GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Apr 2019, 07:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 109
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]

### Show Tags

09 Sep 2014, 21:33
2
11
00:00

Difficulty:

45% (medium)

Question Stats:

67% (02:27) correct 33% (02:36) wrong based on 154 sessions

### HideShow timer Statistics

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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9129
Location: Pune, India
Re: Mr. Smith calculated the average of 10 " three digit numbers". But due  [#permalink]

### Show Tags

09 Sep 2014, 21:35
5
2
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

_________________
Karishma
Veritas Prep GMAT Instructor

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1813
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, 01:14
6
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

_________________
Kindly press "+1 Kudos" to appreciate
##### General Discussion
Intern
Joined: 17 Apr 2012
Posts: 14
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, 06:49
1
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: 142
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

19 Sep 2014, 00:45
WOW!! great approach paresh ..!!
_________________
ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.
Intern
Joined: 23 Mar 2015
Posts: 9
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, 04:52
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: 9129
Location: Pune, India
Mr. Smith calculated the average of 10 " three digit numbers". But due  [#permalink]

### Show Tags

10 May 2015, 20:44
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

Non-Human User
Joined: 09 Sep 2013
Posts: 10587
Re: Mr. Smith calculated the average of 10 " three digit numbers". But due  [#permalink]

### Show Tags

09 Aug 2017, 00:33
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.
_________________
Re: Mr. Smith calculated the average of 10 " three digit numbers". But due   [#permalink] 09 Aug 2017, 00:33
Display posts from previous: Sort by