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GRE Quantitative Comparison Tip #4 – Comparing in Parts

To set up today’s Quantitative Comparison (QC) strategy, please solve the following question:

 

 

 

 

 

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

There are several different ways to solve this question. For example, we could add the fractions in each column, and then rewrite both sums with a common denominator and then compare them (yikes!).  Or, we could use the onscreen calculator to convert each fraction to a decimal and find the sum in each column (yeesh!).

Both of these approaches would take a long time.

Fortunately, we already know that, since the test-makers are reasonable, there MUST be an easier way to solve this question (please read my previous post: The Reasonable Test-Maker).

The fastest way to solve this question is to estimate and compare the columns in parts.

Here’s how it works.

First notice that 213/428 is approximately 1/2. Now, for this question, we need to be a little more accurate than that. Notice that, since 214/428 = 1/2, it must be the case that 213/428 is a little bit less than  1/2, which we’ll denote as 1/2-.

Using similar logic, we can see that, since 3007/9021 = 1/3, it must be the case that 3007/9101 is a little bit less than 1/3, which we’ll denote as 1/3.

Next, since 731/1462 = ½, it must be the case that 741/428 is a little bit more than 1/2, which we’ll denote as 1/2+.

Using the same logic, we can see that 208/597 is a little bit more than 1/3, which we’ll denote as 1/3+.

At this point, we can simplify the two columns as:

 

 

 

 

 

From here, we can compare the two sums in parts.

Since 1/2+is greater than 1/2-, and since 1/3+ is greater than 1/3, the sum of 1/2+ and 1/3+ must be greater than the sum of 1/2- and 1/3-.

As such, the answer must be B.

 

Heres’ the whole series of QC tips:

Tip #1: Dealing with Variables

Tip #2: Striving for Equality

Tip #3: Logic over Algebra

Tip #4: Comparing in Parts

Tip #5: Estimation with a Twist

By the way, students who use Magoosh GRE improve their scores by an average of 8 points on the new scale (150 points on the old scale.) Click here to learn more.

8 Responses to GRE Quantitative Comparison Tip #4 – Comparing in Parts

  1. sachin October 16, 2016 at 12:48 am #

    208/624 would be 1/3. so in this case 208/597 should be little less than 1/3. rather than1/3+.

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert October 18, 2016 at 3:28 am #

      Hi Sachin,

      It is true that 208/624 is exactly 1/3. As we reduce the denominator (which means we divide by a smaller number) our end result increases. We can see this in the decimal forms of these two numbers:

      208/624 = 0.333…
      208/597 = ~0.3484

      We can see that 208/597 is larger than 1/3 after all. I hope that clarifies! 🙂

  2. diti August 2, 2016 at 11:57 am #

    Just a general question, while being under the time pressure of the exam, how do you look at the numbers in the questions and come up with estimations like ‘since 731/1462 = ½’ so fast ?

    • Magoosh Test Prep Expert
      Magoosh Test Prep Expert August 2, 2016 at 1:17 pm #

      In this particular case, it’s a matter of ignoring the last 2 digits in each number. 731 is re-imagined as 7, and 1462 is re-imagined as 14. In other words, 731/1462 approximately equals 7/14, which is the same as 1/2

  3. siddharth mehra June 6, 2013 at 2:35 am #

    Next, since 731/1462 = ½, it must be the case that 741/428 is a little bit more than 1/2, which we’ll denote as 1/2+.

    Using the same logic, we can see that 208/597 is a little bit more than 1/3, which we’ll denote as 1/3+.

    Can u explain above part of explaination?

    • Brent Hanneson June 6, 2013 at 10:56 am #

      Oops, that’s a typo.

      It should read, “since 731/1462 = ½, it must be the case that 741/1462 is a little bit more than 1/2, which we’ll denote as 1/2+”

      We’ll change that right away.

      Cheers,
      Brent

      • Magoosher October 22, 2015 at 6:37 am #

        Another typo:
        “Using similar logic, we can see that, since 3007/9027 = 1/3.”

        3007/9021 = 1/3.

        • Dani Lichliter
          Dani Lichliter October 22, 2015 at 10:47 am #

          Hi there,
          Thanks for catching that typo! I just updated the post with the change.
          Happy studying!
          Dani


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