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^{-.}

Magoosh Test Prep ExpertSeptember 16, 2018 at 12:10 pm#

Hi Mariangela,

You are absolutely right! We encourage students to develop these mental math skills in order to be able to solve these types of questions quickly and efficiently. If you’re interested in developing these skills, I recommend that you check out our free mental math flashcards 🙂

Magoosh Test Prep ExpertOctober 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! 🙂

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 ExpertAugust 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

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This works only if you know what numbers make 1/2 and 1/3.

Hi Mariangela,

You are absolutely right! We encourage students to develop these mental math skills in order to be able to solve these types of questions quickly and efficiently. If you’re interested in developing these skills, I recommend that you check out our free mental math flashcards 🙂

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

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! 🙂

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 ?

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

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?

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

Another typo:

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

3007/9021 = 1/3.

Hi there,

Thanks for catching that typo! I just updated the post with the change.

Happy studying!

Dani