# More Fast Math for the GMAT - Part 7

*by*, Aug 7, 2017

A while back, we started a series on Fast Math for the GMATheres the link if you want to start from the beginning.

In our last installment, I gave you two problems to try. Weve already discussed the first one; heres the second one again (from the free problem set that comes with GMATPrep).

The Earth travels around the Sun at a speed of approximately 18.5 miles per second. This approximate speed is how many miles per hour?(A) 1,080

(B) 1,160

(C) 64,800

(D) 66,600

(E) 3,996,000

What do you think?

Those answers they are seriously far apart. The first two are clumped, then the next two, and that last one is totally different.

Were definitely going to estimate on this one. :) Also, just from glancing at the answers, Im guessing that the correct answer will not be (E). Chances are pretty good that the correct answer will have another close answer based on making some small mistakeor based on making the problem just a little harder to estimate.

Jot down the details.

Where should we start?

How do you go from seconds to hours?

60 seconds 1 minute

60 minutes 1 hour

So we need 60 twice. Are we multiplying? Dividing? Glance at the answers again or think it out logically. All of the answers are greater than 18.5, so I must have to multiply. And logically, that makes sense: If I go 18.5 miles in one second, then I should be able to go a lot further in a whole hour.

Okay, now which clump of answers is the right clump? 18.5 is a really annoying number, but the clumps are so far apart that I can just call that 20 for now.

(20)(60) = 1,200

Hmm. I still need to multiply by another 60, so answers (A) and (B) are out.

But Im only multiplying by another 60, so answer (E) is out, too. Its down to (C) and (D).

If I just multiply by another 60 nowwill it be close enough? Im not sure. I overestimated (from 18.5 to 20) and the two final numbers are pretty close. If the answer is (C), I might think its (D) just from the error I introduced in my estimation.

In fact, (1,200)(60) = 72,000. Definitely not good enough. Okay, what should I do next?

The math that actually needs to happen is this:

(18.5)(60)(60)

The latter two are easy: 3,600. Its that 18.5 thats the problem. I could just do long multiplication at this pointbut long multiplication is so annoying! Also, I just noticed something else.

The final two answers are 64,800 and 66,600. Often, on problems like this, theres a way to calculate just the units digit and use that to answer but on this problem, the units digits are the same. SO annoying.

BUT! I can actually change the problem so that the units digits are different. Heres how.

Again, heres the official math that needs to happen and here are the two answers:

(18.5)(60)(60)

(C) 64,800

(D) 66,600

And heres how Im going to change the problem:

(18.5)(6)(6)

(C) 64,8

(D) 66,6

Wait, what did I just do? :) I gotrid of the two zeros. So now, I just have to figure out what the units digit of (18.5)(36) is6 or 8?

The units digit is 6, so the answer is (D).

Look at that math carefully to see what I didand did notdo. First, I multiplied the 6 by the 5, and carried the 3. Next, I multiplied the 6 by the 8, added the 3 and then only wrote down the units digit. (6)(8) + 3 = 51, but I only wrote down the number 1. Then I stopped working on that line. How did I know that was as far as I needed to go?

Because the number 18.5 has one decimal, I knew that the first number I calculated (which turned out to be 0) would be a decimal, toothe tenths place. The next number to the left will become part of the units digit. I dont care about more than the units digit, so I dont have to keep calculating.

I do have to go to the next number in 36, the 3, to see what that contributes to the units digit. First, at the second step in long multiplication, go down one line and automatically start off with a 0 in what will become the tenths place. Then, multiply the 3 and the 5 to get 15but, again, I care only about the units digit, so I only wrote down the 5.

Finally, 1 + 5 = 6, so the answer must be 66,6 (or 66,600, once I add the zeros back in). Done!

## Key Fast Math Takeaways:

(1) If you think you need to do long division or long multiplication, stop for a moment. Reflect. Even if you have to do partial long division or multiplication, how much do you *really* have to do?

(2) As we discussed last time, dont start solving on PS until youve looked at those answer choices! Sometimes, they contain very important clues about the most efficient way to solve.

* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

###### Recent Articles

###### Archive

- February 2020
- January 2020
- December 2019
- November 2019
- October 2019
- September 2019
- August 2019
- July 2019
- June 2019
- May 2019
- April 2019
- March 2019
- February 2019
- January 2019
- December 2018
- November 2018
- October 2018
- September 2018
- August 2018
- July 2018
- June 2018
- May 2018
- April 2018
- March 2018
- February 2018
- January 2018
- December 2017
- November 2017
- October 2017
- September 2017
- August 2017
- July 2017
- June 2017
- May 2017
- April 2017
- March 2017
- February 2017
- January 2017
- December 2016
- November 2016
- October 2016
- September 2016
- August 2016
- July 2016
- June 2016
- May 2016
- April 2016
- March 2016
- February 2016
- January 2016
- December 2015
- November 2015
- October 2015
- September 2015
- August 2015
- July 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- October 2014
- September 2014
- August 2014
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009