|
Author |
Message |
|
TAGS:
|
|
|
Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 327
Followers: 9
Kudos [?]:
180
[2] , given: 19
|
How many odd three-digit integers greater than 800 are there [#permalink]
 22 May 2010, 21:33
2
This post received
KUDOS
Question Stats:
58% (02:19) correct
41% (01:43) wrong based on 3 sessions
How many odd three-digit integers greater than 800 are there such that all their digits are different? A. 40 B. 60 C. 72 D. 81 E. 104
_________________
press kudos, if you like the explanation, appreciate the effort or encourage people to respond.
Download the Ultimate SC Flashcards
Last edited by Bunuel on 04 Feb 2012, 08:10, edited 1 time in total.
Edited the question and added the OA
|
|
|
|
|
|
|
Intern
Joined: 21 Apr 2010
Posts: 31
GMAT 1: 710 Q48 V40
Followers: 0
Kudos [?]:
15
[1] , given: 0
|
Re: odd 3 digit integers [#permalink]
22 May 2010, 23:03
1
This post received
KUDOS
Alright so you need odd number so the first odd number is 801 and the last odd number is that is different is 987 there a total of {(987-801)/2} + 1 odd numbers. There are 94 odd numbers. Now you need to get rid of odd numbers that violate the rule that each digit must be different. there a total of 5 odd numbers digits per group of tens - >1,3,5,7,9. From 801 to 879 you count all the odds till this point but you discard all the odd in the 80s group which there are 5 -> 81, 83,85,87,89 - and you discard one odd in 50s -> 855 . The 900 forces you to make an additional consideration. There is one less odd per group of ten since you'll have a repeat of 9 - example 909, 919. There are only 4 odd numbers per group of ten and you also get rid of 955. There are a total 8 numbers that you exclude in the 900s on the way up to 987. So the total number of odds you discard is 13 So the answer is 94 -13 = 81 IF that helped a kudo would be nice
_________________
Ps. Kudos are always welcomed ; )
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[8] , given: 829
|
Re: odd 3 digit integers [#permalink]
23 May 2010, 01:23
8
This post received
KUDOS
dimitri92 wrote: Ok so this is a gmatclub test but I don't get the explanation. Can someone help?
How many odd three-digit integers greater than 800 are there such that all their digits are different?
40
60
72
81
104 In the range 800 - 900:1 choice for the first digit: 8; 5 choices for the third digit: 1, 3, 5, 7, 9; 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*5*8 = 40. In the range 900 - 999:1 choice for the first digit: 9; 4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit); 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*4*8 = 32. Total: 40+32 = 72. Answer: C. Hope it's clear.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 327
Followers: 9
Kudos [?]:
180
[1] , given: 19
|
Re: odd 3 digit integers [#permalink]
23 May 2010, 03:44
1
This post received
KUDOS
Bunuel wrote: dimitri92 wrote: Ok so this is a gmatclub test but I don't get the explanation. Can someone help?
How many odd three-digit integers greater than 800 are there such that all their digits are different?
40
60
72
81
104 In the range 800 - 900:1 choice for the first digit: 8; 5 choices for the third digit: 1, 3, 5, 7, 9; 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*5*8 = 40. In the range 900 - 999:1 choice for the first digit: 9; 4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit); 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*4*8 = 32. Total: 40+32 = 72. Answer: C. Hope it's clear. wow amazing approach ... now this is crystal clear !!
_________________
press kudos, if you like the explanation, appreciate the effort or encourage people to respond.
Download the Ultimate SC Flashcards
|
|
|
|
|
|
Manager
Joined: 17 Mar 2010
Posts: 197
Followers: 2
Kudos [?]:
22
[4] , given: 9
|
Re: odd 3 digit integers [#permalink]
23 May 2010, 05:00
4
This post received
KUDOS
I would post another way with little short method.
First of all let's find out all numbers greater then 800 and having all different digits.
For hundreth place you have 2 choices, for tenth digit you have (10-1)=9 choices as one digit out of 10 have already used in hundreth place, for unit's digit you have (10-2) = 8 choices
Total three digit numbers with all different digits greater then 800 = 2*8*9 = 144
As 144 is an even number, half of these will be odd and half of this will be even.
So answer will be 72
Ans: C (72)
Consider giving me KUDOS if you like my post.
|
|
|
|
|
|
CEO
Joined: 17 Nov 2007
Posts: 3596
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 231
Kudos [?]:
1300
[0], given: 346
|
Let's xyz is our integer. x e {8,9} y e {0...9} z e {1,3,5,7,9} So, we have 1[x]*5[z]*(10-2)[y] = 40 integers that begin with 8 and 1[x]*4[z]*(10-2)[y] = 32 integers that begin with 9. N = 40 + 32 = 72
_________________
iOS/Android: GMAT ToolKit - The bestselling GMAT prep app | GMAT Club (free) | PrepGame | GRE ToolKit | LSAT ToolKit
PROMO: Are you an exiting GMAT ToolKit (iOS) user? Get GMAT ToolKit 2 (iOS) for only $0.99 (read more)
Math: GMAT Math Book ||| General: GMATTimer ||| Chicago Booth: Slide Presentation
The People Who Are Crazy Enough to Think They Can Change the World, Are the Ones Who Do.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[0], given: 829
|
Re: M25 Question #20 - Counting Numbers with Unique Digits [#permalink]
19 Jul 2010, 00:08
|
|
|
|
|
|
SVP
Joined: 17 Feb 2010
Posts: 1570
Followers: 12
Kudos [?]:
121
[0], given: 6
|
Re: odd 3 digit integers [#permalink]
23 Aug 2010, 13:43
Hey Bunuel, in the solution below, I did not understand the highlighted part.
How do you get only 5 choices in the range 800 - 900 and 4 choices in the range 900 - 999? Please explain.
In the range 800 - 900:
1 choice for the first digit: 8;
[highlight]5 choices for the third digit: 1, 3, 5, 7, 9;[/highlight]
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*5*8 = 40.
In the range 900 - 999:
1 choice for the first digit: 9;
[highlight]4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);[/highlight]
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*4*8 = 32.
Total: 40+32 = 72.
Answer: C.
Hope it's clear.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[0], given: 829
|
Re: odd 3 digit integers [#permalink]
23 Aug 2010, 13:56
seekmba wrote: Hey Bunuel, in the solution below, I did not understand the highlighted part.
How do you get only 5 choices in the range 800 - 900 and 4 choices in the range 900 - 999? Please explain.
In the range 800 - 900:
1 choice for the first digit: 8;
[highlight]5 choices for the third digit: 1, 3, 5, 7, 9;[/highlight]
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*5*8 = 40.
In the range 900 - 999:
1 choice for the first digit: 9;
[highlight]4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);[/highlight]
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*4*8 = 32.
Total: 40+32 = 72.
Answer: C.
Hope it's clear. Odd numbers should end with odd digit. Hence third digit should be 1, 3, 5, 7 or 9 - 5 choices, but for range 900-999 we can not use 9 as we used it as first digit so only 4 options are available. Hope it's clear.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 17 Feb 2010
Posts: 1570
Followers: 12
Kudos [?]:
121
[0], given: 6
|
Re: odd 3 digit integers [#permalink]
23 Aug 2010, 20:31
thanks so much Bunuel.
Thats silly of me.......totally forgot about the odd numbers between 800 and 1000.
|
|
|
|
|
|
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 420
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Followers: 6
Kudos [?]:
75
[0], given: 50
|
Re: odd 3 digit integers [#permalink]
23 Aug 2010, 20:40
Bunuel wrote: dimitri92 wrote: Ok so this is a gmatclub test but I don't get the explanation. Can someone help?
How many odd three-digit integers greater than 800 are there such that all their digits are different?
40
60
72
81
104 In the range 800 - 900:1 choice for the first digit: 8; 5 choices for the third digit: 1, 3, 5, 7, 9; 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*5*8 = 40. In the range 900 - 999:1 choice for the first digit: 9; 4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit); 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*4*8 = 32. Total: 40+32 = 72. Answer: C. Hope it's clear. Bunuel, Why did you split up the three digit number into two different subsets and then proceed to solve the problem. Is there some subtle logic behind this. Please do share your thoughts on this. This was my approach to solve this problem x y z is the three digit number. Unit digit z has 4 choices (1, 3, 5 and 7), y has 7 choices (0, 1, 3, 5, 2, 4, 6 leaving out 7 with the assumption that it is the number chosen for the unit digit.) and x has 2 choices (8 and 9). Of course multiplying these choices does not lead to any of the answer choice.
_________________
 Support GMAT Club by putting a GMAT Club badge on your blog 
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[0], given: 829
|
Re: odd 3 digit integers [#permalink]
24 Aug 2010, 06:07
ezhilkumarank wrote: Bunuel,
Why did you split up the three digit number into two different subsets and then proceed to solve the problem. Is there some subtle logic behind this.
Please do share your thoughts on this.
This was my approach to solve this problem
x y z is the three digit number. Unit digit z has 4 choices (1, 3, 5 and 7), y has 7 choices (0, 1, 3, 5, 2, 4, 6 leaving out 7 with the assumption that it is the number chosen for the unit digit.) and x has 2 choices (8 and 9).
Of course multiplying these choices does not lead to any of the answer choice. There are 5 choices for units digit when hundreds digit is 8 and 4 when hundreds digit is 9. So you should count numbers in these 2 ranges separately.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 27 Jun 2010
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: odd 3 digit integers [#permalink]
30 Aug 2010, 04:49
Hey Bunuel, in the solution below, I did not understand
How do you get only 5 choices in the range 800 - 900 and 4 choices in the range 900 - 999? Please explain.
In the range 800 - 900:
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. --> this should be 9 digits right why havent u considered 0
1*5*8 = 40.
In the range 900 - 999:
1 choice for the first digit: 9;
4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. -->-> this should be 9 digits right why havent u considered 0
1*4*8 = 32.
Total: 40+32 = 72.
Answer: C.
Hope it's clear.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[0], given: 829
|
Re: odd 3 digit integers [#permalink]
30 Aug 2010, 05:51
Divyababu wrote: Hey Bunuel, in the solution below, I did not understand
How do you get only 5 choices in the range 800 - 900 and 4 choices in the range 900 - 999? Please explain.
In the range 800 - 900:
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. --> this should be 9 digits right why havent u considered 0
1*5*8 = 40.
In the range 900 - 999:
1 choice for the first digit: 9;
4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit);
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. -->-> this should be 9 digits right why havent u considered 0
1*4*8 = 32.
Total: 40+32 = 72.
Answer: C.
Hope it's clear. Odd numbers should end with odd digit. Hence third digit should be 1, 3, 5, 7 or 9 - 5 choices, but for range 900-999 we can not use 9 as we used it as first digit so only 4 options are available. Hope it's clear.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GRE Forum Moderator
Affiliations: PMP certified, IT professional
Joined: 21 Jun 2010
Posts: 218
Location: USA
Schools: CMU, Kelley
Followers: 5
Kudos [?]:
51
[0], given: 2
|
Re: odd 3 digit integers [#permalink]
30 Aug 2010, 06:34
Thanks for the explaination Bunuel.
It is clear to me
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[0], given: 829
|
Re: odd 3 digit integers [#permalink]
01 Sep 2010, 06:38
zerotoinfinite2006 wrote: Bunuel wrote: dimitri92 wrote: Ok so this is a gmatclub test but I don't get the explanation. Can someone help?
How many odd three-digit integers greater than 800 are there such that all their digits are different?
40
60
72
81
104 In the range 800 - 900:1 choice for the first digit: 8; 5 choices for the third digit: 1, 3, 5, 7, 9; 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. ---> I am confused here, how did we get 8? is it 10 - 1 - 1 ? What does first digit and third digit means ?1*5*8 = 40. In the range 900 - 999:1 choice for the first digit: 9; 4 choices for the third digit: 1, 3, 5, 7 (9 is out as it's first digit); 8 choices for the second digit: 10 digits - first digit - third digit = 8 digits. 1*4*8 = 32. Total: 40+32 = 72. Answer: C. Hope it's clear. I am confused with the selection of second digit. 3 digit integer abc: we used 1 digit for the first digit a, 1 digit for the third digit c, so for the second digit b there are 10-1-1=8 digits left.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 17 Feb 2010
Posts: 1570
Followers: 12
Kudos [?]:
121
[0], given: 6
|
Re: odd 3 digit integers [#permalink]
09 Sep 2010, 08:05
Hi Bunuel,
I did not understand why you included 900 again in the range of 900 - 999 (should it not be 901 to 999). Why we counted 900 two times?
[highlight]In the range 800 - 900:[/highlight]
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*5*8 = 40.
[highlight]In the range 900 - 999:[/highlight]
1 choice for the first digit: 9;
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11611
Followers: 1801
Kudos [?]:
9597
[0], given: 829
|
Re: odd 3 digit integers [#permalink]
09 Sep 2010, 08:25
seekmba wrote: Hi Bunuel,
I did not understand why you included 900 again in the range of 900 - 999 (should it not be 901 to 999). Why we counted 900 two times?
[highlight]In the range 800 - 900:[/highlight]
1 choice for the first digit: 8;
5 choices for the third digit: 1, 3, 5, 7, 9;
8 choices for the second digit: 10 digits - first digit - third digit = 8 digits.
1*5*8 = 40.
[highlight]In the range 900 - 999:[/highlight]
1 choice for the first digit: 9; Ass we are counting ODD numbers it doesn't make any difference whether we include even number 900 once, twice or even ten times.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 17 Feb 2010
Posts: 1570
Followers: 12
Kudos [?]:
121
[0], given: 6
|
Re: odd 3 digit integers [#permalink]
09 Sep 2010, 09:05
ok that makes sense.
|
|
|
|
|
|
Manager
Joined: 27 Oct 2011
Posts: 196
Location: United States
Concentration: Finance, Strategy
GMAT 1: Q V
GPA: 3.7
WE: Account Management (Consumer Products)
Followers: 1
Kudos [?]:
25
[0], given: 4
|
Re: odd 3 digit integers [#permalink]
03 Feb 2012, 23:42
much clearer... thanks for the explanation
_________________
DETERMINED TO BREAK 700!!!
|
|
|
|
|
|
|
Re: odd 3 digit integers
[#permalink]
03 Feb 2012, 23:42
|
|
|
|
|
|
|
|
|
|
|
close
