BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

their digits are different

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

their digits are different

by sanju09 » Mon Mar 30, 2009 5:24 am
How many odd three-digit integers greater than 800 are there such that all their digits are different?
A. 40
B. 56
C. 72
D. 81
E. 104

OA C
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Source: — Problem Solving |
Senior | Next Rank: 100 Posts
Posts: 92
Joined: Wed Mar 25, 2009 12:13 pm
Thanked: 10 times

by moutar » Mon Mar 30, 2009 6:12 am
Total number of odd numbers between 800 and 999 = 100

Think which numbers do have a repeated digit.

Between 800 and 899
Numbers in the 80s: 881, 883, 885, 887, 889 (5)
Numbers wth repeated tens and units: 811, 833, 855, 877, 899 (5)
Total = 10

Between 900 and 999 (inclusive):
Numbers with a nine at the end: 909, 919, 929, ..., 999 (10)
Numbers in the nineties: 991, 993, 995, 997 (4)
Numbers wth repeated tens and units: 911, 933, 955, 977 (4)
Total = 18

Gives total = 100 - 10 - 18 = 72 = Answer C
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 246
Joined: Mon May 19, 2008 7:34 am
Location: Texaco Gas Station
Thanked: 7 times

by cubicle_bound_misfit » Mon Mar 30, 2009 7:35 am
Well I am li'l stuck here.

thosand place can be 8 or 9

for case 8 unit place can be 1, 3,5, 7, 9

for any unit place (say 1) and thosand place ( say 8) the tenth place can be filled up in 8 ways

duplice 881,883,885,887,889,991,993,995,997,999

I am getting 5*2*8 -10 = 70 ?

whats wrong?
Cubicle Bound Misfit
Top
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Mon Mar 30, 2009 12:42 pm

by shidoshide » Mon Mar 30, 2009 1:27 pm
cubicle_bound_misfit wrote:Well I am li'l stuck here.

thosand place can be 8 or 9

for case 8 unit place can be 1, 3,5, 7, 9

for any unit place (say 1) and thosand place ( say 8) the tenth place can be filled up in 8 ways

duplice 881,883,885,887,889,991,993,995,997,999

I am getting 5*2*8 -10 = 70 ?

whats wrong?
According to your calculation, 5*2*8, there are no 881, 883, 885, 887, and 889. More specifically,
for 8X1: 8 ways to fill the tenth place should be 0, 2, 3, 4, 5, 6, 7, 9
for 8X3: 8 ways to fill the tenth place should be 0, 1, 2, 4, 5, 6, 7, 9
for 8X5: 8 ways to fill the tenth place should be 0, 1, 2, 3, 4, 6, 7, 9
for 8X7: 8 ways to fill the tenth place should be 0, 1, 2, 3, 4, 5, 6, 9
for 8X9: 8 ways to fill the tenth place should be 0, 1, 2, 3, 4, 5, 6, 7.

Also, there are no 991, 993, 995, 997, 999. More specifically,
for 9X1: 8 ways to fill the tenth place should be 0, 2, 3, 4, 5, 6, 7, 8
for 9X3: 8 ways to fill the tenth place should be 0, 1, 2, 4, 5, 6, 7, 8
for 9X5: 8 ways to fill the tenth place should be 0, 1, 2, 3, 4, 6, 7, 8
for 9X7: 8 ways to fill the tenth place should be 0, 1, 2, 3, 4, 5, 6, 8.
However, for 9X9, this format is not desired.

So, in conclusion, there are totally 5*8 + 4*8 = 72 numbers. Hope this helps!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 246
Joined: Mon May 19, 2008 7:34 am
Location: Texaco Gas Station
Thanked: 7 times

by cubicle_bound_misfit » Tue Mar 31, 2009 2:58 am
Thanks. But pure premutation anyone?
Cubicle Bound Misfit
Top
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Tue Mar 31, 2009 3:09 am
cubicle_bound_misfit wrote:Thanks. But pure premutation anyone?
Sure! First of all there is no thousand's place in the required numbers; refer to your last post. Although there is a hundred's place for all such numbers that can either be filled by a '8' or a '9' here.

When '8' fills the 100's place, 1's place can be filled in 5 ways and 10's in 8 ways; totalling to 5 * 8 = 40.

Or when '9' fills the 100's place, 1's place can be filled in 4 ways and 10's in 8 ways; totalling to 4 * 8 = 32.

Hence such numbers 40 + 32 = 72 in total.
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top
Senior | Next Rank: 100 Posts
Posts: 37
Joined: Sun Jan 25, 2009 5:34 pm

by shargaur » Tue Apr 07, 2009 5:02 pm
we have only two scenario here

odd number 1,3,5,7,9
even number 0,2,4,6,8

Case I : first place filled by 1 (only 8)
Third place filled by 5 options (1,3,5,7,9)
Second place (8)
= 1*8*5 = 40

Case II first place filled by 1(only digit 9)
second place by 8
third place by 4 (1,3,5,7)
=1*8*4=32
total 72
Top
Post new topic Post Reply
• Page 1 of 1