Using the Calculator

Sometimes the computations you need to do in order to answer a question in the Quantitative Reasoning measure are somewhat time-consuming, like long division, or involve square roots. For such computations, you can use the calculator provided with your test.

Although the calculator can shorten the time it takes to perform computations, keep in mind that the calculator provides results that supplement, but do not replace, your knowledge of mathematics. You must use your mathematical knowledge to determine whether the calculator's results are reasonable and how the results can be used to answer a question.

Here are some general guidelines for calculator use in the Quantitative Reasoning measure:

  • Most of the questions don't require difficult computations, so don't use the calculator just because it's available.
  • Use it for calculations that you know are tedious, such as long division; square roots; and addition, subtraction or multiplication of numbers that have several digits.
  • Avoid using it for simple computations that are quicker to do mentally, such as 10 minus 490 4 times 70 4,300 over 10 the positive square root of 25 and 30 squared
  • Avoid using it to introduce decimals if you are asked to give an answer as a fraction.
  • Some questions can be answered more quickly by reasoning and estimating than by using the calculator.
  • If you use the calculator, estimate the answer beforehand so you can determine whether the calculator's answer is "in the ballpark." This may help you avoid key-entry errors.

For a description of the calculator provided for the paper-delivered test, please see page 32 of The Practice Book for the Paper-based GRE® revised General Test, Second Edition.

Guidelines Specific to the On-screen Calculator in the Computer-delivered Test

  • When you use the computer mouse or the keyboard to operate the calculator, take care not to mis-key a number or operation.
  • Note all of the calculator's buttons, including Transfer Display.

    The calculator has buttons to enter and perform basic operations on decimal numbers. It also has parentheses, memory buttons, and a “Transfer Display” button.

  • The Transfer Display button can be used on Numeric Entry questions with a single answer box. This button will transfer the calculator display to the answer box. You should check that the transferred number has the correct form to answer the question. For example, if a question requires you to round your answer or convert your answer to a percent, make sure that you adjust the transferred number accordingly.
  • Take note that the calculator respects order of operations, as explained below.

A mathematical convention called order of operations establishes which operations are performed before others in a mathematical expression that has more than one operation. The order is as follows: parentheses, exponentiation (including square roots), multiplications and divisions (from left to right), additions and subtractions (from left to right). With respect to order of operations, the value of the expression 1 plus 2, times 4 is 9 because the expression is evaluated by first multiplying 2 and 4 and then by adding 1 to the result. This is how the on-screen calculator in the Quantitative Reasoning measure performs the operations. (Note that many basic calculators follow a different convention, whereby they perform multiple operations in the order that they are entered into the calculator. For such calculators, the result of entering 1 plus 2, times 4 is 12. To get this result, the calculator adds 1 and 2, displays a result of 3, then multiplies 3 and 4 and displays a result of 12.)

  • In addition to parentheses, the on-screen calculator has one memory location and three memory buttons that govern it: memory recall M R memory clear M C and memory sum M plus These buttons function as they normally do on most basic calculators.
  • Some computations are not defined for real numbers; for example, division by zero or taking the square root of a negative number. If you enter 6, divided by, 0, equals the word Error will be displayed. Similarly, if you enter 1, plus/minus, positive square root then Error will be displayed. To clear the display, you must press the clear button C
  • The calculator displays up to eight digits. If a computation results in a number greater than 99,999,999, then Error will be displayed. For example, the calculation 10,000,000, times, 10, equals results in Error. The clear button C must be used to clear the display. If a computation results in a positive number less than 0.00000001, or 10-8, then 0 will be displayed.

Below are some examples of computations using the calculator.

  1. Compute 4 plus the fraction 6.73 over 2

    Explanation

    Enter 4, +, 6.73, divided by, 2, equals to get 7.365. Alternatively, enter 6.73, divided by, 2, equals to get 3.365, and then enter +, 4, = to get 7.365.

  2. Compute The negative of the fraction with numerator 8.4 + 9.3, and denominator 70

    Explanation

    Since division takes precedence over addition in the order of operations, you need to override that precedence in order to compute this fraction. Here are two ways to do that. You can use the parentheses for the addition in the numerator, entering Open parenthesis, 8.4, +, 9.3, close parenthesis, divided by, 70, =, plus/minus to get negagitve 0.2528571 Or you can use the equals sign after 9.3, entering 8.4, +, 9.3, divided by, 70, =, plus/minus to get the same result. In the second way, note that pressing the first = is essential, because without it, 8.4, +, 9.3, divided by, 70, =, plus/minus would erroneously compute Negative, open parenthesis, 8.4, + the fraction 9.3 over 70, close parenthesis instead. Incidentally, the exact value of the expression The negative fraction with numerator 8.4, + 9.3 and the denominator 70 is the repeating decimal negative 0.25285714 with a bar over the 6 digits 2 8 5 7 1 4 where the digits 285714 repeat without end, but the calculator rounds the decimal to Negative 0.2528571

  3. Find the length, to the nearest 0.01, of the hypotenuse of a right triangle with legs of length 21 and 54; that is, use the Pythagorean theorem to calculate The positive square root of the quantity, 21 squared plus 54 squared.

    Explanation

    Enter 21, times, 21, +, 54, times, 54, =, positive square root to get 57.939624. Again, pressing the = before the Positive square root is essential because 21, times, 21, +, 54, times, 54, positive square root, equals would erroneously compute 21 squared + 54 times the square root of 54 This is because the square root would take precedence over the multiplication in the order of operations. Note that parentheses could be used, as in open parenthesis, 21, times, 21, close parenthesis, +, open parenthesis, 54, times, 54, close parenthesis, =, positive square root but they are not necessary because the multiplications already take precedence over the addition. Incidentally, the exact answer is a nonterminating, nonrepeating decimal, or an irrational number, but the calculator rounds the decimal to 57.939624. Finally, note that the problem asks for the answer to the nearest 0.01, so the correct answer is 57.94.

  4. Compute Open parenthesis, negative 15, close parenthesis, cubed

    Explanation

    Enter 15, plus/minus, times, 15, plus/minus, times 15, plus/minus, = to get Negative 3,375

  5. Convert 6 miles per hour to feet per second.

    Explanation

    The solution to this problem uses the conversion factors 1 mile equals 5,280 feet and 1 hour equals 3,600 seconds,as follows:

    Open parenthesis, 6 miles over 1 hour, close parenthesis, times, 5,280 feet over 1 mile, times, 1 hour over 3,600 seconds, close parenthesis, = question, feet over second
    Enter 6, times, 5,280, divided by, 3,600, = to get 8.8. Alternatively, enter 6, times, 5,280, = to get the result 31,680, and then enter divided by, 3,600, = to get 8.8 feet per second.
  6. At a fund-raising event, 43 participants donated $60 each, 21 participants donated $80 each and 16 participants donated $100 each. What was the average (arithmetic mean) donation per participant, in dollars?

    Explanation

    The solution to this problem is to compute the weighted mean The fraction with numerator equal to the quantity 43 times 60, +, 21 times 80, +, 16 times 100, and denominator equal to the quantity 43 + 21 + 16 You can use the memory buttons and parentheses for this computation, as follows:

    Enter

    43, times, 60, =, memory sum, 21, times, 80, =, memory sum, 16, times, 100, = memory sum

    to get 73.25, or $73.25 per participant.

    When the Memory sum button is first used, the number in the calculator display is stored in memory and an M appears to the left of the display to show that the memory function is in use. Each subsequent use of the Memory sum button adds the number in the current display to the number stored in memory and replaces the number stored in memory by the sum. When the Memory recall button is pressed in the computation above, the current value in memory, 5,860, is displayed. To clear the memory, use the Memory clear button, and the M next to the display disappears.

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