Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
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.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Dec 1411:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Dec 1310:00 AM EST
-12:00 PM EST
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.- Dec 15
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
15 May 2019, 04:51
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
43% (02:16) correct
58%
(02:13)
wrong
based on 40
sessions
History
Date
Time
Result
Not Attempted Yet
How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s?
A. 55
B. 60
C. 65
D. 70
E. 75
A. 55
B. 60
C. 65
D. 70
E. 75
17 May 2019, 05:43
Kudos
Bookmarks
Bunuel
How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s?
A. 55
B. 60
C. 65
D. 70
E. 75
A. 55
B. 60
C. 65
D. 70
E. 75
The last term must be 0.
To form the first 18 terms, we must combine the following two sequences:
0-1 and 0-1-1
Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent.
To illustrate:
0-1...0-1...0-1...0-1-1
0-1-1...0-1...0-1...0-1
0-1...0-1-1...0-1-1...0-1
Since we must combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:
2x + 3y = 18
Case 1: x=9 and y=0
Number of ways to arrange 9 identical 2-term sequences = 1
Case 2: x=6 and y=2
Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences \(= \frac{8!}{6!2!} = 28\)
Case 3: x=3 and y=4
Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences \(= \frac{7!}{3!4!} = 35\)
Case 4: x=0 and y=6
Number of ways to arrange 6 identical 3-term sequences = 1
Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65
General Discussion
Rakesh1987
Current Student
Joined: 17 Jul 2018
Last visit: 27 Aug 2022
Posts: 66
Own Kudos:
Given Kudos: 100
Location: India
Concentration: Finance, Leadership
Schools: Stern '23 (M$)
GMAT 1: 760 Q50 V44
GPA: 4
Updated on: 22 Aug 2019, 09:43
Originally posted by Rakesh1987 on 21 Aug 2019, 21:46.
Last edited by Rakesh1987 on 22 Aug 2019, 09:43, edited 1 time in total.
Last edited by Rakesh1987 on 22 Aug 2019, 09:43, edited 1 time in total.
Kudos
Bookmarks
Bunuel
How many sequences of 0s and 1s of length 19 are there that begin with a 0, end with a 0, contain no two consecutive 0s, and contain no three consecutive 1s?
A. 55
B. 60
C. 65
D. 70
E. 75
The sequence is like this: 01............10 (19 terms in total)A. 55
B. 60
C. 65
D. 70
E. 75
As two 0s cant be together but two 1s can be lets concentrate on 1s and let use 0 as separator. Our task is to find the number of sequences in which 1s and 11s are separated by 0s.
Minimum number of digit 1 in any sequence is when we use only single 1s and no 11s= (19-1)/2=9. Here there are 9 single 1s.
Maximum number of digit 1 in any sequence is using all pairs of 11s= (19-1)*2/3=12. (Note max is 0110110110....110, also do note 1. first and last digit are 0 2. 11 is allowed but 111 is not allowed).
As we move from 9 to 12 number of 1, we move from 0 pair to 6 pairs- two in each move why??
Because when we use 10 number of 1- if one pair is used then number of 0s to be used is 9+1=10 and number of 1 is also 10, totals to 20. However, we need to make sequence of 19 1s & 0s. Hence, this is not possible and we will have to move in 2- 11s.
Total number of 1---- Pair of 1,11---- Calculation
9----9,0----1
10----6,2----8!/6!2!=28
11----3,4----7!/3!4!=35
12----0,6----1
Total number of sequences is 1+28+35+1=65. C.
Please hit +1 Kudos if you liked the explanation.
