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.
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
24 Jul 2017, 19:56
Kudos
Bookmarks
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
67% (00:12) correct
33%
(02:23)
wrong
based on 3
sessions
History
Date
Time
Result
Not Attempted Yet
In a locality, there are ten houses in a row. On a particular night a thief planned to steal from three houses of the locality. In how many ways can he plan such that no two of them are next to each other?
A. 56
B. 73
C. 80
D. 120
E. None of the above
A. 56
B. 73
C. 80
D. 120
E. None of the above
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
24 Jul 2017, 20:27
Kudos
Bookmarks
Let the houses the thief has planned to steal from be A,B,C, and the other houses be X1,X2,...X7.
Since A,B,C cannot be together, the remaining 7 houses can be placed in the following manner: -X1-X2-X3-X4-X5-X6-X7-, where the "-" denotes the place that can be filled with A,B, or C.
Since there are 8 "-"s and 3 items to fill, the no. of ways this can be done is 8c3 = 56. Ans - A.
Another quick way to work through these sort of problems is to deduct the no. of items that cannot be placed together from the total no. of items, then add 1 and do the combinations. In this case, 10-3+1 = 8c3.
Since A,B,C cannot be together, the remaining 7 houses can be placed in the following manner: -X1-X2-X3-X4-X5-X6-X7-, where the "-" denotes the place that can be filled with A,B, or C.
Since there are 8 "-"s and 3 items to fill, the no. of ways this can be done is 8c3 = 56. Ans - A.
Another quick way to work through these sort of problems is to deduct the no. of items that cannot be placed together from the total no. of items, then add 1 and do the combinations. In this case, 10-3+1 = 8c3.
24 Jul 2017, 20:45
Kudos
Bookmarks
If there are 10 houses and the thief needs to choose from 3 houses,
the total ways in which he can choose 3 houses are \(10c3 = \frac{10*9*8}{3*2} = 120\) ways
The condition is that he can't steal from 2 houses that are next to each other.
One way of finding that out is finding how many such combinations are there are reducing that number
from the total combinations possible, which is 120.
To find out how many ways are there if he steals from houses that are next to each other.
If the houses are next to each other, there are 9 ways of choosing the first 2 houses,
and 8 ways of choosing the next house, so a total of 9*8(72) such combinations.
However, there will be 8 combinations which will end up getting counted twice because
_ _ _ _ _ _ _ _ _ _
is the same as
_ _ _ _ _ _ _ _ _ _
That makes a total of 64 combinations(72 - 8) where the houses he steals from are next to each other.
Hence, the total possibilities are 120 - 64 = 56(Option A)
the total ways in which he can choose 3 houses are \(10c3 = \frac{10*9*8}{3*2} = 120\) ways
The condition is that he can't steal from 2 houses that are next to each other.
One way of finding that out is finding how many such combinations are there are reducing that number
from the total combinations possible, which is 120.
To find out how many ways are there if he steals from houses that are next to each other.
If the houses are next to each other, there are 9 ways of choosing the first 2 houses,
and 8 ways of choosing the next house, so a total of 9*8(72) such combinations.
However, there will be 8 combinations which will end up getting counted twice because
_ _ _ _ _ _ _ _ _ _
is the same as
_ _ _ _ _ _ _ _ _ _
That makes a total of 64 combinations(72 - 8) where the houses he steals from are next to each other.
Hence, the total possibilities are 120 - 64 = 56(Option A)
--== Message from the GMAT Club Team ==--
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
