#CAT 17 QA Q. If you form a subset of integers chosen from between 1 to 3000, such that no two integers add up to a multiple of nine, what can be the maximum number of elements in the subset.

Asked by Last Modified  

3 Answers

Learn CAT Coaching

Follow 1
Answer

Please enter your answer

Ajay Kumar

Tutor

Any number can be expressed of the form: 9K+i; where k= {0,1,2,....} and i={0,1,...,8} Now, we have to select numbers from {1,2,...,3000} in a manner so that final set does not contain any two numbers whose sum is divisible by 9. We have to identify the maximum size of such selection. Now, within 1 to...
read more
Any number can be expressed of the form: 9K+i; where k= {0,1,2,....} and i={0,1,...,8} Now, we have to select numbers from {1,2,...,3000} in a manner so that final set does not contain any two numbers whose sum is divisible by 9. We have to identify the maximum size of such selection. Now, within 1 to 3000, #elements of the form 9k+1 = 334. #elements of the form 9k+2 = 334. #elements of the form 9k+3 = 334. #elements of the form 9k+4 = 333. #elements of the form 9k+5 = 333. #elements of the form 9k+6 = 333. #elements of the form 9k+7 = 333. #elements of the form 9k+8 = 333. #elements of the form 9k = 333. Now, as per condition, if you select any number from the group 9k+i then you can not select number from the group 9k+j where i+j=9. So, in order to maximize the size of selection, you will go for group: 9K+1, 9k+2,9K+3 and 9k+4. So, total (334+334+334+333=1335). Now, you can select exactly one number from the group 9K. (More than one will result their sum divisible by 9). So, total becomes 1336. Now, you have to exclude 1 (from group 9k+1) and 3000 (from group 9k+3). So finally you are with 1334 numbers! read less
Comments
Dislike Bookmark

Iim Ahmedabad + Iit Kharagpur Graduate

numbers can be split into 1mod9,2mod9.. 0mod9(remainder when divided by 9). (1,8) (2,7) (3,6)(4,5) (0,0) make pairs which add upto 9. so only one of these pairs has to be chosen. Hence the answer is (333*4+3+1)= 1336
Comments
Dislike Bookmark

Tutor

The question was meant for aspirants- I had written this in the post/ Admins do not chop off portions from the post when that is relevant/important.hope you understand.
Comments
Dislike Bookmark

View 1 more Answers

Related Questions

Can any one say the Basic secret in western education for students learning - Physics,chemistry,Maths ?
Method of learning. They do not learn too many things but whatever they learn they learn it with good conceptual understanding. In all my 24 years of tutoring experience especially in the last seven year...
Guru
I am S.DHEERAJ REDDY from Hyderabad. I am doing B.Tech first year course in guru ghasidas central university Bilaspur Chattisgarh. I want to continue my further education in familiar institute in computer science. Suggest me which track is good whether CAT/GATE/GRE with the reasons for the better understanding for me?
write your entrance exam first if your scores are good you ll get your choice of college.
Singireddy
I am graduating this year. Also, I've appeared for CAT 2018. I scored 85.5 percentile (90+ percentile both in VA/RC and DI/LR but only 33 percentile in QA). I'll appear this year too. What should be my preparation strategy for QA? Also, my academic background isn't impressive. I am first division though, maintaining 65% right since class 12th, had 92% in 10th class. I'm pursuing a BA in polity, geo and eco. What are the skills I should work on to build a good MBA profile? Thanks in anticipation.
Forget about profile. Just try getting as high a percentile as possible in CAT. Written +GD/PI/WAT form the major chunk of the selection process in any top b school.
Sajal
0 0
5
i found on facebook that no quetion papers of 2009 -2014 not available and http://cat.examgroup.org will provide shortly so can you please provide those papers with solutions
Testfunda google me search karo
Devang
I can't improve my CAT score above 93 percentile..what do i do?
For quantitative aptitude ensure that you get a strong hold on number theory basics. Do solve as many logic puzzles in spare time, as possible. This definitely improves marks in quants section.
Harshit

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Just in 5 seconds

Rahul Ranjan

0 0
0
Cone from basic to advance
A Cone is a 3D geometrical figure and questions related to volume, surface area and slant height are generally asked in the exam. the following expressions give the general formula of the volume v=...

Ravi Rana

2 0
0
C.A Part - 1
All you need to know about US's Mother of All Bombs The United States on April 13, 2017, dropped a massive GBU-43 bomb in eastern Afghanistan against a series of caves used by Islamic State militants....

Shantanav Bhowmik

0 0
0
Permutation and Combination
Fundamental Principle of Counting/Multiplication rule Q1) How many numbers greater than 999 but not greater than 5000 be formed using the digits 0,1,2,3,4 and 5 if (a) repetition of digits is allowed...

Atul M.

Use of "S" and "Of" in English
Hello, candidates due to growing competitions nowadays English is like maths so the things in English should be logical. Here we are going to see proper use of "s" and 'of' in case of possession. Rule1-...

Ravi Rana

0 0
0

Recommended Articles

The Common Admission Test and Syllabus

Conducted by the Indian Institute of Management (IIMs) based on a policy of rotation, CAT examination was started with a concept to encourage excellent students for their business administration programs. It is the admission test for the IIM Ahmedabad, IIM Calcutta, IIM Bangalore, IIM Indore, IIM Lucknow, IIM Kozhikode...

Read full article >

Tips to Bell the 2016 CAT Exam

Almost every Indian student or a young working professional has thought of acing CAT at some point of time in their career. Easily one of the most coveted exams of the year. In addition to rigorous preparations and weekly mock tests, cracking CAT has a lot to do with being confident and believing in yourself from the starting...

Read full article >

Dos and Don’ts of CAT Quantitative Aptitude...

The Quant section happens to be one of the most dreaded sections for CAT aspirants. The general notion among students is - Quantitative section is really difficult to crack. However, this is not the real case. With proper preparation and following some time-tested strategies, cracking the Quant section in CAT is quite plausible....

Read full article >

Are 12th Class Marks Important for CAT Exam?

Common Admission Test or CAT is an admission test for a management program. This is a graduation course that has three sections: Verbal Ability and Reading Comprehension (VARC), Quantitative Ability (QA) and Data Interpretation and Logical Reasoning (DILR). The CAT syllabus could be covered easily if someone starts practising...

Read full article >

Find CAT Coaching near you
CAT Coaching in Mumbai
CAT Coaching in Delhi
CAT Coaching in Hyderabad
CAT Coaching in Bangalore

Looking for CAT Coaching ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you