Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47221

999,999^21 equals:
[#permalink]
Show Tags
14 Sep 2015, 05:03
Question Stats:
69% (01:05) correct 31% (01:16) wrong based on 455 sessions
HideShow timer Statistics




SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: 999,999^21 equals:
[#permalink]
Show Tags
Updated on: 14 Sep 2015, 07:15
Bunuel wrote: 999,999^21 equals:
(A) (9^6)(11^6)
(B) (10^6)(10^5 2)
(C) (10^6)(10^6 2)
(D) (10^5)^2
(E) (10^6)^2
Kudos for a correct solution. Just trying to find a different method (Not a better method essentially) \(999,999^21 = (10000001)^2  1 = (10^61)^2  1 = (10^{12} +1  2*1*10^6)  1 = (10^{12}  2*10^6) = 10^6*(10^62)\) Answer: option C
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Originally posted by GMATinsight on 14 Sep 2015, 06:52.
Last edited by GMATinsight on 14 Sep 2015, 07:15, edited 1 time in total.




Intern
Joined: 30 Aug 2015
Posts: 31
Concentration: Marketing, Finance
WE: Brand Management (Manufacturing)

Re: 999,999^21 equals:
[#permalink]
Show Tags
14 Sep 2015, 11:15
shailendra79s wrote: 999,999²  1 = 999,999²  1² = (999,9991) (999,999+1) = 10^6 (999,998) = 10^6(10^6  2) Answer: C 999,9992−1=(1000000−1)2−1=(106−1)2−1=(1012+1−2∗1∗106)−1=(1012−2∗106)=106∗(106−2) Answer: option C
_________________
Please award kudos if you like my explanation. Thanks




Intern
Joined: 02 Sep 2015
Posts: 1

Re: 999,999^21 equals:
[#permalink]
Show Tags
14 Sep 2015, 05:14
\((999,999)^21 = (999,9991)(999,999+1) = 999,998 \times 1,000,000 = (10^6  2) \times 10^6\)



Current Student
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: 999,999^21 equals:
[#permalink]
Show Tags
14 Sep 2015, 07:10
GMATinsight wrote: Bunuel wrote: 999,999^21 equals:
(A) (9^6)(11^6)
(B) (10^6)(10^5 2)
(C) (10^6)(10^6 2)
(D) (10^5)^2
(E) (10^6)^2
Kudos for a correct solution. Just trying to find a different method (Not a better method essentially) \(999,999^21 = (10000001)^2  1 = (10^61)^2  1 = (10^{12} +1  2*1*10^6)  1 = (10^{12}  2*10^6) = 10^6*(10^62)\) Answer: option E GMATinsight, your answer is correct but the option is NOT E. It should be C. Alternate method: \(999999^21\) will have a unit's digit of 0 . Eliminate option A. For, options B,C,D, look at it like this: using \(a^2b^2=(a+b)(ab)\) \(999999^21 = (999999+1)(9999991) = 10^6*(10^62)\), C is the correct answer. NOte here that maximum power of 10 in \(10^6*(10^62)\) is 11. Thus the answer is in order of 11.Alternately, to eliminate options B,D,E look below: Option B is in the order of \(10^6*(10^4)=10^{10}\). We need \(10^{11}\). Eliminate. Option D is in the order of \(10^{10}\). We need \(10^{11}\). Eliminate. Option E is in the order of \(10^{12}\). We need \(10^{11}\). Eliminate.



SVP
Joined: 08 Jul 2010
Posts: 2120
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: 999,999^21 equals:
[#permalink]
Show Tags
14 Sep 2015, 07:17
Engr2012 wrote: GMATinsight, your answer is correct but the option is NOT E. It should be C. Thank you for bringing in notice.
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Intern
Joined: 03 Feb 2014
Posts: 38
Location: United States
Concentration: Entrepreneurship, General Management
WE: General Management (Other)

Re: 999,999^21 equals:
[#permalink]
Show Tags
14 Sep 2015, 10:58
999,999²  1 = 999,999²  1² = (999,9991) (999,999+1) = 10^6 (999,998) = 10^6(10^6  2) Answer: C
_________________
Shailendra



Manager
Joined: 21 Jun 2014
Posts: 138
Location: United States
Concentration: General Management, Strategy
GPA: 3.4
WE: Engineering (Computer Software)

Re: 999,999^21 equals:
[#permalink]
Show Tags
15 Sep 2015, 18:59
Consider this an algebraic expression of x21 .Break it down to (x1)(x+1) .so it becomes (999,999+1)(999,9991) Reducing it further leads to (1000,000)(999,998) .This expression can be simplified further to be written as: 10^6(10^6 2) . Option C is the correct choice.
_________________
Regards, Manish Khare "Every thing is fine at the end. If it is not fine ,then it is not the end "



Manager
Joined: 29 Jul 2015
Posts: 159

Re: 999,999^21 equals:
[#permalink]
Show Tags
17 Sep 2015, 13:33
Bunuel wrote: 999,999^21 equals:
(A) (9^6)(11^6)
(B) (10^6)(10^5 2)
(C) (10^6)(10^6 2)
(D) (10^5)^2
(E) (10^6)^2
Kudos for a correct solution. \(999,999^21\) = \((10^61)^2  1\) = \(((10^6)^2) + 1  2(10^6) 1\) =\(((10^6)^2)  2(10^6)\) = \((10^6)(10^6 2)\) Answer: C



Math Expert
Joined: 02 Sep 2009
Posts: 47221

Re: 999,999^21 equals:
[#permalink]
Show Tags
20 Sep 2015, 09:10
Bunuel wrote: 999,999^21 equals:
(A) (9^6)(11^6)
(B) (10^6)(10^5 2)
(C) (10^6)(10^6 2)
(D) (10^5)^2
(E) (10^6)^2
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:Here, the given information is in a quiteunusable form. You have no interest in squaring 999999. It’s a ridiculously large number, it will require an insanely long calculation, and most importantly it won’t look at all like the answer choices. The work would all be for naught, as ultimately you’d have to repackage the number to look like one of the expressions in AE. Your mission here is not to calculate this number; as on many algebrabased problems, your mission is to repackage the given information as something much more useful. Two things should lead you to this decision: 1. The number itself is incalculable by hand, so it’s not a calculationbased problem 2. The answer choices are in algebraic form, so you’re looking for an expression and not a number Seeing this, you should recognize that your job is to take the statement given and reframe it as a restatement of the same fact…just a more useful form. Restatements can come in several ways: * Factor common terms to turn addition/subtraction into multiplication * Multiply a fraction by the same numerator and denominator (so it equals 1) to give it a new expression * Take an equation and do the same thing to both sides to change the look of the expression Here, we can use arguably the most powerful repackaging tool in all of algebra; the Difference of Squares rule. This rule states that \(x^2 y^2 =(x y)(x +y)\). And since we already have \(999999^21^2\) (remember: 1 is the same as 1^2), we can change it to \((999999 + 1)(9999991)\). Why? because now we have 1000000 on the left, and that can be repackaged in exponent form as 10^6, which matches the notation in the answer choices. We needed something with an exponent, and transforming this expression as we did allowed us to do that. So we have: \((10^6)(999998)\) And it’s our job now to repackage the term on the right to match an answer choice. This can be done by stating 999998 as (10^62), giving us: \((10^6)(10^6 2)\) which is answer choice C. What’s important to recognize here is that many algebrabased problems will hinge on your ability to take what you’re given and repackage it as something more useful. In this situation, know your assets. Tools like Difference of Squares can make repackaging algebra quite transformative. Seeing the answer choices as a guide is also instrumental to many of these problems as the choices give you a blueprint of what the algebra ultimately needs to look like. Repackaging is a huge component of the business world, as you can see with products like the Nike Free running shoes (want to run barefoot? We can make that happen – just buy these barefootrunning shoes!) and nearly every movie nowadays (remakes having replaced sequels as the easytogreenlight film category). Keep this principle in mind on the GMAT and you, too, can turn nothing into something, repackaging your 570 as a 750 in no time!
_________________
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 Jun 2017
Posts: 78

Re: 999,999^21 equals:
[#permalink]
Show Tags
15 Oct 2017, 06:48
Bunuel wrote: \(999,999^21\) equals:
(A) \((9^6)(11^6)\)
(B) \((10^6)(10^5 2)\)
(C) \((10^6)(10^6 2)\)
(D) \((10^5)^2\)
(E) \((10^6)^2\)
Kudos for a correct solution. (999,9999 1)(999,999 + 1) = 999,998 x 1,000,000 = (10^6  2) (10^6) Thus, the answer is C




Re: 999,999^21 equals: &nbs
[#permalink]
15 Oct 2017, 06:48






