How to use your calculator?

or many students, the addition of the GRE’s onscreen calculator is a godsend. These students take solace in the notion that this new calculator will help them solve tons of questions. The truth of the matter is that almost all math questions on the GRE can be solved without a calculator. Furthermore, in many cases, it will actually take long to solve a question using a calculator that it will to use other techniques. Finally, the test-makers are taking questions that can be easily solved with a calculator and changing the numbers in order to render the calculator useless.

For example, a former GRE question would have asked you to evaluate  – . The slow solution was to perform the actual (tedious) calculations. The fast solution was to recognize that this difference of squares can be factored as , which equals , which equals .

Since this question would be too easy to solve using the onscreen calculator, the test-makers will change the question to  where  and have too many digits for the calculator to handle. As such, you’ll have to solve this question using factoring techniques.

Aside: the onscreen calculator displays up to eight digits. If a computation results in a number greater than  then an ERROR message is displayed. When you evaluate  you get a 9-digit number.

Now, despite the test-makers’ attempts to remove the calculator from your arsenal, thereare times when you can make a few adjustments to a question and then quickly answer it with the calculator.

we can solve the following question using a variety of techniques:

Column A	Column B

1. The quantity in Column A is greater
2. The quantity in Column B is greater
3. The two quantities are equal
4. The relationship cannot be determined from the information given

Notice that these numbers yield products that are too big for the calculator to handle. However, with a few adjustments we can use a calculator to answer the question.

One solution is to first divide each column by 1,000,000. When we do this, we get:

Column A	Column B

From here, we can rewrite this as:

Column A	Column B

And this is the same as:

Column A	Column B

At this point, we can use the calculator enter all of these values, and each resulting product will have fewer than 8 digits.

So, with a small modification, we can answer this question using a calculator.

Now, can you think of another approach that allows you to use a calculator to solve the original question (without dividing by 1,000,000 or any other powers of 10)?

Here’s the original question:

Column A	Column B

Another approach is to first divide both sides by 641,713 to get:

Column A	Column B

Then, divide both sides by 897,189 to get:

Column A	Column B

At this point, we can enter all of these values into the calculator and compare the columns.

Next, we’ll examine another way to thwart the GRE and use the onscreen calculator to solve questions that, at first glance, appear to render the calculator useless:

The square root of 2 billion is between

1. 2,000 and 5,000
2. 5,000 and 15,000
3. 15,000 and 30,000
4. 30,000 and 50,000
5. 50,000 and 90,000

Try to identify at least two ways to solve the above question.

Aside: Please notice that 2 billion is too large to fit in the onscreen calculator.

Non-calculator solution

This approach uses the following rule: 

First we need to recognize that:

From here, we can see that since  and  then  must lie between 4 and 5. In other words, we can say that  equals 4.something.

If   equals 4.something, then  must lie between 40,000 and 50,000.

As such the answer must be D.

Calculator solution

With a slight modification, we can use the onscreen calculator to solve the question within seconds.

First recognize that:

From here we can use the calculator to evaluate both roots. When we do this, we get:

So, the answer must be D.