GMAT-esque Challenge Question: Today is the Day… To Get Better at GMAT Math

It’s March 15, and now that the hysteria over Pi Day (good ol’ 3-14) is over, the true GMAT math geeks can celebrate an even more exciting use of math and dates (and, no, we don’t mean impressing your dates with math tricks. Not that that’s not a good idea, of course).

Today is 3/15, a not-all-that-unique case of the month being a factor of the day (3 is a factor of 15, so you could factor the date 3/15 into 1/5. It’s almost like it’s January 5th all over again!).

Now, why is this important? Because the GMAT loves to test factors and multiples, so if you can think of something as little as the calendar each day in terms of factors and multiples, in really no extra time at all (you do, after all, check the date at least once a day, right?) become incrementally more prepared for GMAT math. So take this pop quiz:

How many days per calendar year* is the month a factor of the day?

The answer will be posted shortly; please post your answers and thought processes in the comments field, and enjoy your easily-reducing day! You won’t have another until Sunday, 3/18.

* Hint: It doesn’t matter if it’s Leap Year. 2 is not a factor of 29.

Good luck!


Solution: 90

All 31 days in January, because 1 is a factor of all integers

14 of the 28 days in February (because every other day is divisible by 2)

10 of the 31 days in March (the multiples of 3 between 3 and 30)

7 days in April (the multiples of 4 between 4 and 28)

6 days in May (the multiples of 5 between 5 and 30)

5 days in June (the multiples of 6 between 6 and 30)

4 days in July (the multiples of 7 between 7 and 28)

3 days in August (the multiples of 8 between 8 and 24… so, so close if only the month were 32 days long!)

3 days in September (9th, 18th, 27th)

3 days in October (10th, 20th,30th)

2 days in November (11th, 22nd)

2 days in December (12th, 24th)

And there you have it! As you can see, as you move through the months, your job starts to get easier as you pick up on the patterns and are able to reuse some of your previous insights… This is a very valuable skill to remember on test day!

Will you take the GMAT in June or later? On March 21 we will run a free live online seminar to help you get up to speed on the new Integrated Reasoning section coming in June. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter!