NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 20:50 It is currently 24 Apr 2024, 20:50
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Members of a certain website are required to select passwords that are

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618835 [2]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Members of a certain website are required to select passwords that are [#permalink] New post   04 May 2020, 05:23
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

76% (02:28) correct 24% (03:07) wrong based on 29 sessions
Hide Show timer Statistics
Members of a certain website are required to select passwords that are exactly six characters long. The first four characters may be selected from any of the 26 letters from A to Z (not case-sensitive) or any of the digits 0-9, but the last two characters of the password must be selected from only the digits 0-9. For Instance, abcd45, 8hi976. and 5dog56 are valid passwords. A hacker writes a computer program mat will test every permissible password combination at a rate of 72 passwords per second. How long, IN HOURS, will it take the hacker's program to test every permissible password combination?


A. 18
B. 62
C. 648
D. 1,080
E. 38,880

Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
C
User avatar
B
Enchanting
Intern
Intern
Joined: 07 Apr 2020
Posts: 44
Own Kudos [?]: 85 [0]
Given Kudos: 2
Send PM
Re: Members of a certain website are required to select passwords that are [#permalink] New post   04 May 2020, 12:04
Bunuel wrote:
Members of a certain website are required to select passwords that are exactly six characters long. The first four characters may be selected from any of the 26 letters from A to Z (not case-sensitive) or any of the digits 0-9, but the last two characters of the password must be selected from only the digits 0-9. For Instance, abcd45, 8hi976. and 5dog56 are valid passwords. A hacker writes a computer program mat will test every permissible password combination at a rate of 72 passwords per second. How long, IN HOURS, will it take the hacker's program to test every permissible password combination?


A. 18
B. 62
C. 648
D. 1,080
E. 38,880

Are You Up For the Challenge: 700 Level Questions



    Character of password = 6
      Note:- there is no restriction of repetition of character
    The total number of ways in which one character or number can be selected = 26 + 10 = 36
    The number of ways in which first four characters can be selected = \(36C1*36C1*36C1*36C1=36*36*36*36\)
    The number of ways in which last two characters of password can be selected = \(10C1*10C1=10*10\)
      Total number of ways of selecting password = \(36*36*36*36*10*10\)
    Number of seconds in hacking password = \(\frac{36*36*36*36*10*10}{72}\)
    Number of hours in hacking password = \(\frac{36*36*36*36*10*10}{72*60*60} = 648\).
Answer: Option C.
User avatar
L
GMATWhizTeam
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3409
Own Kudos [?]: 1800 [1]
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Send PM
Re: Members of a certain website are required to select passwords that are [#permalink] New post   04 May 2020, 12:15
1
Bookmarks
Expert Reply
Bunuel wrote:
Members of a certain website are required to select passwords that are exactly six characters long. The first four characters may be selected from any of the 26 letters from A to Z (not case-sensitive) or any of the digits 0-9, but the last two characters of the password must be selected from only the digits 0-9. For Instance, abcd45, 8hi976. and 5dog56 are valid passwords. A hacker writes a computer program mat will test every permissible password combination at a rate of 72 passwords per second. How long, IN HOURS, will it take the hacker's program to test every permissible password combination?


A. 18
B. 62
C. 648
D. 1,080
E. 38,880

Are You Up For the Challenge: 700 Level Questions



Solution


    • Since it is not mentioned that letters or digits cannot repeat, so considering the case when digits and characters can repeat.
      o The number of ways in which first 4 characters can be selected \(= 36^4 = 51*35*33\)
      o The number of ways in which last two character can be selected \(= 10^2 = 45\)
      o So, total number of possible passwords \(= 36^4*10^2\)
    • Thus, time required to test every permissible password combination in hours \(= \frac{36^4*10^2}{72*60*60} = 648\)
Thus, the correct answer is Option C.
User avatar
D
minustark
Senior Manager
Senior Manager
Joined: 14 Jul 2019
Status:Student
Posts: 478
Own Kudos [?]: 369 [0]
Given Kudos: 52
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Send PM
Reviews Badge
Re: Members of a certain website are required to select passwords that are [#permalink] New post   04 May 2020, 13:54
Bunuel wrote:
Members of a certain website are required to select passwords that are exactly six characters long. The first four characters may be selected from any of the 26 letters from A to Z (not case-sensitive) or any of the digits 0-9, but the last two characters of the password must be selected from only the digits 0-9. For Instance, abcd45, 8hi976. and 5dog56 are valid passwords. A hacker writes a computer program mat will test every permissible password combination at a rate of 72 passwords per second. How long, IN HOURS, will it take the hacker's program to test every permissible password combination?


A. 18
B. 62
C. 648
D. 1,080
E. 38,880

Are You Up For the Challenge: 700 Level Questions

Possible combinations = 36*36*36*36*10*10
Required seconds = 18*36*36*10*10
Required hour = 6*3*6*6*6*6*10*10/60*60 = 6*3*6*6 = 18*36 = 360+288=648.
C is the answer
GMAT Club Bot
gmatclubot
Re: Members of a certain website are required to select passwords that are [#permalink]
04 May 2020, 13:54
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions