If you’ve been studying for the GRE for any length of time, you’ve probably come across the term “smart numbers.” This is one of those GRE math strategies that can make a big difference, especially when you're dealing with variables, percentages, or ratios in word problems.

Smart numbers are numbers you choose to simplify calculations in a problem that involves variables or unknowns. The trick is to pick real numbers that are easy to work with and still preserve the logic of the problem.

Let’s take a basic example. Suppose a question asks: “The price of an item is increased by 20% and then decreased by 40%. What percent of the original price is the final price?” You don’t need to set up complex algebra here. Instead, assign a “smart number” for the original price—100 is often a good choice when dealing with percentages.

Start with 100:

• A 20% increase brings the price to 100 x 1.2 = 120
  
• A 40% decrease then gives you 120 x 0.6 = 72

Now just compare: 72 is 72% of the original 100. So the answer is 72%.

The great thing about smart numbers is that they save you from getting tangled in unnecessary algebra. That said, you need to make sure you’re allowed to use them. This strategy works best when:

• The problem doesn’t specify particular values
  
• The question asks for a relative value (e.g., a percent, a ratio, a comparison)
  
• The answer choices are also relative or in variable form

On the flip side, don’t use smart numbers if a question is asking for a specific value or if plugging in numbers would disrupt the logic of the problem. In those cases, stick to solving algebraically.

As you prep, get in the habit of looking at problems and asking yourself, “Can I use smart numbers here?” With practice, you’ll start spotting opportunities where this strategy will save you time and reduce mental clutter.

Reach out to me with any questions about your GRE prep. Happy studying!

Warmest regards,

Scott Woodbury-Stewart
Founder & CEO, Target Test Prep