Oct 14 08:00 PM PDT  11:00 PM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R2.**Limited for the first 99 registrants. Register today! Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 17 May 2017
Posts: 119
GPA: 3

If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
Updated on: 24 Jun 2017, 06:37
Question Stats:
57% (01:17) correct 43% (01:41) wrong based on 283 sessions
HideShow timer Statistics
If n is greater than 20, what is the number closest to n^100  n^90? A) n^90 B) n^100 C) n^99 D) n^190 E) n^10
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by haardiksharma on 24 Jun 2017, 05:50.
Last edited by haardiksharma on 24 Jun 2017, 06:37, edited 3 times in total.




Math Expert
Joined: 02 Sep 2009
Posts: 58311

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
24 Jun 2017, 06:42




Manager
Joined: 30 Mar 2017
Posts: 69

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
24 Jun 2017, 05:58
It can be deduced to n^90(n^101) Since n is greater than 20 so n^101~ n^10. So it will be closest to n^100. B Sent from my Moto G (5) Plus using GMAT Club Forum mobile app



Manager
Joined: 17 May 2017
Posts: 119
GPA: 3

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
24 Jun 2017, 06:43



Manager
Joined: 05 Nov 2014
Posts: 103
Location: India
Concentration: Strategy, Operations
GPA: 3.75

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
24 Jun 2017, 06:58
Solution:
n>20. n^100n^90 .Take n to be 100 for example. 100^100100^90. Simplifying, 100^90{(10^10) 1} Comparing to the value of 10^10, 1 is negligible.
Therefore, the answer is Option B.



Senior Manager
Joined: 28 May 2017
Posts: 281
Concentration: Finance, General Management

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
24 Jun 2017, 07:05
haardiksharma wrote: If n is greater than 20, what is the number closest to n^100  n^90?
A) n^90 B) n^100 C) n^99 D) n^190 E) n^10 n^100  n^90 n^90 (n^10  1) Since n is greater than 20, n^20 would be a very large number. Thus we may we write n^90 (n^10  1) = n^90 (n^10) = n^100 Answer B
_________________
If you like the post, show appreciation by pressing Kudos button



VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1017
WE: Supply Chain Management (Energy and Utilities)

If n is greater than 20, what number is closest to n^100  n^90
[#permalink]
Show Tags
07 Jul 2018, 20:37
\(n^{100}n^{90}\) can be written as \(n^{90}(n^{10}1)\) \((n^{10}1)\) can be approximated to \(n^{10}\) since 1 is negligible in comparison to \(n^{10}\) when n>20. So our expression becomes \(n^{90}*n^{10}=n^{100}\). Ans. (B) Posted from my mobile device
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12

If n is greater than 20, what number is closest to n^100  n^90
[#permalink]
Show Tags
08 Jul 2018, 12:05
Karthik200 wrote: If n is greater than 20, what number is closest to \(n^{100}  n^{90}\)
A. \(n^{90}\) B. \(n^{100}\) C. \(n^{99}\) D. \(n^{190}\) E. \(n^{10}\) Since n is a number greater than 20, for simplicity sake, let's assume this number to be \(25\) or \(5^2\) \((5^2)^{100}  (5^2)^{90} = 5^{200}  5^{180} = 5^{180}(5^{20}  1) = 5^{180}(5^{20}) = 5^{180+20} = 5^{200} = (5^2)^{100}\) This is because \(3125*3125*3125*3125  1\) is almost the same as \(3125*3125*3125*3125\). So, we can extrapolate this result for n = 25 to show that \(n^{100}  n^{90} = n^{100}\) (Option B)
_________________
You've got what it takes, but it will take everything you've got



Intern
Joined: 08 Jul 2018
Posts: 39

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
11 Jul 2018, 22:43
Karthik200 wrote: If n is greater than 20, what number is closest to \(n^{100}  n^{90}\)
A. \(n^{90}\) B. \(n^{100}\) C. \(n^{99}\) D. \(n^{190}\) E. \(n^{10}\) \(n^{90} (n^{10}1)\) \(n^{90+10}\) (1 can be neglected) B
_________________
“Pain + Reflection = Progress” ― Ray Dalio



Director
Joined: 12 Feb 2015
Posts: 915

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
16 Jul 2018, 09:22
\(n^{90}\) * \((n^{10}1)\) is as good as \(n^{90}*n^{10} = n^{100}\) Hence option B is the correct answer.
_________________



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
19 Jul 2018, 12:36
haardiksharma wrote: If n is greater than 20, what is the number closest to n^100  n^90?
A) n^90 B) n^100 C) n^99 D) n^190 E) n^10 Factoring n^90 from both terms, we have: n^90(n^10  1). Now, since n is relatively large, we see that (n^10  1) is essentially equal to n^10. We can thus simplify the expression n^90(n^10  1) to n^90(n^10) = n^100. Answer: B
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



VP
Joined: 09 Mar 2016
Posts: 1230

If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
27 Jul 2018, 09:42
pushpitkc wrote: Karthik200 wrote: If n is greater than 20, what number is closest to \(n^{100}  n^{90}\)
A. \(n^{90}\) B. \(n^{100}\) C. \(n^{99}\) D. \(n^{190}\) E. \(n^{10}\) Since n is a number greater than 20, for simplicity sake, let's assume this number to be \(25\) or \(5^2\) \((5^2)^{100}  (5^2)^{90} = 5^{200}  5^{180} = 5^{180}(5^{20}  1) = 5^{180}(5^{20}) = 5^{180+20} = 5^{200} = (5^2)^{100}\) This is because \(3125*3125*3125*3125  1\) is almost the same as \(3125*3125*3125*3125\). So, we can extrapolate this result for n = 25 to show that \(n^{100}  n^{90} = n^{100}\) (Option B)
pushpitkc what is formula of exponents when i need to perform subtraction \(Y^xz^q\) for example \(6^{18}5^8\) how should I solve this



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
27 Jul 2018, 22:03
dave13 wrote: pushpitkc wrote: Karthik200 wrote: If n is greater than 20, what number is closest to \(n^{100}  n^{90}\)
A. \(n^{90}\) B. \(n^{100}\) C. \(n^{99}\) D. \(n^{190}\) E. \(n^{10}\) Since n is a number greater than 20, for simplicity sake, let's assume this number to be \(25\) or \(5^2\) \((5^2)^{100}  (5^2)^{90} = 5^{200}  5^{180} = 5^{180}(5^{20}  1) = 5^{180}(5^{20}) = 5^{180+20} = 5^{200} = (5^2)^{100}\) This is because \(3125*3125*3125*3125  1\) is almost the same as \(3125*3125*3125*3125\). So, we can extrapolate this result for n = 25 to show that \(n^{100}  n^{90} = n^{100}\) (Option B)
pushpitkc what is formula of exponents when i need to perform subtraction \(Y^xz^q\) for example \(6^{18}5^8\) how should I solve this Hey dave13Unfortunately, there is no formula to solve \(6^{18}  5^8\) as the bases have no common factor However, if the expression we were asked to find the value for was \(6^{18}  3^8\), we could simplify it as follows  \(3*2^{18}  3^8\) = \(3^8(3^{10}*2^{18}  1)\) P.S there must be a common factor in Y and z(which I have highlighted in your post) for us to make this simplification. Hope this clears your confusion!
_________________
You've got what it takes, but it will take everything you've got



Math Expert
Joined: 02 Sep 2009
Posts: 58311

Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
Show Tags
28 Jul 2018, 04:27
pushpitkc wrote: dave13 wrote: pushpitkc wrote: If n is greater than 20, what number is closest to \(n^{100}  n^{90}\)
A. \(n^{90}\) B. \(n^{100}\) C. \(n^{99}\) D. \(n^{190}\) E. \(n^{10}\)
Since n is a number greater than 20, for simplicity sake, let's assume this number to be \(25\) or \(5^2\)
\((5^2)^{100}  (5^2)^{90} = 5^{200}  5^{180} = 5^{180}(5^{20}  1) = 5^{180}(5^{20}) = 5^{180+20} = 5^{200} = (5^2)^{100}\)
This is because \(3125*3125*3125*3125  1\) is almost the same as \(3125*3125*3125*3125\).
So, we can extrapolate this result for n = 25 to show that \(n^{100}  n^{90} = n^{100}\)(Option B)
pushpitkc what is formula of exponents when i need to perform subtraction \(Y^xz^q\) for example \(6^{18}5^8\) how should I solve this Hey dave13Unfortunately, there is no formula to solve \(6^{18}  5^8\) as the bases have no common factor However, if the expression we were asked to find the value for was \(6^{18}  3^8\), we could simplify it as follows  \(3*2^{18}  3^8\) = \(3^8(3^{10}*2^{18}  1)\) P.S there must be a common factor in Y and z(which I have highlighted in your post) for us to make this simplification. Hope this clears your confusion! You can factor \(6^{18}  5^8\) by applying a^2  b^2 = (a  b)(a + b): \(6^{18}  5^8=(6^{9})^2  (5^4)^2=(6^9  5^4)(6^9 + 5^4)\). But the easiest approach to solve this problem is given HERE or in any of the links given in this post.
_________________




Re: If n is greater than 20, what is the number closest to n^100  n^90?
[#permalink]
28 Jul 2018, 04:27






