# GRE Quantitative Comparison Tip #4 – Comparing in Parts

Our fourth article in the GRE Quantitative Comparison series will show you another quick trick for comparing values in two columns. Let’s take a look at this problem:

Column A                                       Column B

(221)/(400)  +  (3090)/(9060)      (720)/(1450) + (200)/(603)

(A) Quantity A is greater.

(B) Quantity B is greater.

(C) The two quantities are equal.

(D) The relationship cannot be determined from the information given.

The traditional way to compare these columns would be to add the quantities together by looking for a common denominator. After combining the fractions, we would analyze the results. We could also type the numbers into the calculator, convert the fractions into decimals, add the decimals together, and compare the values in both columns.

Comparing in Parts: Use Logic!

Instead of using these methods, let’s think back to the logic we used in the last article [insert link]. We aren’t going to solve these fractions. To save time, we’ll estimate the values and then compare these simpler fractions to get our answer. Take a closer look at these fractions:

Column A                                           Column B

(221)/(400)  +  (3090)/(9060)      (720)/(1450) + (200)/(603)

First of all, we know that 221/400 is larger than 200/400, which is 1/2. We’ll replace 221/400 by 1/2+ to show that it’s a bit more than 1/2. We can use the same method with 3090/9060. One third would be equivalent to 3020/9060, so we know that 3090/9060 is a little bigger than 1/3, and we’ll write it as 1/3+.

Now we’ve simplified Column A to:

1/2+   +   1/3+

We can estimate the values in Column B in the same way. 720/1450 is less than 1/2, so we can replace it with 1/2-. 200/603 is less than 1/3, so we’ll estimate it as 1/3-. Now we will put all the pieces together to compare the columns.

Column A               Column B

1/2+   +   1/3+     1/2-   +   1/3-

Even though we’ve only estimated the values of these fractions, we can analyze the parts of each column and determine the relationship between the values.

Comparing Estimates Rather than Performing Calculations

Since 1/2+ is always more than 1/2-, we know that the first part of Column A is larger than the first term in Column B. Similarly, 1/3+ is greater than 1/3-, so the second term in Column A is still larger than the second term in Column B. By this reasoning, the sum of both fractions must be larger for Column A than for Column B. This information lets us pick Choice (A) Quantity A is greater. By using this fast estimation technique, we’ve solved this GRE question without doing much math.