|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
12 Feb 2021, 09:00
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
11% (02:47) correct
89%
(02:50)
wrong
based on 45
sessions
History
Date
Time
Result
Not Attempted Yet
What is the number of integer between 1 and 10000 with a least one 8 and at least one 9 as digits ?
A. 970
B. 971
C. 972
D. 973
E. 974
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
A. 970
B. 971
C. 972
D. 973
E. 974
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
12 Feb 2021, 10:45
Kudos
Bookmarks
Bunuel
We need to divide and conquer for this question, I pick out the possible scenarios then multiply the number of scrambles for each scenario.
Case 1: 4 unique digit's, (e.g. 8901, 0198). We can describe this as 8 9 A B, the two blanks have 8 options and 7 options (include 0 as an option). This would have \(1*1*(8C2)\) cases and each case has 4! scrambles, resulting in \(28*4! = 672\) numbers.
Case 2: 8*9 AA, where A is 0 to 7. Each case has \(\frac{4!}{2}\) scrambles so \(8*4! / 2 = 96\) numbers.
Case 3: 8988 or 8999, scambled. Only two cases and each has 4 scrambles, 8 numbers total.
Case 4: 89 + (8 or 9) + (0 to 7). (E.g. 8189, 9098). 2*8 cases and each case has \(\frac{4!}{2}\) scrambles. \(16*12 = 192\) numbers.
Case 5: 8989 scrambled, \(\frac{4!}{(2*2)} = 6\) cases.
In total we have 672 + 96 + 8 + 192 + 6 = 974 cases.
Ans: E
25 May 2024, 03:35
Kudos
Bookmarks
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
