GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 02 Jul 2020, 01:46

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

How many 3-digit numbers greater than 500 contain the digit 9 appearin

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64880
How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 12 May 2020, 06:15
1
1
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

66% (02:06) correct 34% (02:13) wrong based on 94 sessions

HideShow timer Statistics

DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 1968
Location: India
Premium Member
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 12 May 2020, 07:30
2
1
Number that contains only one 9= 1*9*9+4*1*9+4*9*1= 153

Number that contains two 9's= 1*1*9+4*1*1+1*9*1= 22

Number that contains three 9's= 1*1*1=1

Total numbers = 153+22+1=176





Bunuel wrote:
How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?

A. 191
B. 189
C. 176
D. 175
E. 153


Are You Up For the Challenge: 700 Level Questions
Intern
Intern
avatar
B
Joined: 24 Jan 2019
Posts: 5
CAT Tests
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 12 May 2020, 07:40
1
1
Total nos - Nos that contain no 9

5*10*10 - 4*9*9 =176

Posted from my mobile device
Intern
Intern
User avatar
B
Joined: 13 Jun 2019
Posts: 20
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 13 May 2020, 05:04
1
I think the answer is 175
As statement says 3-digit numbers greater than 500 . This means \(501<=x<=999\)
Therefore

Step 1:- total number of numbers between 501 and 999 (all inclusive) = \(5 * 10 * 10 = 500 - 1 = 499\)
We can also find this by \(999-501 = 498+1 = 499\) (Adding 1 to include 501)

Step 2:- total number of numbers which does not contain 9 =\( 4 * 9 * 9 = 324\)

Step 3:- total number of numbers containing at least one 9 = \(499 - 324 = 175\)
_________________

Shrekey

DS Forum Moderator
User avatar
V
Joined: 19 Oct 2018
Posts: 1968
Location: India
Premium Member
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 13 May 2020, 05:15
1
You count 500 in Step 2....Deduct there too. You'll get 176. Point is it does not matter whether you count from 500 or 501, Numbers that contain 9 remain the same

Another way is-

Numbers from 501-599 that contain 9 = 10+10-1=19 (Deduct 1, as we counted 599 twice)

Numbers from 600-699 that contain 9 = 10+10-1=19

Numbers from 700-799 that contain 9 = 10+10-1=19

Numbers from 800-899 that contain 9 = 10+10-1=19

Numbers from 900-999 that contain 9 = 100

Total numbers = 19*4+100=176


rsrighosh wrote:
I think the answer is 175
As statement says 3-digit numbers greater than 500 . This means \(501<=x<=999\)
Therefore

Step 1:- total number of numbers between 501 and 999 (all inclusive) = \(5 * 10 * 10 = 500 - 1 = 499\)
We can also find this by \(999-501 = 498+1 = 499\) (Adding 1 to include 501)

Step 2:- total number of numbers which does not contain 9 =\( 4 * 9 * 9 = 324\)

Step 3:- total number of numbers containing at least one 9 = \(499 - 324 = 175\)
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10998
Location: United States (CA)
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 19 May 2020, 06:37
3
1
Bunuel wrote:
How many 3-digit numbers greater than 500 contain the digit 9 appearing at least once?

A. 191
B. 189
C. 176
D. 175
E. 153



All 100 numbers in the 900s have at least one digit of 9, The number of numbers in 500s, 600s, 700s, and 800s that have at least one digit of 9 must be equal. That is, there is the same amount of numbers in 500s that have at least one digit of 9 as in 600s, 700s, or 800s. If this amount is x, then the total number of numbers is 4x + 100. Notice this must be an even number and since 176 is the only even number in the given choices, 176 must be the correct answer.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Intern
Intern
avatar
B
Joined: 23 Feb 2020
Posts: 43
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 30 May 2020, 05:11
rsrighosh wrote:
I think the answer is 175
As statement says 3-digit numbers greater than 500 . This means \(501<=x<=999\)
Therefore

Step 1:- total number of numbers between 501 and 999 (all inclusive) = \(5 * 10 * 10 = 500 - 1 = 499\)
We can also find this by \(999-501 = 498+1 = 499\) (Adding 1 to include 501)

Step 2:- total number of numbers which does not contain 9 =\( 4 * 9 * 9 = 324\)

Step 3:- total number of numbers containing at least one 9 = \(499 - 324 = 175\)


Hi rsrighosh
Can you please further elabourate step 2. Or first solution jn step 1. I coukdnot understand that method.

Thank you!

Posted from my mobile device
IESE School Moderator
avatar
S
Joined: 11 Feb 2019
Posts: 264
CAT Tests
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin  [#permalink]

Show Tags

New post 30 May 2020, 05:29
1
C.

500-599 => 19 times
600-699= > 19 times
700-799 => 19 times
800-899= > 19 times
900-999 => 100 times

Counting: 176
_________________

Cheers,
NJ
GMAT Club Bot
Re: How many 3-digit numbers greater than 500 contain the digit 9 appearin   [#permalink] 30 May 2020, 05:29

How many 3-digit numbers greater than 500 contain the digit 9 appearin

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





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