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# Mr. Smith calculated the average of 10 " three digit numbers". But due

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Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 130
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink]

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09 Sep 2014, 20:33
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45% (medium)

Question Stats:

65% (02:09) correct 35% (02:01) wrong based on 142 sessions

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Mr. Smith calculated the average of 10 " three digit numbers". But due to a mistake he reversed the digits of a number and thus his average increased by 29.7. The difference between the unit digit and hundreds digit of that number is :

a) 4
b) 3
c) 2
d) 1
e) 0
[Reveal] Spoiler: OA
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Joined: 16 Oct 2010
Posts: 7934
Location: Pune, India
Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink]

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09 Sep 2014, 20:35
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Ashishmathew01081987 wrote:
Mr. Smith calculated the average of 10 " three digit numbers". But due to a mistake he reversed the digits of a number and thus his average increased by 29.7. The difference between the unit digit and hundreds digit of that number is :

a) 4
b) 3
c) 2
d) 1
e) 0

Since the average increased by 29.7 and there were a total of 10 numbers, it means the incorrect number was 297 greater than the correct number.

Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.

100c + 10b + a - (100a + 10b + c) = 297
99c - 99a = 99(c - a) = 297
297 = 99*3 = 99(c - a)
So c - a = 3

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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1839 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink] ### Show Tags 10 Sep 2014, 00:14 6 This post received KUDOS Ashishmathew01081987 wrote: Mr. Smith calculated the average of 10 " three digit numbers". But due to a mistake he reversed the digits of a number and thus his average increased by 29.7. The difference between the unit digit and hundreds digit of that number is : a) 4 b) 3 c) 2 d) 1 e) 0 Let the total of first 9 numbers = x Let the 10th number = abc = 100a + 10b + c (3 digit number expansion) Let the total of 10 numbers = t Average $$= \frac{x + abc}{10} = t$$ x + 100a + 10b + c = 10t ................. (1) 10th number reversed = cba = 100c + 10b + a New Average$$= \frac{x + cba}{10} = t + 29.7$$ x + 100c + 10b + a = 10t + 297 ............... (2) (2) - (1) 99(c-a) = 297 c-a = 3 Answer = B _________________ Kindly press "+1 Kudos" to appreciate Intern Joined: 17 Apr 2012 Posts: 16 Location: United States WE: Information Technology (Computer Software) Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink] ### Show Tags 10 Sep 2014, 05:49 1 This post received KUDOS average difference is 29.7 for 10 integer. with all 9 number remaining the same, difference between the 10th number will be 297. a b c c b a ------ 2 9 7 ------ in the subtraction, b - b should be 0. but it is 9. hence it has borrowed 1 from a. after borrowing 1, (a-c) = 2. So adding 1, difference between unit and hundred digits will be, (a-c) = 3 Manager Status: PLAY HARD OR GO HOME Joined: 25 Feb 2014 Posts: 173 Location: India Concentration: General Management, Finance Schools: Mannheim GMAT 1: 560 Q46 V22 GPA: 3.1 Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink] ### Show Tags 18 Sep 2014, 23:45 WOW!! great approach paresh ..!! _________________ ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD. Intern Joined: 23 Mar 2015 Posts: 10 Location: India Concentration: Operations, Technology GMAT 1: 690 Q49 V34 GMAT 2: 700 Q49 V35 Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink] ### Show Tags 09 May 2015, 03:52 One question that came up while solving this problem was which digits were reversed i.e.whether it is between 1000s & 100s, 100s & unit or 1000s & unit. It couldn't be between 100s & unit because then we will get only a 2-digit or 1-digit difference but here it is coming as 297. It couldn't be between 1000s & 100s because then the last digit of difference quoted would have been 0 (eg: 812 - 182 = 630 ). So it must be 1000s & unit. Any other easy ways to identify which positions got swapped OR any other thought process to get rid of this step ? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7934 Location: Pune, India Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink] ### Show Tags 10 May 2015, 19:44 anilbhatt1 wrote: One question that came up while solving this problem was which digits were reversed i.e.whether it is between 1000s & 100s, 100s & unit or 1000s & unit. It couldn't be between 100s & unit because then we will get only a 2-digit or 1-digit difference but here it is coming as 297. It couldn't be between 1000s & 100s because then the last digit of difference quoted would have been 0 (eg: 812 - 182 = 630 ). So it must be 1000s & unit. Any other easy ways to identify which positions got swapped OR any other thought process to get rid of this step ? When you reverse the digits of a 3 digit number, abc, you get cba. If you reverse the digits of a 4 digit number, abcd, you get dcba. and so on... Until and unless you are given some specific information such as "the last two digits of a 4 digit number were reversed" - In that case, abcd becomes abdc. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink]

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19 May 2016, 03:39
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).

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Re: Mr. Smith calculated the average of 10 " three digit numbers". But due [#permalink]

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08 Aug 2017, 23:33
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.
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Re: Mr. Smith calculated the average of 10 " three digit numbers". But due   [#permalink] 08 Aug 2017, 23:33
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