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 350,000 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:

How many integers k greater than 100 and less than 1000 are [#permalink]
17 Sep 2010, 04:39

1

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

58% (03:28) correct
42% (02:23) wrong based on 67 sessions

How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?

How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reverced, the resulting integer is k + 99?

50 60 70 80 90

please provide explaination .. with minimal calculations

Some wording. Anyway:

\(k\) is 3-digit integer. Any 3 digit integer can be expressed as \(100a+10b+c\).

Now, we are told that \((100a+10b+c)+99=100c+10b+a\) --> \(99c-99a=99\) --> \(c-a=1\) --> there are 8 pairs of \(c\) and \(a\) possible such that their difference to be 1: (9,8), (8,7), ..., and (2,1) (note that \(a\) can not be 0 as \(k\) is 3-digit integer and its hundreds digit, \(a\), is more than or equal to 1).

Also, \(b\), tens digit of \(k\), could tale 10 values (0, 1, ..., 9) so there are total of 8*10=80 such numbers possible.

How many integers k greater than 100 and less than 1000 are there such that if the hundreds and the unit digits of k are reverced, the resulting integer is k + 99?

50 60 70 80 90

please provide explaination .. with minimal calculations

Not sure if this is the shortest.. But this is how I did this

There are 8 sets of integers with hundreds and units digits exchanged that satisfies k + 99. 1. 102 | 201 (satisfies k+99, where k = 102) 2. 203 | 302 (satisfies k+99, where k = 203) 3. ... 4. ... 5. ... 6. ... 7. 708 | 807 8. 809 | 908

Re: How many integers k greater than 100 and less than 1000 are [#permalink]
10 Jan 2014, 07:46

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. _________________

How many integers K greater that 100 and less than 1000 are [#permalink]
15 May 2014, 12:45

How many integers K greater that 100 and less than 1000 are there such that if the hundreds and the units digits of K are reversed, the resulting integer is K+99?

Re: How many integers K greater that 100 and less than 1000 are [#permalink]
15 May 2014, 17:22

2

This post received KUDOS

Ans is D. The hundredth digit is always smaller from units digit by 1 as obtained by solving the equation 100a+10b+c+99=100c+10b+a. So 'a' can have values from 1 to 8 and for every value of a, 'b' varies from 0 to 9. So total integers are 8×10.

Re: How many integers K greater that 100 and less than 1000 are [#permalink]
15 May 2014, 17:22

tinku21rahu wrote:

How many integers K greater that 100 and less than 1000 are there such that if the hundreds and the units digits of K are reversed, the resulting integer is K+99?

a) 50 b) 60 c) 70 d) 80 e) 90

I think the answer is D - 80 integers. My logic is as follows:

Since we are adding 99, the hundreds digit will need to be less than the ones digit if the corresponding number when the two digits flipped is to be larger. Since the change in magnitude is just shy of 100, the different between the two can only be one.

Look at an example case of 100 < X < 200

102 -> 201

112 -> 211

...

192 -> 291

What about for 800 < X < 900?

809 -> 908

819 -> 918

...

899 -> 998

For each of these samples, there are 10 numbers between the two stated bounds (the tens digit ranges from 0 to 9). Since we can't do this for 900 < X < 1,000, there are 8 sets of 10, or 80 total integers.

Hopefully that makes sense (and correct!). Let me know if I'm missing something here!

Re: How many integers K greater that 100 and less than 1000 are [#permalink]
16 May 2014, 07:15

GordonFreeman: What you said said is 100% correct and that was the way i solved it, but that took me lot of time, Do you feel there is any easier was like PuneetSood Said.

PuneetSood: What you said seems to be an Easy Way. Thank You!

Re: How many integers K greater that 100 and less than 1000 are [#permalink]
16 May 2014, 07:43

tinku21rahu wrote:

GordonFreeman: What you said said is 100% correct and that was the way i solved it, but that took me lot of time, Do you feel there is any easier was like PuneetSood Said.

PuneetSood: What you said seems to be an Easy Way. Thank You!

PuneetSood's method is definitely slicker than mine. I only started my GMAT journey this week so when I approach problems like this I like to see all the moving parts. After I am more comfortable with a problem type I would opt for an approach like PuneetSood's.

Re: How many integers K greater that 100 and less than 1000 are [#permalink]
16 May 2014, 18:13

tinku21rahu wrote:

GordonFreeman: What you said said is 100% correct and that was the way i solved it, but that took me lot of time, Do you feel there is any easier was like PuneetSood Said.

PuneetSood: What you said seems to be an Easy Way. Thank You!

From here, we can assume that the hundreds digit and units digit must be 1 digit apart in order to satisfy this condition.

Only 9 options are possible: 9x8,8x7,7x6,6x5,5x4,4x3,3x2,2x1,1x0

We are also told in the question stem that we are restricted among 3 digits only which eliminates the 1x0 option. Now, there are only 8 possible options left. Since there is no restriction in the tens digits,

Re: How many integers K greater that 100 and less than 1000 are [#permalink]
26 May 2014, 23:59

Expert's post

tinku21rahu wrote:

How many integers K greater that 100 and less than 1000 are there such that if the hundreds and the units digits of K are reversed, the resulting integer is K+99?

a) 50 b) 60 c) 70 d) 80 e) 90

Merging similar topics. Please refer to the discussion above. _________________

Re: How many integers k greater than 100 and less than 1000 are [#permalink]
27 May 2014, 16:04

Let the 3 digit number be xyz If the units and hundred's digit is reversed then the number becomes zyx

Given:- 100z + 10y + x = 100x + 10y + z + 99

100z + 10y + x = 100x + 10y + z + 99

or, 99z - 99x = 99 or, 99(z-x)=99 or, z=x+1

which means z can take only 1 value i.e 1 more than x

Now in the original number xyz, y can take 10 values 0 through 9 x can take 1-8(8 values) and for each x, z can take exactly 1 value (from 2 through 9)

so 8 (values for x and z) X 10 (values of y) = 80. Hence D

gmatclubot

Re: How many integers k greater than 100 and less than 1000 are
[#permalink]
27 May 2014, 16:04

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...