Solve DAT Questions Without a Calculator

It’s no secret that mastery of the sciences is essential for success on the DAT, yet all the hard work you devoted to studying can prove futile without honing your math skills. With the exception of the quantitative reasoning section which has a calculator, you only have your brain, laminated paper, and a felt tip marker for the rest of the exam! This can be intimidating, so we’ve outlined some tips and tricks on how to prepare for and solve DAT questions without a calculator.

I. Quick Tips

Know your basics

It would be pointless to attempt memorizing the entire times table, yet there are a few values you should be comfortable with such as basic logarithms and converting between significant figures. Check out our algebra cheat sheet for some of the basics you should memorize before test day.'

Start practicing early

If math is your weak point, the last thing you want is to wait until the day of your exam to start solving problems without a calculator. Treat every practice problem (outside of the QR section) like the real thing by solving calculation problems by hand instead of sneaking a calculator.

II. Approaching Arithmetic

Simplify expressions where possible

To reduce the risk of making an error when working with large expressions, simplify values and expressions as much as possible. To simplify fractions, divide the numerator and denominator by a common multiple so that each is reduced to a smaller value. This process can also be used on equations with expressions that use variables instead of numbers. Check out our example below to see simplification in action on a DAT-style chemistry question.

Use friendly numbers

Rounding to friendly numbers, such as from 1.98 to 2, or from 1097 to 1100 will make calculations much easier! When rounding to get friendly numbers, it is important to keep note of which direction you rounded, as your actual value will be slightly greater or lower than the value you calculated by rounding. For multiplication, rounding up will result in a value higher than the actual answer, while with division, rounding up will result in a value lower than the actual answer, and vice versa for rounding down. The example below gives an example of using rounding to get a friendly number for calculation.

Work with and eliminate answer choices

Looking at and eliminating answer choices can help guide your calculation and increase your chances of getting the question correct. For example, if you see that the trend in your calculation does not match some of the answer choices, you can eliminate those options. There may also be instances where the question simply requires you to plug in the given values and set up an equation without doing any calculations. In this instance, looking at the answer choices can save you time and help you determine how to approach the question. The example below shows how the elimination of answer choices can be useful in solving a calculation question.

III. Example Walkthrough Question

This may seem a bit complicated, so let’s put these tricks to the test with an example question. Try out the question on your own with all the tips and tricks mentioned above and then check out the solution to see if you got it right! For more practice questions like this one check out DATBooster! 

This may seem a bit complicated, so let’s put these tricks to the test with an example question: 

What is the final concentration of a 500ml solution of 2.5M acetate that is diluted to a final volume of 748mL?

1. a. 0.7M
    
2. b. 1.7M
    
3. c. 2.7M
    
4. d. 3.7M

Step 1. Use Friendly Numbers

After we recognize that this is a dilution problem, we plug our given values into the dilution equation. However, 748 is a complicated number that can make our calculation more difficult, and this can be rounded up to the friendly number of 750. Because we rounded up, we must remember that our actual answer choice will be larger than the value we get by rounding, but since we only increased our value by 2, the actual answer will not be much different than the one we calculate.

$M_1{V}_1=M_2{V}_2$

$500L\times 2.5M=748L\times X$

$500L\times 2.5M=750L\times X$

$\frac{500L\times 2.5M}{750L}=X$

Step 2. Eliminate Answer Choices 

Before we even begin our calculations, we can recognize that our final concentration must be smaller than the initial concentration. This is because there is an inverse relationship between molarity and volume, so since the volume increased, our concentration must decrease. As a result, we can eliminate choices C and D. Without doing a single calculation, we have already increased our chances of getting the question correct from 25% to 50%.‎

1. a. 0.7M
    
2. b. 1.7M
    
3. c. 2.7M
    
4. d. 3.7M

Step 3. Simplify 

There are two ways to use simplification in this example.

$\frac{500L\times 2.5M}{750L}=X$

Option 1.

We calculate the numerator to get 1250 moles. We can then recognize that 1250 and 750 are each divisible by 250. Therefore, we can simplify to get 5/3. This will give us a final value of 1.66666M, which rounds to answer choice B, 1.7M.

$\frac{500L\times 2.5M}{750L}=\frac{1250mol}{750L}=\frac{5}{3}=X$

$\frac{5moles}{3ml}=1\frac{2}{3}M=1.66M=\mathbf{1}\mathbf{.}\mathbf{7}\mathit{M}=X$

Option 2.

We begin by splitting the equation into 2 values: 500L/750L and 2.5M. We have not changed the equation but have only split it into two more manageable terms. Looking at this equation, we can see that 500 and 750 are both divisible by 25. Therefore, we will simplify these values to give 2ml and 3ml respectively. We can then recombine our equation and solve it to once again get 5/3, which rounds to answer choice B, 1.7M.

$\frac{500L}{750L}\times 2.5M=\frac{2L}{3L}\times 2.5M=X$

$\frac{2L\times 2.5M}{3L}=\frac{5moles}{3L}=1\frac{2}{3}M=X$

$1\frac{2}{3}M=1.6666M=1.7M=X$

IV. Final Advice

Solving math problems without a calculator may seem daunting, but there is no reason to panic. Most of the values given to you on the DAT will be easy and straightforward. However, in the case that you face a difficult or time-consuming calculation, it is in your best interest to guess an answer, mark the question, and move on. You can always return to more difficult questions later on. Nevertheless, following the techniques listed above can help you quickly and accurately answer math questions without a calculator.

If you are interested in learning more about other DAT topics, be sure to check out our other articles. These articles contain more tips and tricks on the DATBooster website as well as an in depth tutorial one using Anki!

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• Prepare for the DAT using Anki
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