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Many GMAT test-takers, particularly those who don’t consider math their strongest subject, start to panic when they learn that they won’t have access to a calculator for the Quant section of the exam.
The truth is that no student, regardless of his or her math proficiency, needs a calculator to do GMAT Quant. In fact, GMAT Quant questions are specifically designed to be answered without the use of a calculator. This is because GMAT Quant tests your use of logic and your conceptual knowledge, not your ability to perform complex mathematical calculations.
Remember, the GMAT assesses your skills in areas that will be important in business school. Being able to input numbers into a calculator won’t tell admissions committees much about your readiness for an MBA program. Thus, if you want to earn a high GMAT Quant score, you should think of it not as a math test, but as a logic test.
TTP PRO TIP:
No student, regardless of his or her math proficiency, needs a calculator to do GMAT Quant.
Of course, earning a competitive Quant score takes more than just a change in mindset. In this article, we’ll go over 10 key strategies that every test-taker needs, in order to conquer GMAT Quant without the use of a calculator.
Here are the topics we’ll cover:
- Strategy 1: Learn the Types of Concepts Tested in GMAT Quant
- Strategy 2: Drill with Realistic GMAT Quant Practice Questions
- Strategy 3: Regularly Practice Arithmetic and Basic Math Functions
- Strategy 4: Use Estimation When Possible
- Strategy 5: Always Seek to Simplify Terms
- Strategy 6: Develop Your Number Sense
- Strategy 7: Look Out for Units Digits
- Strategy 9: Stop Yourself When Calculations Get Overly Complex
- Strategy 10: Never Use a Calculator During Your GMAT Prep
- Key Takeaways
- What’s Next?
Let’s begin by focusing on the conceptual nature of GMAT Quant.
Strategy 1: Learn the Types of Concepts Tested in GMAT Quant
When you begin familiarizing yourself with the content tested in GMAT Quant, you’ll quickly see that the content is quite conceptual in nature. In other words, the questions you face are not calculation-heavy.
Let’s look at a few examples of tasks you could be asked to complete in the Quant section of the GMAT. For each set of tasks, note that the task you may be asked to perform does not require a calculator, while the task you would never be asked to perform would require a calculator.
You may be asked to … Determine whether the standard deviation of a set is zero.
You’ll never be asked to … Calculate the standard deviation of a set of numbers.
You may be asked to … Determine the remainder when 299 is divided by 3.
You’ll never be asked to … Divide 299 by 3.
You may be asked to … Determine the sum of the first 100 positive even integers.
You’ll never be asked to … Calculate the product of the first 100 positive even integers.
Now, if you can’t yet recognize why the first task in each set doesn’t require a calculator to complete, don’t worry. As you learn how to recognize which concept is being tested in a given question and how to apply that concept to efficiently answer the question, you’ll see that you don’t need a calculator after all. Notably, the key is to find a rigorous, comprehensive, trusted GMAT prep course, so that you can master the material tested.
TTP PRO TIP:
As you learn to recognize and apply the concepts being tested in GMAT Quant questions, you’ll see that you don’t need a calculator after all.
Strategy 2: Drill with Realistic GMAT Quant Practice Questions
While the first step in mastering GMAT Quant is to learn the content tested, the next step is to practice, applying the principles and concepts you’ve learned. By engaging in answering practice questions, you’ll refine your skills at recognizing which concept is being tested by a particular question. It will become second nature to use efficient methods to solve GMAT Quant questions.
Consider the following question, for example:
What is the units digit of 749?
Upon seeing this question, was your first reaction that the only way to solve this problem is by using a calculator? If so, you’re not alone. The good news is that there is an elegant solution for questions involving units digit patterns, and that solution does not require a flurry of intricate calculations on a calculator. Check out the background surrounding the procedure and the solution to the above question here:
https://gmat.targettestprep.com/lesson/429
Once you understand the methods used to obtain the units digit of 749, this problem becomes relatively easy. (By the way, the answer is 7.) However, developing the skills to attack problems such as this one certainly does not happen overnight. Hence, you have to practice many problems of each question type tested on the GMAT to ensure you’ve gained mastery. That is why the TTP course contains more than 30 problems just on units digit patterns. As a result, after you answer these questions, the skills you need to attack such questions will be second nature.
We’ll discuss units digit patterns more a little later, but keep in mind that a “practice makes perfect” mentality applies to every other Quant concept as well.
TTP PRO TIP:
After learning a Quant concept, be sure to practice many questions on just that concept, until answering such questions becomes second nature.
Strategy 3: Regularly Practice Arithmetic and Basic Math Functions
Although GMAT Quant doesn’t require complex calculations, you will need to perform some basic math to answer certain questions. Force yourself to master basic operations, such as multiplication, division, addition, and subtraction, using pen and paper. Obviously, the more you practice, the more comfortable you’ll become at, say, multiplying 37 by 41 or dividing 996 by 6 without using a calculator. However, we have gotten used to letting a calculator do the work when it comes to even the simplest calculations. In reality, calculations such as these don’t require much time or effort if you get used to performing them.
If the sight of 67 x 101 or similar calculations gives you heart palpitations, you need to regularly practice doing mild multiplication and division problems by hand, so that, when you encounter similar math on test day, you have no issues efficiently multiplying or dividing numbers without a calculator.
A good way to practice basic calculations, in addition to doing GMAT Quant problems, is to stop using your calculator (whenever you can) in everyday life. For example, if you need to figure out the sale price of a $200 item that is marked down by 15%, rather than using your calculator, write out the calculation and perform the arithmetic. If you need to split a $250 dinner check 6 ways, again, write out the division and do the calculation. The more you practice basic operations, the more prepared you’ll be to use them on GMAT test day.
TTP PRO TIP:
In addition to doing GMAT Quant problems, a good way to practice basic calculations, such as multiplication and division, is to stop using your calculator in everyday life.
Strategy 4: Use Estimation When Possible
If you ever run into a situation in which you are about to do complicated math calculations to arrive at an answer to a GMAT Quant question, you likely can answer the question using estimation. In fact, you may run into problems that force you to do complex math calculations if estimation is not used. This point is highlighted by the following compound interest problem:
Example
At the end of his one-year investment, Charles received $54,080, including interest and principal from a certain investment. If the investment paid an annual interest of 8 percent compounded semi-annually, which of the following is the amount of money that Charles originally invested?
- $45,000
- $50,000
- $54,000
- $59,000
- $62,000
Let’s first look at the “exact” solution to the problem. It requires that we use the compound interest formula, which has both fractions and exponents. And then, we must perform an unwieldy division problem to arrive at the final answer.
Solution:
We can plug the given values into the compound interest formula. Since the investment is compounded semi-annually, then we will have n = 2
#$\begin{array}{*{20}{l}}
{ \Rightarrow A = P{{\left( {1 + \frac{r}{n}} \right)}^{nt}}}\\
{ \Rightarrow 54,080 = P{{\left( {1 + \frac{{0.08}}{2}} \right)}^{2 \times 1}}}\\
{ \Rightarrow 54,080 = P{{\left( {1 + 0.04} \right)}^2}}\\
{ \Rightarrow 54,080 = P{{\left( {1.04} \right)}^2}}\\
{ \Rightarrow 54,080 = P \times 1.0816}\\
{ \Rightarrow P = \frac{{54,080}}{{1.0816}}}\\
{ \Rightarrow P = \$ 50,000}
\end{array}#$
Charles originally invested $50,000.
Note: By looking at each answer choice, it would have been possible to determine that #$\frac{54,080}{1.0816}#$ is closest to 50,000.
Answer: B
Here is an alternate solution using estimation.
Notice that the answer choices are widely spaced. This is a hint that estimation will be successful.
First, notice that Charles’ investment grew to $54,080 by the end of one year. Thus, he could not have started the year with $54,000, $59,000, or $62,000. This leaves only $45,000 or $50,000 as the two possible correct answer choices.
Even though his interest was calculated twice during the year, we can estimate how much he earned by taking 8% of $50,000, which is $4,000, yielding a year-end (estimated) balance of $54,000. Alternately, taking 8% of $45,000, which is $3,600, yields a year-end (estimated) balance of $48,600, which is not even close to $54,080.
So it is obvious that he must have started the year with $50,000. Note that you could have arrived at this solution by using estimation, with almost no calculation required.
TTP PRO TIP:
Before you do complicated math calculations to arrive at an answer to a GMAT Quant question, consider that you likely can use some estimation.
Strategy 5: Always Seek to Simplify Terms.
There will be many times on the GMAT when you are presented with seemingly complicated expressions involving time-consuming multiplication followed by division of large, unwieldy numbers. These expressions usually can be simplified to much cleaner expressions. Consider the following example:
Example
#$\frac{{3 \times 7}}{{9 \times 13}} \times \frac{{17 \times 31 \times 47}}{{7 \times 5}} \times \frac{{13 \times 9 \times 5}}{{3 \times 17 \times 31}}#$ =
- 13
- 17
- 29
- 33
- 47
On the surface, this problem appears to be quite lengthy. In fact, if you multiplied across the numerators and denominators, you’d have (304,287,165)/(6,474,195), which would be difficult to divide within two minutes without using a calculator. Fortunately, there is a very elegant way to simplify the expression by vertically and diagonally canceling terms, thereby avoiding time-consuming multiplication and division.
Solution:
The temptation could be to just start multiplying all of the numerators and all of the denominators and then divide the final fraction. This would be prone to error, and it would be time consuming. Instead, notice that each number in the numerators also exists in the denominators, with the exception of 47.
#$\begin{array}{*{20}{l}}
{ \Rightarrow \frac{{\bcancel{3} \times \bcancel{7}}}{{\bcancel{9} \times \bcancel{{13}}}} \times \frac{{\bcancel{{17}} \times \bcancel{{31}} \times 47}}{{\bcancel{7} \times \bcancel{5}}} \times \frac{{\bcancel{{13}} \times \bcancel{9} \times \bcancel{5}}}{{\bcancel{3} \times \bcancel{{17}} \times \bcancel{{31}}}} = 47}\\
{}
\end{array}#$
Each number, with the exception of 47, cancels itself from the fractions. Thus, 47 is the result. Notice that we employed cross cancel, and no multiplication was necessary after cross cancel. Can you imagine how time consuming this would have been had we first multiplied all of the numerators and all of the denominators? Remember that whenever possible, we should simplify.
Answer: E
While this problem directly tests the idea of simplifying terms, look to simplify across all types of GMAT Quant questions. Any time you are presented with complicated-looking equations or expressions, your first move should always be to simplify down to smaller, cleaner terms.
TTP PRO TIP:
Any time you are presented with complicated-looking equations or expressions, your first move should always be to simplify down to smaller, cleaner terms.
Strategy 6: Develop Your Number Sense
Number sense is a very important skill to develop for answering GMAT Quant questions. In fact, the GMAT may present an array of complex-looking questions that appear to necessitate the use of a calculator but actually can be solved by using number sense. Let’s discuss a couple of ways to use number sense.
Number Sense in Evaluating Fractions
Although we have been taught that we can compare fractions most easily by finding a common denominator, you may be presented with GMAT questions that contain fractions that are just too complicated for you to easily find a common denominator. That’s when number sense comes into play. Consider the following example:
Example
Which of the following fractions is greatest?
- #$\frac{6}{{14}}#$
- #$\frac{8}{{18}}#$
- #$\frac{34}{{70}}#$
- #$\frac{200}{{401}}#$
- #$\frac{302}{{602}}#$
Solution:
The fractions in answer choices A through D are all a bit less than #$\frac{1}{{2}}#$. The fraction in answer choice E is just a bit more than #$\frac{1}{{2}}#$. Thus, #$\frac{302}{{602}}#$ is the largest fraction of the five.
Answer: E
It’s clear from evaluating the answer choices that we won’t be able to get a common denominator for these fractions; however, we can recognize that since 7/14, 9/18, 35/70, 200.5/401, and 301/602 are all equal to 1/2, answers A, B, C, and D are all less than 1/2, and answer choice E is greater than 1/2. It’s important to note that we did not have to do any messy calculations to come up with an answer. Rather, we used our number sense and knowledge of fractions to determine which fraction was the greatest.
Number Sense in Evaluating Ugly Numbers with Exponents and Roots
Another way the GMAT tests number sense is by presenting ugly or large numbers, and then asking about those numbers when they are either raised to exponents or placed inside roots. The good news is that there are some basic rules you can follow to answer specific questions about such numbers without doing any complicated math. These rules can be reviewed on page 1 and 5 of our free equation guide. Let’s look at an example question:
Example
If n = –0.1238, which of the following must be true?
- #${{\rm{n}}^2} > {\rm{n}}#$
- #${{\rm{n}}^4} > {{\rm{n}}^{13}}#$
- #${{\rm{n}}^7} > {{\rm{n}}^5}#$
- I only
- I and II
- I and III
- II and III
- I, II and III
Solution:
Recognize that this is an unfriendly number. What is really being tested in this situation is how negative proper fractions are affected when raised to certain exponents. To make this easier, let’s choose an easier fraction to work with such as #$\ – \frac{1}{2}#$.
I. #${{\rm{n}}^2} > {\rm{n}}#$
Any negative value raised to an even exponent will always become positive whereas any negative value raised to an odd exponent will always remain negative. Thus, the square, being positive, must be greater than the negative fraction. This is true.
II. #${{\rm{n}}^4} > {{\rm{n}}^{13}}#$
Any negative value raised to an even exponent will always become positive whereas any negative value raised to an odd exponent will always remain negative. This is true.
III. #${{\rm{n}}^7} > {{\rm{n}}^5}#$
Since n is negative, both n7 and n5 will be negative. Because n7 and n5 have the same sign, let’s test n = #$\ – \frac{1}{2}#$:
#$\begin{array}{*{20}{l}}
{ \Rightarrow {{\left( { – \frac{1}{2}} \right)}^7} > {{\left( { – \frac{1}{2}} \right)}^5}}\\
{ \Rightarrow – \frac{1}{{128}} > – \frac{1}{{32}}}
\end{array}#$
This is also true.
Answer: E
While, in the solution, we replaced the provided decimal with the much cleaner number of -1/2, we could have found the answer even more easily by using number sense and following a few rules.
1) A negative proper fraction when raised to an even power will be greater than the original fraction. This is why I and II are correct.
2) A negative proper fraction when raised to an odd power will increase in value. This is why n7 is greater than n5 and why III is also true.
As you can see, developing your number sense is invaluable for efficiently attacking complicated-looking GMAT Quant problems and will allow you to solve those problems while doing very little math.
TTP PRO TIP:
Developing your number sense will help you deal with unwieldy fractions and numbers with exponents or roots so that you can solve complicated-looking GMAT Quant problems using very little math.
Strategy 7: Look Out for Units Digits
As we mentioned earlier, the GMAT may test you specifically on units digits patterns, in questions such as What is the units digit of 5720? In addition to knowing how to answer those questions, we should strategically use units digits to avoid doing large, unnecessary calculations. In fact, whenever you see large answer choices, it’s always a good idea to check whether each answer choice has a different units digit. If so, you likely can arrive at the correct answer by simply determining the units digit of the answer rather than actually completing the multiplication. Consider the following example:
Example
#$\frac{{{3^{30}} – {2^{30}}}}{{{3^{15}} – {2^{15}}}} #$ is equal to which of the following?
- 14,381,675
- 14,441,623
- 14,485,772
- 14,609,707
- 14,722,819
Solution:
#$\begin{array}{*{20}{l}}
{ \Rightarrow \frac{{{3^{30}} – {2^{30}}}}{{{3^{15}} – {2^{15}}}}}\\
{ \Rightarrow \frac{{{{\left( {{3^{15}}} \right)}^2} – {{\left( {{2^{15}}} \right)}^2}}}{{{3^{15}} – {2^{15}}}}}\\
{ \Rightarrow \frac{{\left( {{3^{15}} + {2^{15}}} \right)\left( {{3^{15}} – {2^{15}}} \right)}}{{{3^{15}} – {2^{15}}}}}\\
{ \Rightarrow {3^{15}} + {2^{15}}}
\end{array}#$
Units digits of powers of 3 follow a 3–9–7–1 pattern. Thus, 315 has a units digit of 7. Units digits of powers of 2 follow a 2–4–8–6 pattern. Thus 215 has a units digit of 8. Since 7 + 8 = 15, 315 + 215 has a units digit of 5. Because only 14,381,675 has a units digit of 5, answer choice A is the correct answer.
Answer: A
After simplifying the original expression, we are left with 315 + 215. Actually calculating the sum of 215 and 315 by hand would be very time-consuming and error-prone. In fact, the only way to do that calculation in around two minutes is with a calculator. However, looking at the answer choices, we see that each answer choice has a different units digit, and thus we can use our knowledge of units digit patterns to avoid doing complex math. So, although this problem did not ask about units digits directly, we strategically used our knowledge of units digit patterns to arrive at the correct answer and within a reasonable amount of time.
TTP PRO TIP:
Be familiar with situations in which the use of patterns in units digits can make quick work of a GMAT Quant question.
Strategy 8: Become an Expert at Prime Factorization
Prime factorization is a key skill because it allows you to break larger numbers down into more digestible pieces. There will be times on the GMAT when you are faced with what looks like complex division, but by breaking the divisor into primes, you can avoid doing complex division. Although some problems will directly test you on prime factorization, you also can use prime factorization for problems involving other topics. Consider the following example:
Example
#${3^{10}} – {2^{10}}#$ is a multiple of all of the following numbers except:
- 5
- 25
- 55
- 75
- 211
Solution:
#$\begin{array}{*{20}{l}}
{ \Rightarrow {3^{10}} – {2^{10}}}\\
{ \Rightarrow {{\left( {{3^5}} \right)}^2} – {{\left( {{2^5}} \right)}^2}}\\
{ \Rightarrow \left( {{3^5} – {2^5}} \right)\left( {{3^5} + {2^5}} \right)}\\
{ \Rightarrow \left( {243 – 32} \right)\left( {243 + 32} \right)}\\
{ \Rightarrow \left( {211} \right)\left( {275} \right)}\\
{ \Rightarrow 211 \times 5 \times 5 \times 11}
\end{array}#$
Since 75 = 3 × 5 × 5 and 310 – 210 = 211 × 5 × 5 × 11 doesn’t have a factor of 3, 310 – 210 is not a multiple of 75.
Answer: D
It’s important to note that, although this problem does not ask us to use prime factorization, we strategically prime factorized (211)(275) and 75 in order to see that because (211)(275) does not contain a prime factor of 3, but 75 does, (211)(275) cannot be a multiple of 75.
TTP PRO TIP:
Strategically using units digits or prime factorization in questions that don’t directly ask about those concepts can help you avoid performing lengthy multiplication or division.
Strategy 9: Stop Yourself When Calculations Get Overly Complex
As we’ve already discussed, the GMAT is not going to ask you to perform long, tedious calculations by hand. Thus, if you find yourself carrying out extremely difficult and convoluted math calculations in the Quant section, you’ve probably gone down the wrong path. Here is a great example:
Example
14! is equal to which of the following?
- 87,178,291,200
- 88,180,293,207
- 89,181,294,209
- 90,000,000,003
- 91,114,114,114
Notice that, if you actually did out the math, it would look like this:
14 x 13 x 12 x 11 … x 3 x 2 x 1
Since such lengthy calculations very likely can’t be done in just two minutes, you can quickly determine that you’ve done something wrong. At that point, stop and ask yourself, How else can I solve this problem?
The solution is to utilize the rule that says that any factorial of 5! or greater always ends in 0. Thus, without using any calculation at all, you would immediately choose choice A as the answer, as it is the only choice that ends in 0.
You want to avoid going down a rabbit hole and losing precious time on the GMAT by doing unnecessarily large calculations. Thus, if you find yourself doing overly complex, lengthy calculations, stop and consider an alternative route.
TTP PRO TIP:
If you find yourself performing a tedious calculation that likely couldn’t be done by anyone within two minutes, stop and ask yourself how else you might be able to solve the given problem.
Strategy 10: Never Use a Calculator During Your GMAT Prep
If you’re going to give your best performance on test day, then you have to practice as you would play. In other words, using a calculator during GMAT Quant prep isn’t going to do much to help you prepare for a test that doesn’t allow the use of a calculator. You have to learn to answer GMAT Quant questions without falling back on a calculator when the going gets tough. Even if you’re just starting your GMAT prep and aren’t very familiar with some of the concepts tested in GMAT Quant, you must resist the urge to let a calculator do the work for you.
TTP PRO TIP:
To give your best performance on test day, you must practice in the same way you will play — without a calculator.
Similarly, if during your GMAT prep, you find yourself constantly wanting to reach for your calculator to wade through drawn-out, mind-bending calculations, then it’s time to brush up on your knowledge of key math rules and concepts. Our free, downloadable GMAT equation guide is a great place to start.
TTP PRO TIP:
If you’re constantly reaching for a calculator during your prep, brush up on your knowledge of key math rules.
Key Takeaways
In summary, the reason you can’t use a calculator on GMAT Quant is that the Quant section primarily tests your ability to use logic, not your ability to perform complex calculations.
The better you know the content and concepts tested in GMAT Quant and the more you practice applying that knowledge to answer questions, the easier it will be to see exactly what is going on in a particular Quant question and why a calculator isn’t actually necessary to find a solution. More to the point, if you need a calculator to solve a GMAT question, you probably don’t yet know how to handle that type of question. So, rather than conclude that a particular practice question is flawed or pull out a calculator to answer the question, spend as much time as you need thinking about all of the possible strategies that you could use to answer that question.
Ask yourself the following:
- Can I use estimation?
- Can I avoid doing math by focusing on the units digit?
- Can I use the difference of squares?
- Can I simplify before calculating?
- Can I use prime factorization?
- Can I solve by using my number sense?
Although you may not always be able to determine the right strategy by deeply analyzing each question you practice with, in time, you won’t default to a calculator when solving GMAT practice questions.
What’s Next?
In this article, we’ve discovered some noteworthy ways to survive the GMAT Quant section without a calculator. There is good news for surviving the Data Insights section of the GMAT: you are allowed to use a calculator, albeit a basic one. Read our article about the Data Insights calculator and how to use it to maximize your success on this tough section of the GMAT.
