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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

09 Sep 2014, 21:33

1

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

65% (02:09) correct
35% (02:00) wrong based on 139 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 :

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

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

Show Tags

10 Sep 2014, 01:14

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)

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

Show Tags

10 Sep 2014, 06:49

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

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 ?

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.
_________________

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

Show Tags

19 May 2016, 04:39

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.
_________________

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.
_________________