It is currently 14 Dec 2017, 20:36

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M22-16

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42604

Kudos [?]: 135673 [0], given: 12706

M22-16 [#permalink]

Show Tags

New post 16 Sep 2014, 00:16
Expert's post
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

52% (01:24) correct 48% (02:40) wrong based on 46 sessions

HideShow timer Statistics

Kudos [?]: 135673 [0], given: 12706

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42604

Kudos [?]: 135673 [2], given: 12706

Re M22-16 [#permalink]

Show Tags

New post 16 Sep 2014, 00:16
2
This post received
KUDOS
Expert's post
Official Solution:

How many three-digit integers greater than 710 are there such that all their digits are different?

A. 198
B. 202
C. 207
D. 209
E. 212


First find how many integers between 700 and 999 are such that all their digits are different.

We have : \(\text{(3 options for the first digit)}*\text{(9 options for the second digit)}*\text{(8 options for the third digit)} = 216\) numbers.

Among these 216 numbers, 9 (701, 702, 703, 704, 705, 706, 708, 709, 710) are not bigger than 710. The answer to the question is therefore \(216 - 9 = 207\).


Answer: C
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135673 [2], given: 12706

Intern
Intern
avatar
Joined: 19 Sep 2011
Posts: 2

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

Re: M22-16 [#permalink]

Show Tags

New post 28 Nov 2015, 04:53
i think you have missed one number 707

216-10

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

Expert Post
2 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5352

Kudos [?]: 6132 [2], given: 121

Re: M22-16 [#permalink]

Show Tags

New post 28 Nov 2015, 06:27
2
This post received
KUDOS
Expert's post
ekia wrote:
i think you have missed one number 707

216-10


Hi,
216 is the total number where all digits are different..
707 has 7 at two places, so 707 has not been taken as a part of these 216 numbers..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6132 [2], given: 121

Manager
Manager
avatar
Joined: 05 Aug 2015
Posts: 55

Kudos [?]: 39 [0], given: 36

Re: M22-16 [#permalink]

Show Tags

New post 12 Mar 2016, 13:19
Hi guys, I understand the solution above but have trouble seeing what I did wrong - can you please help?

If the first digit is 7: 2nd slot can be anything from #2 to #9 with the exception of 7, so that's 9-2+1-1=7; 3rd slot can be anything from #1 to #9 with the exception of #7 and the digit in the 2nd slot, so that's 9-1+1-2=7; so the total number of digit combinations is 7*7 = 49 numbers

If the first digit is 8: 2nd slot can be anything from #0 to #9 with the exception of 9, so that's 9-0+1-1=9; 3rd slot can be anything from #0 to #9 with the exception of #8 and the digit in the 2nd slot, so that's 9-0+1-2=8; so the total number of digit combinations is 9*8 = 72 numbers

If the first digit is 9: the combination is the same as if the first digit is 8. So, 72.

Together there are 49 + 2*72 = 193 combinations ...

What did I do wrong? Thank you!!
_________________

Working towards 25 Kudos for the Gmatclub Exams - help meee I'm poooor

Kudos [?]: 39 [0], given: 36

Intern
Intern
avatar
Joined: 25 Jul 2015
Posts: 1

Kudos [?]: [0], given: 5

Re M22-16 [#permalink]

Show Tags

New post 28 May 2016, 05:35
I think this is a high-quality question and I don't agree with the explanation. Question asks for three-digit integers such that all their digits are different, then below numbers should not be included right?
example - 777, 788, 799, 888, 899, 877 etc..

Kudos [?]: [0], given: 5

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42604

Kudos [?]: 135673 [0], given: 12706

Re: M22-16 [#permalink]

Show Tags

New post 28 May 2016, 05:37
santanu1b wrote:
I think this is a high-quality question and I don't agree with the explanation. Question asks for three-digit integers such that all their digits are different, then below numbers should not be included right?
example - 777, 788, 799, 888, 899, 877 etc..


Yes, those numbers should not and are not included.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135673 [0], given: 12706

Intern
Intern
avatar
Joined: 16 Feb 2012
Posts: 11

Kudos [?]: 7 [0], given: 3

GMAT 1: 650 Q47 V33
Reviews Badge
Re: M22-16 [#permalink]

Show Tags

New post 04 Dec 2016, 07:37
Bunuel,

I solved the question in the below way. Please correct me if wrong.

Per the question, we have 3 options(7,8,9) for the first digit.

1) 188 = 64 ----- 7 is the first digit here

2) 198 = 72 ------ 8 is the first digit here

3) 198 = 72 ------- 9 is the first digit here

So total is 64+72+72 = 208.
However, in the first case we have to remove one number to account for 710. So answer is 207.

Kudos [?]: 7 [0], given: 3

Intern
Intern
avatar
B
Joined: 17 Feb 2017
Posts: 5

Kudos [?]: 0 [0], given: 1

CAT Tests
Re: M22-16 [#permalink]

Show Tags

New post 30 Nov 2017, 00:54
happyface101 wrote:
Hi guys, I understand the solution above but have trouble seeing what I did wrong - can you please help?

If the first digit is 7: 2nd slot can be anything from #2 to #9 with the exception of 7, so that's 9-2+1-1=7; 3rd slot can be anything from #1 to #9 with the exception of #7 and the digit in the 2nd slot, so that's 9-1+1-2=7; so the total number of digit combinations is 7*7 = 49 numbers

If the first digit is 8: 2nd slot can be anything from #0 to #9 with the exception of 9, so that's 9-0+1-1=9; 3rd slot can be anything from #0 to #9 with the exception of #8 and the digit in the 2nd slot, so that's 9-0+1-2=8; so the total number of digit combinations is 9*8 = 72 numbers

If the first digit is 9: the combination is the same as if the first digit is 8. So, 72.

Together there are 49 + 2*72 = 193 combinations ...

What did I do wrong? Thank you!!




I also approached the question in the above way.

Bunuel, can you please explain?

Kudos [?]: 0 [0], given: 1

Manager
Manager
User avatar
G
Joined: 27 Dec 2016
Posts: 199

Kudos [?]: 50 [0], given: 228

Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Premium Member CAT Tests
Re: M22-16 [#permalink]

Show Tags

New post 04 Dec 2017, 14:45
jasanisanket24 wrote:
happyface101 wrote:
Hi guys, I understand the solution above but have trouble seeing what I did wrong - can you please help?

If the first digit is 7: 2nd slot can be anything from #2 to #9 with the exception of 7, so that's 9-2+1-1=7; 3rd slot can be anything from #1 to #9 with the exception of #7 and the digit in the 2nd slot, so that's 9-1+1-2=7; so the total number of digit combinations is 7*7 = 49 numbers

If the first digit is 8: 2nd slot can be anything from #0 to #9 with the exception of 9, so that's 9-0+1-1=9; 3rd slot can be anything from #0 to #9 with the exception of #8 and the digit in the 2nd slot, so that's 9-0+1-2=8; so the total number of digit combinations is 9*8 = 72 numbers

If the first digit is 9: the combination is the same as if the first digit is 8. So, 72.

Together there are 49 + 2*72 = 193 combinations ...

What did I do wrong? Thank you!!




I also approached the question in the above way.

Bunuel, can you please explain?


Try to explain :

- You did the correct calculation for 8 and 9 hundred digit.
- Anyway, you miscalculated for the 7 hundred digit : don't forget the 0 number in the ten and unit digit. That's why, the number of digits possible is 1*8*7, not 1*7*7. After this, you must add manually the number from 710-719 (which is 7 different number).

Hope it helps.
_________________

There's an app for that - Steve Jobs.

Kudos [?]: 50 [0], given: 228

Re: M22-16   [#permalink] 04 Dec 2017, 14:45
Display posts from previous: Sort by

M22-16

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.