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How to Use Your Calculator on the GRE

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 {203^2} – {201^2}. 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 (203+201)(203-201), which equals (404)(2), which equals 808.
Since this question would be too easy to solve using the onscreen calculator, the test-makers will change the question to 20003^2- 20001^2 where 20003^2 and 20,001^2have 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 99999999 then an ERROR message is displayed. When you evaluate 20,003^2 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 AColumn 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 AColumn B

From here, we can rewrite this as:
Column AColumn B

And this is the same as:
Column AColumn 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 AColumn B

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

Then, divide both sides by 897,189 to get:
Column AColumn 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: 
sqrt{ab} = sqrt{a}sqrt{b}
First we need to recognize that:
sqrt{2 billion} = sqrt{2,000,000,000}
=sqrt{20} * 10,000
From here, we can see that since sqrt{16}=4 and sqrt{25}=5 then sqrt{20} must lie between 4 and 5. In other words, we can say that sqrt{20} equals 4.something.
If  sqrt{20} equals 4.something, then = sqrt{20} * 10,000 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:
sqrt{2 billion} = sqrt{2,000,000,000}
From here we can use the calculator to evaluate both roots. When we do this, we get:
sqrt{2,000}sqrt{1,000,000} = 44.7 * 1,000 = 44,700
So, the answer must be D.

Student New GRE Experience: Umul

Here’s Umul’s advice for preparation and test day, based on his exam experience. If you’d like to read others like these, or submit your own write-up after you take your exam, head over to our Student New GRE Experiences page. Enjoy!

“Hi, this is Umul from Pakistan. I took my new GRE today, and I feel I should write about it so others can learn from my experience just like I learnt so much from them.

I previously took the old GRE and my score was a 1160, a 700 on math and a 460 on the verbal around early 2009 (i.e. almost 2.5 years ago). I messed up both of my sections pretty badly, since I totally ran out of time on the math section and the verbal section I just did not get. After landing the Fulbright scholarship, they asked me to retake my GRE as they wanted me to improve my quant score for getting into better universities. I am going for a Masters in energy resources, hence my math (I am guessing) was not competitive enough as a foreign student. Also, my undergraduate degree was a BSc honours in Mathematics from LUMS in Pakistan.

I have been working for the past three years and had to retake my GRE on short notice, so I prepared in a roundabout way for a month: for verbal, I mainly used word lists from Barron’s and Kaplan’s high frequency list, which I think was enough, as I knew most of the words on the test.

My first section was math, which went very well. The questions were easy, since I had really practiced my math timing: I prepared according to the 30 minutes for 30 questions strategy. which made it easier, since the actual test is 35 mins and 20 questions. The second math section was tougher, which I could tell by the difficulty level of the questions.

The second section was verbal, which I completely messed up! I think I hadn’t practiced verbal timing much, although I had practiced doing questions a lot. I panicked and guessed on about 5 to 6 questions on the first section. However, ETS was very helpful, they gave me a baby-level second verbal section, to help me get through the exam, so the second verbal section was very easy and I am guessing I did fine on that one after messing the first one completely. So, people out there, don’t be scared– if you mess up , the program makes sure that if you’ve panicked but still know your verbal, you won’t automatically drop to a 130-type score!

So my final score was 150(450)on the verbal and a 163(780) on the math. I was expecting a bit better on the math as it went extremely well, and was relieved by the verbal . But (oh well) my target of improving my math score had been met.

What would I do differently? I wish had worked more on the Verbal timing than doing the actual questions as I didn’t think the timing would be a problem. The new GRE expects one to comprehend stuff really fast and makes you do lots of critical thinking!

The best place to practice is the 23 Tests by ETS– it gives loads and loads of practice material and it has an old Analytical ability section, from which lots of one-sentence critical reading passages are given. Also, practicing on the comp is a must. There’s very limited software available, but I guess one has to make do!

Anyway, best of luck to all you future GRE takers!”

1 comment:

Bane said...

If you need some more info on GRE calculator

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