GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Oct 2019, 05:16

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

What is the probability that a 3-digit positive integer picked at rand

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
Joined: 23 Dec 2009
Posts: 35
Schools: HBS 2+2
WE 1: Consulting
WE 2: Investment Management
What is the probability that a 3-digit positive integer picked at rand  [#permalink]

Show Tags

New post 30 Dec 2009, 04:43
1
9
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (02:25) correct 51% (02:32) wrong based on 258 sessions

HideShow timer Statistics

What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?

A. 271/900
B. 27/100
C. 7/25
D. 1/9
E. 1/10

I guessed A, pressed for time. How would I do this problem without manually figuring out how many digits have at least one 7?


When I did it again for correctness, I did the following:

|{700...799}| = 100 integers.
|{107, 117, 127, 137, 147, 157, 167, 187, 197}| = 9 per set of 100, therefore, 72 integers (8 sets, excluding 700s).
|{170, 171, 172, 173, 174, 175, 176, 178, 179}| = 9 per set of 100, therefore, 72 integers (8 sets, excluding 700s).
|{177, 277, 377, 477, 577, 677, 877, 977}| = 8 integers

Total integers with at least one 7 = 100 + 72 + 72 + 8 = 252
Total outcomes = 999 - 100 + 1 = 900

Probability = 252/900 = 7/25. That. took. forever. :evil:

_________________
My GMAT quest...

...over!
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58449
Re: What is the probability that a 3-digit positive integer picked at rand  [#permalink]

Show Tags

New post 30 Dec 2009, 07:31
10
R2I4D wrote:
What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?

A. 271/900

B. 27/100

C. 7/25

D. 1/9

E. 1/10

I guessed A, pressed for time. How would I do this problem without manually figuring out how many digits have at least one 7?

OA is C.


When I did it again for correctness, I did the following:

|{700...799}| = 100 integers.
|{107, 117, 127, 137, 147, 157, 167, 187, 197}| = 9 per set of 100, therefore, 72 integers (8 sets, excluding 700s).
|{170, 171, 172, 173, 174, 175, 176, 178, 179}| = 9 per set of 100, therefore, 72 integers (8 sets, excluding 700s).
|{177, 277, 377, 477, 577, 677, 877, 977}| = 8 integers

Total integers with at least one 7 = 100 + 72 + 72 + 8 = 252
Total outcomes = 999 - 100 + 1 = 900

Probability = 252/900 = 7/25. That. took. forever. :evil:


There are total 900 3 digit numbers;

3 digit number with no 7 =8*9*9=648 (first digit can take 8 values from 1 to 9 excluding 7; second and third digits can take 9 values from 0 to 9 excluding 7),

P(at least one 7)=1-P(no 7)=1-648/900=252/900=7/25

Answer: C.
_________________
Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Joined: 22 Dec 2009
Posts: 253
GMAT ToolKit User
Re: What is the probability that a 3-digit positive integer picked at rand  [#permalink]

Show Tags

New post 01 Jan 2010, 10:52
6
Question a 3-digit positive integer picked at random will have one or more "7" in its digits
can be approached by finding out the number of positive integers which would not have 7 at all and then subtracting the posb from the overall posb combinations.

3 Digit Number posb = 9 x 10 x 10 = 900

3 digit number not having 7 in it all = 8 x 9 x 9 = 648

Therefore 3 digits number having atleast one 7 in them = 900 - 648 = 252

Hence probability \(= \frac{252}{900} = \frac{7}{25}\). Hence answer is C
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!! :beer

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|


~~Better Burn Out... Than Fade Away~~
General Discussion
Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 71
Re: What is the probability that a 3-digit positive integer picked at rand  [#permalink]

Show Tags

New post 07 Jun 2012, 22:39
some one please point the flaw in my logic

want to do it the longer way for more understanding .

at least one 7 means , one , two or three 7's

lets take scenarios, first digit 7 , two digits 7 , all three digits 7

1) first digit to be seven , non seven , non seven

(1/9 ) * 9/10 * 9/10 = 81/900=9/100 first digit cannot be zero , so there are 9 total possibilities for the first , from

1 ,2 , 3, 4, 5, 6, 7, 8, 9. For the second and third we have 10 possibilities now we can have zero , from which favorable are nine, , as we are are excluding 7


( case 2) 7 , 7 , non seven

1/9 * 1/10 *9/10 * 3 = 3/100 here we are multiplying by 3 , because the 2 seven's can occur in 3 ways

( case 3) 7, 7 , 7

1/9 * 1/10 * 1/10 = 1/ 900


so at least one 7

9/100 + 3/100 + 1/900 = 109/900 = wrong answer !! :oops:

what am I missing guys ?

I know the alternate way , 1- p ( all not seven ) , that's fine , but I want to understand what's wrong with this way .

Appreciate your help. Thank you
Manager
Manager
User avatar
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 114
Location: Philippines
Concentration: General Management, Finance
GPA: 3.22
WE: Corporate Finance (Consulting)
Re: What is the probability that a 3-digit positive integer picked at rand  [#permalink]

Show Tags

New post 07 Jun 2012, 23:06
Bunuel wrote:
R2I4D wrote:
What is the probability that a 3-digit positive integer picked at random will have one or more "7" in its digits?

A. 271/900

B. 27/100

C. 7/25

D. 1/9

E. 1/10

I guessed A, pressed for time. How would I do this problem without manually figuring out how many digits have at least one 7?

OA is C.


When I did it again for correctness, I did the following:

|{700...799}| = 100 integers.
|{107, 117, 127, 137, 147, 157, 167, 187, 197}| = 9 per set of 100, therefore, 72 integers (8 sets, excluding 700s).
|{170, 171, 172, 173, 174, 175, 176, 178, 179}| = 9 per set of 100, therefore, 72 integers (8 sets, excluding 700s).
|{177, 277, 377, 477, 577, 677, 877, 977}| = 8 integers

Total integers with at least one 7 = 100 + 72 + 72 + 8 = 252
Total outcomes = 999 - 100 + 1 = 900

Probability = 252/900 = 7/25. That. took. forever. :evil:


There are total 900 3 digit numbers;

3 digit number with no 7 =8*9*9=648 (first digit can take 8 values from 1 to 9 excluding 7; second and third digits can take 9 values from 0 to 9 excluding 7),

P(at least one 7)=1-P(no 7)=1-648/900=252/900=7/25

Answer: C.


Oh man my mistake was 9 * 9 * 9 and then you mentioned that first digit can only take values from 1 2 3 4 5 6 7 8 9 and not 0 because that will make it a 2 digit number.

Argh! traps traps traps!
_________________
Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt
Intern
Intern
avatar
B
Joined: 11 Sep 2018
Posts: 26
Location: India
Concentration: Finance, Strategy
Schools: LBS '21, ISB '20
WE: Accounting (Non-Profit and Government)
Re: What is the probability that a 3-digit positive integer picked at rand  [#permalink]

Show Tags

New post 17 Nov 2018, 12:32
Joy111 wrote:
some one please point the flaw in my logic

want to do it the longer way for more understanding .

at least one 7 means , one , two or three 7's

lets take scenarios, first digit 7 , two digits 7 , all three digits 7

1) first digit to be seven , non seven , non seven

(1/9 ) * 9/10 * 9/10 = 81/900=9/100 first digit cannot be zero , so there are 9 total possibilities for the first , from

1 ,2 , 3, 4, 5, 6, 7, 8, 9. For the second and third we have 10 possibilities now we can have zero , from which favorable are nine, , as we are are excluding 7


( case 2) 7 , 7 , non seven

1/9 * 1/10 *9/10 * 3 = 3/100 here we are multiplying by 3 , because the 2 seven's can occur in 3 ways

( case 3) 7, 7 , 7

1/9 * 1/10 * 1/10 = 1/ 900


so at least one 7

9/100 + 3/100 + 1/900 = 109/900 = wrong answer !! :oops:

what am I missing guys ?

I know the alternate way , 1- p ( all not seven ) , that's fine , but I want to understand what's wrong with this way .

Appreciate your help. Thank you



You are considering 'only one 7' as your first case by counting numbers in the form of 7xy,7xx,7yy. What about x7y,y7x,xx7,yy7,xy7,yx7?? By counting such possible numbers, the number of events will increase.
Hope this helps.
:)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13271
Re: Probability of 7s  [#permalink]

Show Tags

New post 30 Sep 2019, 02:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Probability of 7s   [#permalink] 30 Sep 2019, 02:30
Display posts from previous: Sort by

What is the probability that a 3-digit positive integer picked at rand

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





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