**Can Plugging In Work on Quantitative Comparison?**

Plugging in, a great strategy on problem solving, can also be very effective on the current and new GRE’s quantitative comparisons. The ground rules for plugging in on quantitative comparison, however, are a little different. But before I explain how, why don’t you try to crack the following problem.

Xyla can paint a fence in 6 hrs. Working alone, Yarba can paint the same fence in x hours. Working together they can complete the task in 2.1 hrs.

Column A | Column B |

x | 3 |

*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*

**Don’t Dive in Head First with the Algebra**

Solving for x can be very challenging. You’ll be dealing with complex fractions and could easily mess up some of the math. Plugging in, on the other hand, can make things a lot easier.

Wait a second, you’re probably thinking. Wouldn’t it take much longer just plugging in a random value for x? Yes, it definitely would. But with this question, we do not want to plug in any random value. We already have a value staring at us. And that is the 3 in Column B.

Maybe you’ve balked, thinking that this is a GRE quantitative comparison problem and therefore, we’re not looking for a specific answer. You could go on to reason that in problem solving, we can always work with the five answer choices. But in quantitative comparison, we do not want a specific value, we simply want to know which side is greater.

**The Hypothetical **

While it is true that we do not want to solve for a specific value on Quantitative Comparison, let’s still assume that x is 3. Let’s further assume that plugging 3 back into the problem gives us 2.1 hours. Then we could conclude that the x has to equal 3, and, therefore, the answer is (C).

What if we’d plugged in 3 and gotten a total work rate lower than 2.1? Then we would know that a rate of 3 hrs is too fast. We would have to slow down Yarba and we would do so by increasing x, the amount of hours it takes her to finish the job by herself. In this case Column A would be bigger.

The final possibility is if we had plugged in 3 and gotten a number larger than 2.1. Then we would know that x has to be lower than 3, because we need a faster work rate. The answer then would be (B).

**The Approach**

Now that we’ve gone through all the possible scenarios, let’s plug in 3 and see what we get. Click here For a brush up on work rate formula.

1/6 + 1/3 = 1/TWR

Total Work Rate = 6 x 3/9 = 2

So, we’ve plugged in 3 and we’ve gotten a number lower than 2.1. Therefore, 3 hrs is too fast (or to low). We have to slow Yarba down a little. And to slow someone down, we have to increase the amount of time it takes him/her to finish the job. Thus, Column A is bigger.

**Algebra** **– Friend or Foe?**

Had we attempted to solve the problem algebraically, we would have set up an equation that looked like this: 1/6 + 1/x = 10/21. You can try this at home, but don’t be surprised if you get stuck along the way. First off, there are many steps and secondly, when you finally solve for x you get 126/39 – hardly a friendly number. But you can avoid all this if you simply remember that there is an easier way—Plugging In.

Try plugging in with different GRE math question types, as well!

I had solved using algebraic expressions.i got x value as 42/13 which is greater 3.so the answer should be A.

Yes, 42/13 is a simplification of Chris’s 126/39 figure for the algebraic solution. And you’re right– an algebraic solve will ultimately lead you to the same answer as plugging in. (Although as Chris mentioned, there are a lot more steps in that case!)

I didn’t think there was enough info to do the problem because it doesn’t state what column A and column B represent. Please help.

Hi Betsy,

Thanks for reaching out to Magoosh! Right above the columns here, we state the problem: Xyla can paint a fence in 6 hrs. Working alone, Yarba can paint the same fence in x hours. Working together they can complete the task in 2.1 hrs.

So, column A represents how long it takes Yarba to paint a fence by herself. We are comparing this with the number in Column B, which is 3. Basically, we need to determine whether it takes Yarba less than 3, exactly 3 or more than three hours to paint the fence (or if there isn’t enough information to answer the question!)

Does that answer your question?

Ok, I had to backtrack and read 2 older posts, but now I get it. 😉 Really, this is genius; so a simple solution to what could be a monstrously complex problem. Thanks 🙂

Wowww…this really sums up how we need to approach a quantitative comparison question

The first thought that runs through the head is ok, lets quickly create the equations and solve it out (which is what GRE wants us to do and 🙂 )

Really need to pause a moment and look through the problem

I am already using Magoosh as the first choice prep material and i am really enjoying it

Thanks Chris

Hi Shreejit,

You got it! The GRE wants you to get out of the “equation box” and think logically. 2-minutes of laboriously writing out equations can become sub-30 seconds of not even having to lift a pencil.

Glad you are enjoying Magoosh 🙂

Genius. Brilliant! Thanks for sharing this tip that is specific for quantitative comparison question, since you previously also discussed how to use techniques for multiple choice. Balances and rounds out your strategies for work-rate problems on the GRE!