January 21, 2019 January 21, 2019 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday. January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 Nov 2010
Posts: 34
Location: United States
Concentration: Technology, Leadership
GPA: 3.7
WE: Engineering (Other)

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
25 Mar 2013, 13:09
Is there an easy way to do 1.03^8, than multiplying 1.03 8 times? I am slow at calculations
_________________
Do not dwell in the past, do not dream of the future, concentrate the mind on the present moment.
Push +1 kudos button please, if you like my post.



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1060
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
25 Mar 2013, 13:50
The GMAT won't ask you to calculate that number, maybe you need just an approximation... \((1.03)^8=(1.03)^4(1.03)^4=(1.03)^2*(...)=(1+0.03)^2*(...)=(1+0.0009+0.06)*(...)=~(1.06)(1.06)(1.06)(1.06)=~1.12*1.12=~1.25\)
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Math Expert
Joined: 02 Sep 2009
Posts: 52343

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
10 Jul 2013, 23:11



Intern
Joined: 02 Oct 2014
Posts: 2
Concentration: General Management, Finance
GMAT Date: 11202014

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
26 Oct 2014, 08:34
Hi, Nice post ... ready reckoner



Manager
Joined: 21 Jan 2014
Posts: 96
GPA: 4

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
17 Feb 2016, 03:38
Great Post and thanks Bunuel for sharing it!
I have one question based on the following question:
Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4
20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.
Does someone knows something about?
Thanks in advance!



Math Expert
Joined: 02 Sep 2009
Posts: 52343

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
17 Feb 2016, 03:42
pepo wrote: Great Post and thanks Bunuel for sharing it!
I have one question based on the following question:
Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4
20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.
Does someone knows something about?
Thanks in advance! Please read the whole thread: mathnumbertheorypercents9170840.html#p1202382Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 21 Jan 2014
Posts: 96
GPA: 4

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
17 Feb 2016, 07:20
Bunuel wrote: pepo wrote: Great Post and thanks Bunuel for sharing it!
I have one question based on the following question:
Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4
20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.
Does someone knows something about?
Thanks in advance! Please read the whole thread: mathnumbertheorypercents9170840.html#p1202382Thank you. Already read it, I but don't get the easyness



CEO
Joined: 20 Mar 2014
Posts: 2636
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Math: Number Theory  Percents
[#permalink]
Show Tags
17 Feb 2016, 08:07
pepo wrote: Bunuel wrote: pepo wrote: Great Post and thanks Bunuel for sharing it!
I have one question based on the following question:
Example: If $20,000 is invested at 12% annual interest, compounded quarterly, what is the balance after 2 year? Solution: Balance=20,000∗(1+0.12/4)^2∗4=Balance=20,000∗(1+0.12/4)^2∗4= =20,000∗(1.03)^8=25,335.4
20,000∗(1.03)^8: How am I supposed to perform this calculation in less than 2 minutes? there must be a shortcut in order to avoid perform the exponents.
Does someone knows something about?
Thanks in advance! Please read the whole thread: mathnumbertheorypercents9170840.html#p1202382Thank you. Already read it, I but don't get the easyness You are considering this question in complete vacuum and as such not helping yourself in understanding the nuances involved. You can also look at it this way: for any period >1 , compound interest > simple interest (or CI is JUST greater than SI) for the same rate. Rate of interest for quarterly compounding = 12/3 = 3% Number of quarters in 2 years = 8 Thus SI for this= 20000*3*8/100 = 4800 > balance after 2 years = 20000+4800=24800 and hence the final answer will be just greater than 24800. Now in GMAT PS, if the options given to you are spread far apart, then this approximation will give you the correct answer. But if not, then use the binomial theorem to calculate \((1.03)^8\): \((1.03)^8 = (1+0.03)^8 = 1^8*(0.03)^0+8*1^7*(0.03)^1+28*1^6*(0.03)^2\).... (this last term and the following terms will have 0.03 in 0.03^3 and higher powers making these terms very small compared with others, so neglect them). Thus, \((1.03)^8 = (1+0.03)^8 = 1^8*(0.03)^0+8*1^7*(0.03)^1 = 1+0.24 \approx\) 1.24 Hope this helps. P.S.: Binomial theorem expansion for \((a+b)^n = \sum_{\substack{0\leq k\leq n}} \binom{n}{k} a^n*b^k\), where \(\binom{n}{k} = {C^n_k}\)



Manager
Joined: 21 Jan 2014
Posts: 96
GPA: 4

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
17 Feb 2016, 08:59
Thanks for the reply!
I haven't heard about binomial theorem so I thing I will go for approximation.



NonHuman User
Joined: 09 Sep 2013
Posts: 9462

Re: Math: Number Theory  Percents
[#permalink]
Show Tags
04 Apr 2018, 06:39
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Math: Number Theory  Percents &nbs
[#permalink]
04 Apr 2018, 06:39



Go to page
Previous
1 2 3
[ 50 posts ]



