Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 03:13

Close

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
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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many three-digit integers exist such that all their digi

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 26 Jun 2011
Posts: 249
Location: India
GMAT 1: 760 Q51 V41
Followers: 10

Kudos [?]: 31 [0], given: 26

How many three-digit integers exist such that all their digi [#permalink] New post 24 Dec 2011, 02:51
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:34) correct 29% (01:11) wrong based on 51 sessions
How many three-digit integers exist such that all their digits are even?

A. 80
B. 100
C. 120
D. 125
E. 135
[Reveal] Spoiler: OA

_________________

The chase begins ...

Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 549
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 60

Kudos [?]: 272 [0], given: 11

Re: How many three-digit integers exist such that all their digi [#permalink] New post 24 Dec 2011, 03:49
The hundreds digit can be filled in 4 ways (2,4,6,8 but not 0 as in that case the number will become two digit instead of three digit) and the next two can be filled in 5 ways each. Therefore total such numbers = 4 x 5 x 5 = 100
_________________

GyanOne | http://www.GyanOne.com | +91 9899831738

Get a free detailed MBA profile evaluation

Top MBA Rankings and MBA Admissions blog


Image

Director
Director
avatar
Joined: 28 Jul 2011
Posts: 583
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1

Kudos [?]: 38 [0], given: 16

GMAT Tests User
Re: How many three-digit integers exist such that all their digi [#permalink] New post 24 Dec 2011, 06:21
got 100 but took 3 min, but above approach is excellent
_________________

+1 Kudos If found helpful..

Manager
Manager
avatar
Joined: 26 Jun 2011
Posts: 249
Location: India
GMAT 1: 760 Q51 V41
Followers: 10

Kudos [?]: 31 [0], given: 26

Re: How many three-digit integers exist such that all their digi [#permalink] New post 24 Dec 2011, 09:02
GyanOne wrote:
The hundreds digit can be filled in 4 ways (2,4,6,8 but not 0 as in that case the number will become two digit instead of three digit) and the next two can be filled in 5 ways each. Therefore total such numbers = 4 x 5 x 5 = 100


The question says : All digits must be even. Is zero considered even on GMAT? I know the approach, but this is my doubt.
If not, answer should be 4*4*4 = 64.
_________________

The chase begins ...

Director
Director
avatar
Joined: 28 Jul 2011
Posts: 583
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1

Kudos [?]: 38 [0], given: 16

GMAT Tests User
Re: How many three-digit integers exist such that all their digi [#permalink] New post 24 Dec 2011, 18:37
vailad wrote:
GyanOne wrote:
The hundreds digit can be filled in 4 ways (2,4,6,8 but not 0 as in that case the number will become two digit instead of three digit) and the next two can be filled in 5 ways each. Therefore total such numbers = 4 x 5 x 5 = 100


The question says : All digits must be even. Is zero considered even on GMAT? I know the approach, but this is my doubt.
If not, answer should be 4*4*4 = 64.



In Gmat 0 is considered Even so 100 is the answer
_________________

+1 Kudos If found helpful..

Manager
Manager
avatar
Joined: 26 Apr 2011
Posts: 226
Followers: 0

Kudos [?]: 31 [0], given: 12

GMAT ToolKit User GMAT Tests User
Re: How many three-digit integers exist such that all their digi [#permalink] New post 26 Dec 2011, 04:30
total ways =4*5*5=100
Manager
Manager
User avatar
Joined: 03 Jan 2013
Posts: 53
GPA: 3.8
WE: Engineering (Computer Software)
Followers: 0

Kudos [?]: 10 [0], given: 44

Re: How many three-digit integers exist such that all their digi [#permalink] New post 10 Jan 2013, 18:06
dreamchase wrote:
How many three-digit integers exist such that all their digits are even?

80
100
120
125
135


I happened to solve it in less than 30 seconds but wouldn't suggest the approach.
Based on the question, range in which the numbers suggested can exist is from 200 - 888 (both inclusive).
It all starts as 200, 202,204,206,208 --> 5 numbers.
Again it will should start from 220,222,....228 ----> 5 numbers

In 200's, we will have 25 numbers like that. Again, 300's cant have any, nor can 500's or 700's.
Thus, we will be getting valid numbers only from 200's, 400's, 600's, 800's ----> 25*4=100.

If you can think fast, then you can narrow it on to the answer, sooner.
_________________

Giving kudos is a way to appreciate the help done to you.
VOTE: Best resource for Verbal in GMAT
VOTE: Best resource for Quant in GMAT

Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 92
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 24 [0], given: 0

Re: How many three-digit integers exist such that all their digi [#permalink] New post 11 Jan 2013, 06:49
4 possibilities for 1st digit --> 2,4,6,8
5 possibilities for 2nd digit ---> 0,2,4,6,8
5 possibilities for 3rd digit ----> 0,2,4,6,8

Therefore.. 4x5x5 = 100 different even numbers (B)
Manager
Manager
User avatar
Joined: 12 Jan 2013
Posts: 58
Location: United States (NY)
GMAT 1: 780 Q51 V47
GPA: 3.89
Followers: 11

Kudos [?]: 48 [0], given: 13

Re: How many three-digit integers exist such that all their digi [#permalink] New post 12 Jan 2013, 22:28
anuj4ufriends wrote:
I happened to solve it in less than 30 seconds but wouldn't suggest the approach.
Based on the question, range in which the numbers suggested can exist is from 200 - 888 (both inclusive).
It all starts as 200, 202,204,206,208 --> 5 numbers.
Again it will should start from 220,222,....228 ----> 5 numbers

In 200's, we will have 25 numbers like that. Again, 300's cant have any, nor can 500's or 700's.
Thus, we will be getting valid numbers only from 200's, 400's, 600's, 800's ----> 25*4=100.

If you can think fast, then you can narrow it on to the answer, sooner.


Well, I still did it in less than 10 seconds using the 4*5*5 approach. I was recently helping out a friend to prepare for his GMAT, and he was amazed by the simplicity of this approach in a very similar problem. He was also trying to count the numbers, but he was not nearly as fast... It reminds me the story about John von Neumann and the Two Trains puzzle. In case you don't remember, here is the puzzle:

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards the other at a speed of 75 km/h. Upon reaching the other train, the fly turns around and continues towards the first train. How many kilometers does the fly travel before getting squashed in the collision of the two trains?

[Reveal] Spoiler:
John von Neumann is reputed to have immediately answered with the correct result. When subsequently asked if he had heard the short-cut solution, he answered no, that his immediate answer had been a result of explicitly summing the series.

_________________

Sergey Orshanskiy, Ph.D.
I tutor in NYC: http://www.wyzant.com/Tutors/NY/New-Yor ... ref=1RKFOZ

Manager
Manager
User avatar
Joined: 03 Jan 2013
Posts: 53
GPA: 3.8
WE: Engineering (Computer Software)
Followers: 0

Kudos [?]: 10 [0], given: 44

Re: How many three-digit integers exist such that all their digi [#permalink] New post 12 Jan 2013, 22:31
SergeyOrshanskiy wrote:
anuj4ufriends wrote:
I happened to solve it in less than 30 seconds but wouldn't suggest the approach.
Based on the question, range in which the numbers suggested can exist is from 200 - 888 (both inclusive).
It all starts as 200, 202,204,206,208 --> 5 numbers.
Again it will should start from 220,222,....228 ----> 5 numbers

In 200's, we will have 25 numbers like that. Again, 300's cant have any, nor can 500's or 700's.
Thus, we will be getting valid numbers only from 200's, 400's, 600's, 800's ----> 25*4=100.

If you can think fast, then you can narrow it on to the answer, sooner.


Well, I still did it in less than 10 seconds using the 4*5*5 approach. I was recently helping out a friend to prepare for his GMAT, and he was amazed by the simplicity of this approach in a very similar problem. He was also trying to count the numbers, but he was not nearly as fast... It reminds me the story about John von Neumann and the Two Trains puzzle. In case you don't remember, here is the puzzle:

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards the other at a speed of 75 km/h. Upon reaching the other train, the fly turns around and continues towards the first train. How many kilometers does the fly travel before getting squashed in the collision of the two trains?

[Reveal] Spoiler:
John von Neumann is reputed to have immediately answered with the correct result. When subsequently asked if he had heard the short-cut solution, he answered no, that his immediate answer had been a result of explicitly summing the series.


That's the reason why I said I dont suggest it.
_________________

Giving kudos is a way to appreciate the help done to you.
VOTE: Best resource for Verbal in GMAT
VOTE: Best resource for Quant in GMAT

Director
Director
avatar
Joined: 17 Apr 2013
Posts: 510
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 23 [0], given: 238

CAT Tests
Re: How many three-digit integers exist such that all their digi [#permalink] New post 19 Jun 2014, 01:46
Bunuel,

This is Quantitative :: Problem solving :: Probability & Combinations :: M13-14

0 is also an even integer
so last digit can be filled in 5 ways- 0,2,4,6,8

for both second and third digit there are 5 possibilities-

5 X 5 X 5 = 125
_______________

This is the solution given at Gmatclubtest

The first digit can be any of the four: 2, 4, 6, or 8. For both second and third digits, there are 5 possibilities. The answer is 4∗5∗5=100.
The correct answer is B
_________________

Like my post Send me a Kudos :) It is a Good manner.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19027
Followers: 3359

Kudos [?]: 24348 [0], given: 2677

Re: How many three-digit integers exist such that all their digi [#permalink] New post 19 Jun 2014, 01:49
Expert's post
honchos wrote:
How many three-digit integers exist such that all their digits are even?

A. 80
B. 100
C. 120
D. 125
E. 135

Bunuel,

This is Quantitative :: Problem solving :: Probability & Combinations :: M13-14

0 is also an even integer
so last digit can be filled in 5 ways- 0,2,4,6,8

for both second and third digit there are 5 possibilities-

5 X 5 X 5 = 125
_______________

This is the solution given at Gmatclubtest

The first digit can be any of the four: 2, 4, 6, or 8. For both second and third digits, there are 5 possibilities. The answer is 4∗5∗5=100.
The correct answer is B


If the first digit is 0, then the number becomes two-digit, not three-digit.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 17 Apr 2013
Posts: 510
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 23 [0], given: 238

CAT Tests
Re: How many three-digit integers exist such that all their digi [#permalink] New post 19 Jun 2014, 01:52
Bunuel wrote:
honchos wrote:
How many three-digit integers exist such that all their digits are even?

A. 80
B. 100
C. 120
D. 125
E. 135

Bunuel,

This is Quantitative :: Problem solving :: Probability & Combinations :: M13-14

0 is also an even integer
so last digit can be filled in 5 ways- 0,2,4,6,8

for both second and third digit there are 5 possibilities-

5 X 5 X 5 = 125
_______________

This is the solution given at Gmatclubtest

The first digit can be any of the four: 2, 4, 6, or 8. For both second and third digits, there are 5 possibilities. The answer is 4∗5∗5=100.
The correct answer is B


If the first digit is 0, then the number becomes two-digit, not three-digit.


My fault, i thought with first digit you mean unit digit. I took the explanation in the reverse order.
My bad I am sorry.

Solution was slightly confusing, if terms like unit,tens and 100th digits were used the confusion would have been avoided.

Thanks Bunuel.
_________________

Like my post Send me a Kudos :) It is a Good manner.

Re: How many three-digit integers exist such that all their digi   [#permalink] 19 Jun 2014, 01:52
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic How many three-digit integers are not divisible by 3 ? gmatcracker2010 3 12 Jun 2010, 11:02
1 How many odd three-digit integers elmagnifico 15 23 Sep 2008, 06:01
1 of the three-digit integers greater than 700, how many have sondenso 5 28 Apr 2008, 22:20
How many positive three-digit positive integers are kevincan 5 19 Sep 2006, 12:43
Of the three-digit integers greater than 700, how many have omomo 4 18 Feb 2006, 14:44
Display posts from previous: Sort by

How many three-digit integers exist such that all their digi

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.