Ballparking: Helpful Skills

When students start Ballparking, they often find it a bit nerve-racking. That's understandable because there can be some level of uncertainty when your estimate doesn't match the answer choices exactly. Conquering that discomfort is a big part of mastering the GMAT. Luckily, there are some general rules that can help make sure your Ballparks are found quickly and accurately. Consider the following calculation: > $$19.74\times 0.26$$ Ballparking 19.74 as 20 is easy, but what should you do with 0.26?

That wouldn't work. If you Ballpark 0.26 as 0, then you'd get results like $$20 \times 0 = 0$$. That's definitely not what you'd most likely be looking for. When you multiply and divide with numbers between -1 and 1, small numerical changes can result in large changes in the answer. So make sure your Ballparked value is as close to the original as possible.

That's not it. When you multiply and divide with numbers between -1 and 1, make sure your Ballparked value is as close to the original as possible. A small change can result in a large change to the answer. If you ballpark 0.26 as 1, then you'd end up with something like $$20 \times 1 = 20$$. Since 0.26 is significantly less than $$\frac{1}{2}$$, your answer should almost certainly be lower than 10.

Exactly! When you multiply and divide with numbers between -1 and 1, small changes can result in large changes in the answer. While you might want to generally Ballpark with integers, that won't always work. Fractions are your best friend when it comes to Ballparking numbers between -1 and 1. You might not have fond memories of fractions, but it'll be much faster using them than trying to multiply with decimals. In this case, 0.26 is very close to 0.25, which is $$\frac{1}{4}$$. Multiplying by $$\frac{1}{4}$$ is the same as dividing by 4, so > $$20 \times \dfrac{1}{4} = \dfrac{20}{4} = 5$$. > This is very close to the actual answer, which is about 5.13.

Suppose you need to Ballpark an answer for > $$7.5 \times 8.5$$. > In which direction should you round the values to get the most accurate Ballpark?

That won't be the most accurate. If you round both numbers up, then the Ballpark will definitely be higher than the actual value. To get a more accurate estimate, you should round one value up and one value down.

That won't quite do it. If you round both numbers down, then the Ballpark will definitely be smaller than the actual value. To get a more accurate estimate, you should round one value up and one value down.

Precisely! When you round one value up and the other value down, you will end up with a more accurate Ballpark.

Doing so offsets the increase in one value with a decrease in the value. Suppose, instead, that you're Ballparking this subtraction problem: > $$3{,}467 - 819$$. > How do you think you should round the values to get the most accurate Ballpark in this case?

Nice catch! With subtraction, you don't want to apply the same rule as with multiplication.

Actually, no. You might think that the same rule applies here as with multiplication, but that's not the case.

Since the numbers in a subtraction work in opposite directions, you want to round them in the same way. For which other operation should you adjust numbers in the same direction when Ballparking?

That's not right. For example, if you round both numbers in an addition up, then the Ballpark will definitely be greater than the actual value. With addition, you should round numbers in opposite directions.

Indeed! Division acts like subtraction in that one number is trying to increase the answer and the other is trying to reduce it. That means you should round numbers in the same direction.

So to Ballpark for a single, accurate value, remember: - addition and multiplication: **try to round values in opposite directions**; and - subtraction and division: **try to round values in the same direction**. But often, there are times where even an accurate Ballpark value can be improved upon.

Suppose you're Ballparking the sum of $$\sqrt{82}$$, which is slightly larger than 9, and $$\sqrt{66}$$, which is slightly larger than 8. Which of the following values should you eliminate as impossible for the value of $$\sqrt{82}+\sqrt{66}$$?

Nice job! Even though you might Ballpark the answer as 17 or 18, you know that the value **must** be greater than 17. So no matter how close an answer is to your Ballpark, if it isn't greater than 17, it should be eliminated.

That's not right. This is the correct value of the sum, at least to two decimal places. So it definitely shouldn't be eliminated.

That's right! If you round one number up and the other down, then you would get a sum of 18 (either $$9+9$$ or $$10+8$$). Since you round up much farther than you round down, the answer must be less than 18, and thus can't be 18.51.

So while a single Ballpark value can be good, it's often even better to find a range where you're 100% certain you can eliminate answer choices that are outside that range. That will help you be confident about the values you eliminate. Summing up: [[summary]]

Ballpark it as 0

Ballpark it as 1

Ballpark it as a fraction

Round both values up to 8 and 9

Round both values down to 7 and 8

Round one up and the other down

Round them in the same direction

Round them in opposite directions

Addition

Division

Proceed to step

16.97

17.18

18.51