate and avoid long, complicated calculations. Most importantly, learn to avoid solving math the “traditional” way.
In the question above, should we really divide any number by 198,567? No! Let’s approximate both the numbers and quickly restate the questions:
4,000,000,000/200,000 = ?
Cancel out the zeros and we get: 40,000/2 = 20,000
Easy calculation in mere few seconds.
Let’s look at another question:
2.A jet airplane approaching the town of New York, which lies at a straight line distance of six miles from New Jersey, reads on its radar a distance of six and one-half miles between the airplane and New Jersey’s airport at the instant the airplane passes directly above New York. At that moment, what is the airplane’s height, in miles?
a.1.5
b.2.5
c.3.5
d.5.0
e.6.5
Critical Success Factor: Simplify confusing problems. Use diagrams, sketches or equations.
GMAT word problems are often presented in a confusing manner. It challenges you to “simplify” the problem by using diagrams, sketches or equations – anything that helps you to answer the question quickly and clearly. If you can simplify the problem successfully, you will be few seconds away from the solution. Avoid complicated calculations that we showed you above, use your scratch paper to set up problems in this way. Here is how the question looks like after translated as a sketch:
Now, if you go back to your high school days and recall Pythagoras theorem (a2 + b2 = c2), you will find above math problem quite straightforward. You can also think of a shortcut and find the correct answer without performing the necessary calculations. We know few right-angled triangles with sides forming ratios of whole numbers such as 3,4,5 and the 5, 12, 13. You can find the ratio that is consistent with one of these two and you can find the correct answer.
One last sample question and it is a “difficult” one:
3.For any non-prime integer q, the “proverbial” of q is the product of the largest and smallest prime numbers that divide evenly into q plus the difference of the largest and smallest prime numbers that divide evenly into q. Which of the following, if increased by five, has the greatest proverbial?
a.9
b.15
c.19
d.21
e.49
Critical Success Factor: “Difficult” GMAT math problems often test your reading skills and your calmness. You can make it easier by focusing on the answer choices.
Have you ever heard of a “proverbial”? I have not! The GMAT test makers sometimes create “new” math concepts just to see how well you adapt to the unknown. When you see one of these problems, read the question very carefully and take the question apart step-by-step. You can often make it easier by focusing on the answer choices. Here is how to solve such problem:
Start with the question itself:
Which of the following, if increased by five, has the greatest proverbial?
Clearly, we have to add five to each answer choice before we move any further. This gives you:
9 + 5 = 14
15 + 5 = 20
19 + 5 = 24
21 + 5 = 26
49 + 5 = 54
Now, let us see about this “proverbial” concept:
For any non-prime integer q, the “proverbial” of q is the product of the largest and smallest prime numbers that divide evenly into q plus the difference of the largest and smallest prime numbers that divide evenly into q.
So, to find the proverbial of an answer choice, we will need its “largest and smallest prime numbers that divide evenly into (it)” – in simpler terms, we need the largest and smallest prime factors. So, let us see what we get:
14 –> 2 & 7
20 -> 2 & 5
24 –> 2 & 3
26 –> 2 & 13
54 –> 2 & 3
Without going a step further, which answer choice do you think will give us the largest proverbial? You don’t need to be a mathematician to focus on 26 as the likely answer. The full solution is below:
LPF = Largest Prime Factor
SPF = Smallest Prime Factor
Equation: Proverbial = (LPF x SPF) + (LPF – SPF)
14 –> 2 & 7 –> Proverbial = (7 x 2) + (7 – 2) = 19
20 –> 2 & 5 –> Proverbial = (5 x 2) + (5 – 2) = 13
24 –> 2 & 3 –> Proverbial = (3 x 2) + (3 – 2) = 7
26 –> 2 & 13 –> Proverbial = (13 x 2) + (13 – 2) = 37
54 –> 2 & 3 –> Proverbial = (3 x 2) + (3 – 2) = 7
The other quantitative question type is the Data Sufficiency. In our next post, we will share with you strategies to solve such problems.
This post first appeared in our blog here
Also Read:
Strategies and Advice on Preparing for the GMAT – Part 1
Strategies and Advice on GMAT Preparation – Part 3 : Data Sufficiency
Strategies and Advice on GMAT Preparation – Part 4: Sentence Correction
The good news about the problem-solving type question of the GMAT is that it does not test advanced mathematical concepts, such as calculus, differentiation, or regression. The bad news is that it does include the basic mathematical concepts (arithmetic, algebra, geometry, percentages, fractions, elementary statistics, combinations, and permutations) and can appear to be quite difficult if you don’t have a quantitative background. Therefore, you need to spend time improving your knowledge of the quantitative concepts by revising your high school math books.
Problem-solving questions are typically straightforward in nature. The questions are presented like a mathematical puzzle and you are asked to select the best option from the five options given. Below you will find few questions and strategies to give you a sense of how to solve this question type.
We know the typical steps in solving a problem – read the question, find out the problem, perform the calculations and arrive at the answer. Almost half of the problem-solving questions are word problems (i.e. the problems are given in prose rather than in mathematical notations - “What does five minus three equal?” rather than “5 – 3 = ?”). In total, you will find about 22 problem-solving questions in the quantitative section. Let us go over few sample questions and discuss strategies to solve such questions:
1.What is the closest approximation of four billion divided by 198,567?
a.20.5
b.200
c.2500
d.20000
e.25000
Critical Success Factor: Avoid unnecessary calculation. Use approximation techniques.
Speed is critical for attaining a top 10% GMAT match score. Learn to approximate and avoid long, complicated calculations. Most importantly, learn to avoid solving math the “traditional” way.
In the question above, should we really divide any number by 198,567? No! Let’s approximate both the numbers and quickly restate the questions:
4,000,000,000/200,000 = ?
Cancel out the zeros and we get: 40,000/2 = 20,000
Easy calculation in mere few seconds.
Let’s look at another question:
2.A jet airplane approaching the town of New York, which lies at a straight line distance of six miles from New Jersey, reads on its radar a distance of six and one-half miles between the airplane and New Jersey’s airport at the instant the airplane passes directly above New York. At that moment, what is the airplane’s height, in miles?
a.1.5
b.2.5
c.3.5
d.5.0
e.6.5
Critical Success Factor: Simplify confusing problems. Use diagrams, sketches or equations.
GMAT word problems are often presented in a confusing manner. It challenges you to “simplify” the problem by using diagrams, sketches or equations – anything that helps you to answer the question quickly and clearly. If you can simplify the problem successfully, you will be few seconds away from the solution. Avoid complicated calculations that we showed you above, use your scratch paper to set up problems in this way. Here is how the question looks like after translated as a sketch:
Now, if you go back to your high school days and recall Pythagoras theorem (a2 + b2 = c2), you will find above math problem quite straightforward. You can also think of a shortcut and find the correct answer without performing the necessary calculations. We know few right-angled triangles with sides forming ratios of whole numbers such as 3,4,5 and the 5, 12, 13. You can find the ratio that is consistent with one of these two and you can find the correct answer.
One last sample question and it is a “difficult” one:
3.For any non-prime integer q, the “proverbial” of q is the product of the largest and smallest prime numbers that divide evenly into q plus the difference of the largest and smallest prime numbers that divide evenly into q. Which of the following, if increased by five, has the greatest proverbial?
a.9
b.15
c.19
d.21
e.49
Critical Success Factor: “Difficult” GMAT math problems often test your reading skills and your calmness. You can make it easier by focusing on the answer choices.
Have you ever heard of a “proverbial”? I have not! The GMAT test makers sometimes create “new” math concepts just to see how well you adapt to the unknown. When you see one of these problems, read the question very carefully and take the question apart step-by-step. You can often make it easier by focusing on the answer choices. Here is how to solve such problem:
Start with the question itself:
Which of the following, if increased by five, has the greatest proverbial?
Clearly, we have to add five to each answer choice before we move any further. This gives you:
9 + 5 = 14
15 + 5 = 20
19 + 5 = 24
21 + 5 = 26
49 + 5 = 54
Now, let us see about this “proverbial” concept:
For any non-prime integer q, the “proverbial” of q is the product of the largest and smallest prime numbers that divide evenly into q plus the difference of the largest and smallest prime numbers that divide evenly into q.
So, to find the proverbial of an answer choice, we will need its “largest and smallest prime numbers that divide evenly into (it)” – in simpler terms, we need the largest and smallest prime factors. So, let us see what we get:
14 –> 2 & 7
20 -> 2 & 5
24 –> 2 & 3
26 –> 2 & 13
54 –> 2 & 3
Without going a step further, which answer choice do you think will give us the largest proverbial? You don’t need to be a mathematician to focus on 26 as the likely answer. The full solution is below:
LPF = Largest Prime Factor
SPF = Smallest Prime Factor
Equation: Proverbial = (LPF x SPF) + (LPF – SPF)
14 –> 2 & 7 –> Proverbial = (7 x 2) + (7 – 2) = 19
20 –> 2 & 5 –> Proverbial = (5 x 2) + (5 – 2) = 13
24 –> 2 & 3 –> Proverbial = (3 x 2) + (3 – 2) = 7
26 –> 2 & 13 –> Proverbial = (13 x 2) + (13 – 2) = 37
54 –> 2 & 3 –> Proverbial = (3 x 2) + (3 – 2) = 7
The other quantitative question type is the Data Sufficiency. In our next post, we will share with you strategies to solve such problems.
This post first appeared in our blog here
Also Read:
Strategies and Advice on Preparing for the GMAT – Part 1
Strategies and Advice on GMAT Preparation – Part 3 : Data Sufficiency
Strategies and Advice on GMAT Preparation – Part 4: Sentence Correction
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