Consider the following question:

**Set T consists of all multiples of 5 from 30 to 225 inclusive**

Column A | Column B |
---|---|

Mean of Set T | Median of Set T |

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

As you can imagine, we really don’t want to calculate the mean and median of set T. Fortunately, we can apply a nice rule that says:

*If the numbers in a set are equally spaced, then the mean and median of that set are equal.*

What does it mean to have “equally spaced” numbers?

“Equally spaced” means that, if the numbers in a set are arranged in ascending order, then the difference between any two adjacent numbers will always be the same.

So, in the set {30, 35, 40, . . . , 215, 220, 225}, the difference between any two adjacent numbers will always equal 5. As such, the mean of this set will equal the median of this set (which means the answer to the above question is C). Notice that we can answer this question without making any calculations whatsoever. We can answer it by recognizing that the numbers in the set are equally spaced.

Similarly, the numbers in the set {5, 8, 11, 14, 17, 20, 23} are equally spaced. As such, the mean of this set will equal the median of this set.

As you might imagine, this little rule as a shortcut can come in handy. It will help you quickly answer the original question, and it will help you answer this one:

**Set X: {-27, -20, -13, -6, 1, 8, 15}**

**Set Y: {-23, -19, -15, -11, -7, -3, 1, 5, 9, 13}**

Column A | Column B |
---|---|

Mean of set X | Mean of set Y |

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

Column A: Since the numbers in set X are equally spaced, the mean will equal the median. We can quickly find the median by locating the middlemost element: {-27, -20, -13, **-6**, 1, 8, 15}. Set X has 7 elements and the middlemost element is **-6**. So, the median of set X is -6, which means the mean of set X is -6 as well.

Column B: The numbers in set Y are also equally spaced, so the mean will equal the median. Set Y has 10 elements, so there are two middlemost elements: {-23, -19, -15, -11, **-7**, **-3**, 1, 5, 9, 13}. As such, the median of set Y will equal the average (mean) of **-7** and **-3**, which is -5. So, if the median of set Y is -5, then the mean of set Y is -5 as well

So, using our rule, we found that Column A = -6, and Column B= -5. As such, the answer to the question is B.

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Hello,

For the first example, I selected choice D since I was unsure if any of the numbers repeated. For questions like this, is it safe to assume none of the numbers occur more than once?

Hmm…that’s a good question. I’m not a 100% sure on that, and it does seem a bit misleading. I’d be inclined to edit this question so it is ambiguous that each of the multiples appears exactly once. Sorry for any confusion 🙂

Thank you so much! 😀

Great tip 🙂 i used to skip such questions(example 1), due to lack of time. with this tip, it sounds so simple..Thank !!

absolutely, love the tactics!!! can u please post, more of such nice tactics..it will be very much helpful.

Great! Happy you found that helpful :). We’ll try to keep posting such helpful tips.

its great shortcut.. reduces whole calculation.. thanks Brent 🙂

Wow, excellent shortcut! Super helpful 🙂

nice tactic..wish to learn many tactics like this…

We’re glad you like them! You can find all of Brent’s posts here: http://magoosh.com/gre/author/brent/

thanks…nice shortcut particularly the second application.

You’re welcome, glad we could help! 🙂