-
Target Test Prep 20% Off Flash Sale is on! Code: FLASH20
Redeem
Executive Assessment: Fast Math for Faster Solutions - Part 4
Welcome to the fourth installment of Fast Math for the EA! If youre just joining us now, head back to the first part and work your way back here.
I have two more problems for you from the official free practice set (these are labeled #5 and #7 in the PS set on the EA website, as of September 2017). Give yourself 4 minutes to complete the set. Good luck!
Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by?(A) 32.25%
(B) 31.00%
(C) 30.25%
(D) 30.00%
(E) $22.50
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 20 minutes?(A) 80
(B) 100
(C) 150
(D) 240
(E) 300
Did you spot any opportunities to make these problems easier to solve?
Our theme for this set is: Draw / Step It Out. Dont think algebra or formulas or whatever. Pretend your boss just handed you a pen and an envelope and asked you to figure this out. Whats your quick-and-dirty, back-of-the-envelope approach?
Heres the first problem.
Increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by?
So Im your boss and Im going to give you a raise. Im also giving you a choice: You can have a straight 30% raise, or you can have two 15% raises, one after the other. In other words, Ill apply the first 15% raise to your current salary, and then Ill apply a second 15% raise to the new salary.
Do you have a preference? If so, which one would you choose?
First, there is a difference between those two calculationsone will result in a higher salary than the otherso you should definitely have a preference. :D Next, which one is the higher one?
Lets say your salary is $100. A straight 30% raise will make your new salary $130.
Now do the two 15% raises. The first 15% raise will get you to $115. Next, dont do the math, but think about what happens for the second 15% raise. The first time, you took 15% of the starting salary, $100. But this second time, youre going to take 15% of your new, larger salary of $115. So 15% of that number will be more than $15 and your new-new salary will be more than $130.
In other words, you definitely want the 15% + 15% again raise, not the one-time 30% raise.
Here are the answer choices for the problem. What do you notice?
(A) 32.25%(B) 31.00%
(C) 30.25%
(D) 30.00%
(E) $22.50
The answer has to be more than 30%, so eliminate choices (D) and (E). How much more? Okay, lets go do some math to figure that out.
Start: $100
Increase #1: +15% so the dollar amount goes from $100 to $115
Increase #2: +15%, so the dollar amount goes from $115 to ?
Take 15% of 115. Thats an annoying number, so use percent benchmarks to solve (percent benchmarks are taught in the original Fast Math series for the GMAT, linked in the very first article in this series).
You want 15%. Thats made up of 10% and 5%.
10% of 115 = 11.5
5% of 115 = half of above = 11.5 / 2 = 5.75
15% = 10% + 5% = 11.5 + 5.75 = 17.25
The new increase is $17.25, but that still needs to be added to the starting point of $115. That math is slightly annoyingbut you can make it a bit easier.
Glance at the answers. Hmm, two actually do have a 0.25 at the end (if only one had, you could have just picked that one).
Okay, if you added a straight $15 to $115, youd get $130. Youre actually adding $17.25, or $2.25 more than $130in other words, $132.25. You started at $100 and are now at $132.25, so the percentage increase is 32.25.
The correct answer is (A). Nice!
What about the second one?
If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 20 minutes?
Again, imagine your boss asking you to figure this out on the back of an envelope right now.
+1 person every 15 seconds
They want 20 minutes uhh
Too annoying. Okay, how many is that in just 1 minute?
+1 in 15 seconds = +4 in 1 minute. Good.
So how to go from 1 minute to 20 minutes? Multiply by 20!
+4 in 1 minute = +4(20) in 20 minutes
80!
The correct answer is (A).
You can do this the textbook way: set up a proportion to convert from seconds to minutes and then another one to get to 20 minutes. But thats like creating busywork. You arent required to show your workyou just need to select the correct answer. Since you can just logic this one out on paper, go for it. :)
Join me next time, for another installment in this series.
Key Takeaways for EA Fast Math:
(1) Whenever possible pretend someones asking you to do this in the real world. That will take you away from textbook math and put you firmly in the realm of just thinking the steps through the way you normally would in the real world.
(2) If the numbers in the problem or answers (or both!) seem annoying (e.g., that second 15% calculation), theres probably a shortcut somewhere. In this case, we used two techniques: percent benchmarks to find the 17.25 figure more easily and then real-world logic / math sense to make the addition step easier than having to add 115 and 17.25.
(3) Turn that knowledge into Know the Code flash cards:
* Executive Assessment questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
Recent Articles
Archive
- April 2024
- March 2024
- February 2024
- January 2024
- December 2023
- November 2023
- October 2023
- September 2023
- July 2023
- June 2023
- May 2023
- April 2023
- March 2023
- February 2023
- January 2023
- December 2022
- November 2022
- October 2022
- September 2022
- August 2022
- July 2022
- June 2022
- May 2022
- April 2022
- March 2022
- February 2022
- January 2022
- December 2021
- November 2021
- October 2021
- September 2021
- August 2021
- July 2021
- June 2021
- May 2021
- April 2021
- March 2021
- February 2021
- January 2021
- December 2020
- November 2020
- October 2020
- September 2020
- August 2020
- July 2020
- June 2020
- May 2020
- April 2020
- March 2020
- 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