Find the best tutors and institutes for CAT Coaching

Find Best CAT Coaching

No matching category found.

No matching Locality found.

Outside India?

Search for topics

#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.

Tutor

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

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

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.

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

Related Lessons

Tricks in Maths
Hi everyone here I am going to solve a fundamental question related to quant the answer of which probably most of you know, but the method is critical that applies to other topics like time and distance,...

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=...

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-...
Find CAT Coaching near you

Looking for CAT Coaching ?

Find best CAT Coaching in your locality on UrbanPro.

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you

Find Best CAT Coaching ?

Find Now »

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 25 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 6.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more