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

Redeem

Counting - How many odd integers from 100 to 999 . ..

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Counting - How many odd integers from 100 to 999 . ..

by Brent@GMATPrepNow » Thu Jan 29, 2009 7:40 am
How many odd integers from 100 to 999 consist of 3 different digits?
A) 288
B) 300
C) 320
D) 360
E) 405

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Source: — Problem Solving |
User avatar
Community Manager
Posts: 1049
Joined: Sun Apr 06, 2008 5:15 pm
Location: Pittsburgh, PA
Thanked: 113 times
Followed by:27 members
GMAT Score:710

by dmateer25 » Thu Jan 29, 2009 8:02 am
The ones digit can be 1, 3, 5, 7, or 9

So there are 5 possibilities


The hundreds digit can be 1 through 9 but not what the ones digit is.

So there are 8 possibilities


The tens digit can be 0 through 9 but cannot be the same as the ones or hundreds digit.

So there are 8 possibilities


_ _ _

8 x 8 x 5 = 320

I will go with C
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 29, 2009 8:12 am
C it is!
Nice explanation, dmateer25
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Master | Next Rank: 500 Posts
Posts: 158
Joined: Tue Sep 30, 2008 8:47 am
Thanked: 23 times
Followed by:1 members
GMAT Score:660

by DeepakR » Thu Jan 29, 2009 8:22 am
I just have a doubt, i was actually thinking this way as:

Units digit - 1,3,5,7,9 = 5
Tens digit - 0 to 9 (except the one mentioned in units) = 9
Hundreds digit - 1 to 9 (except the one mentioned in units and tens) = 7

So the answer might be 5*9*7 = 315. But i am missing something. Can someone please help me..

- Deepak
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 29, 2009 8:34 am
DeepakR wrote:I just have a doubt, i was actually thinking this way as:

Units digit - 1,3,5,7,9 = 5
Tens digit - 0 to 9 (except the one mentioned in units) = 9
Hundreds digit - 1 to 9 (except the one mentioned in units and tens) = 7

So the answer might be 5*9*7 = 315. But i am missing something. Can someone please help me..

- Deepak
There's a slight problem with this approach.
If you select a 0 for the tens digit, then there are 8 options for the hundreds digit. If you select a non-zero number for the tens digit, then there are 7 options for the hundreds digit.

We can still use your approach, however we need to consider two cases:

Case 1: A zero in the tens place
# of ways to select units digit = 5 (1,3,5,7,9)
# of ways to select tens digit = 1 (must select 0)
# of ways to select units digit = 8 (cannot use the selected units digit or zero)
Case 1 total = 5x1x8= 40

Case 1: A non-zero in the tens place
# of ways to select units digit = 5 (1,3,5,7,9)
# of ways to select tens digit = 8 (cannot use the selected units digit or zero)
# of ways to select units digit = 7 (cannot use the selected units, the selected tens digit, or zero)
Case 2 total = 5x8x7= 280

Grand total = 280+40=320
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1