At a mathematics competition, a professor gives a new definition that a number is called defector if it is impossible to factorise the given number. He then calls a number super defector if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are super defectors?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

CAT Exam > CAT Questions > At a mathematics competition, a professor giv...

Join the Discussion on the App

At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.

How many 3-digit numbers are 'super defectors'?

a)
21
b)
19
c)
13
d)
8
e)
Less than 821

Correct answer is option 'D'. Can you explain this answer?

Join for Free

Join for Free

Verified Answer

At a mathematics competition, a professor gives a new definition that ...

Solution: Let abc be a 3-digit 'super defector' number.So, a, b, c, ab, be and abc are all defectors, a, b and c are prime numbers, b and c cannot be 2 and 5. a, b and c can also take value 1. Values of 'ab' such that'ab' is a defector are: 11, 13, 17, 23, 31, 37, 53, 71, 73
For abc to be a 3-digit 'super defector' number, values that c can take for various cases is given below: ab - 11 => c - 3 ab = 13 => c = 1, 7 ab = 17 => c = 3 ab = 31 => c = 1, 3, 7 ab = 37 => c = 3 For ab = 23, 53, 71 and 73, there is no possible value of c for which abc will be a 3-digit 'super defector' number.
Thus, we have 8 such numbers. Hence, option 4.

This question is part of UPSC exam. View all CAT courses

View all answers Start learning for free

Explore Courses for CAT exam

Similar CAT Doubts

At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?

View answer

Directions: Read the following passage and solve the questions based on it.a. Six Indian professors from six different institutions(Jupiter, Mars, Mercury, Neptune, Pluto, Uranus) went to China to attend an international conference on "Sustainability and Innovation in Management: A Global Scenario" and they stayed in six successive rooms on the second floor of a hotel (201 - 206).b. Each of them has published papers in a number of journals and has donated to a number of institutions last year.c. The professor in room no. 202 has published in twice as many journals as the professor who donated to 8 institutions last year.d. The professor from Uranus and the Professor in room number 206 together published in a total of 40 journals.e. The professor from Jupiter published in 8 journals less than the professor from Pluto but donated to 10 more institutions last year.f. Four times the number of 4 journal publications by the professor in room number 204 is lesser than the number of institutions to which he donated last year.g. The professor in room number 203 published in 12 journals and donated to 8 institutions last year.h. The professor who published in 16 journals donated to 24 institutions last year.i. The professor in room number 205 published in 8 journals and donated to 2 institutions less than the professor from Mercury last year. The Mercury professor is staying in an odd numbered room.j. The Mars professor is staying two rooms ahead of Pluto professor who is staying two rooms ahead of the Mercury professor in ascending order of room numbers.k. The professors from Mercury and Jupiter do not stay in room number 206.Q. How many institutions did the Jupiter professor donate to last year?

View answer

Directions: Read the following passage and solve the questions based on it. a. Six Indian professors from six different institutions (Jupiter, Mars, Mercury, Neptune, Pluto, Uranus) went to China to attend an international conference on "Sustainability and Innovation in Management: A Global Scenario" and they stayed in six successive rooms on the second floor of a hotel (201 - 206). b. Each of them has published papers in a number of journals and has donated to a number of institutions last year. c. The professor in room no. 202 has published in twice as many journals as the professor who donated to 8 institutions last year. d. The professor from Uranus and the Professor in room number 206 together published in a total of 40 journals. e. The professor from Jupiter published in 8 journals less than the professor from Pluto but donated to 10 more institutions last year. f. Four times the number of 4 journal publications by the professor in room number 204 is lesser than the number of institutions to which he donated last year. g. The professor in room number 203 published in 12 journals and donated to 8 institutions last year. h. The professor who published in 16 journals donated to 24 institutions last year. i. The professor in room number 205 published in 8 journals and donated to 2 institutions less than the professor from Mercury last year. The Mercury professor is staying in an odd numbered room. j. The Mars professor is staying two rooms ahead of Pluto professor who is staying two rooms ahead of the Mercury professor in ascending order of room numbers. k. The professors from Mercury and Jupiter do not stay in room number 206. How many institutions did the Jupiter professor donate to last year?

View answer

Badrinath College of Engineering (BCE) was established on 1st May 1993 on the 60th birth anniversary of Mr. Prakash Badrinath with 4, 5, 3 and 2 professors in Civil, Mechanical, Electrical and Information Technology department respectively. On 1st of June 1993 one more professor joined. On every 1st June of the subsequent years up to 1996 one professor is recruited for one of the departments with the salary of Rs. 15,000 per month. So, at the end of 4 years, 4 new professors were recruited across 4 departments. Professors who joined in May 1993 were placed in different pay scales based on their experience and qualifications, with the minimum of Rs. 15,000 per month and difference between any two pay scales is in multiples of Rs. 5,000. Each department has only one head of the department and he is paid more than the others. After completion of one year of service, each professor is given an annual increment of Rs. 3,000 effective from 1st June every year. During the period from 1st May 1993 to 31st May 1996 only one professor resigned across the four departments.The table given below shows the annual average monthly salary of the professors of BCE for each department as on 1st June every year.Electrical department has a tradition that none of the professor gets the same salary. Professor Kulkami and Professor Rathwa are in the electrical department of the college from its inception and none from them is the head of the department. What is the salary of the third professor who joined along with Prof. Kulkami and Prof. Rathwa, for the month of June 1996?

View answer

Directions: Read the following passage and solve the questions based on it.a. Six Indian professors from six different institutions(Jupiter, Mars, Mercury, Neptune, Pluto, Uranus) went to China to attend an international conference on "Sustainability and Innovation in Management: A Global Scenario" and they stayed in six successive rooms on the second floor of a hotel (201 - 206).b. Each of them has published papers in a number of journals and has donated to a number of institutions last year.c. The professor in room no. 202 has published in twice as many journals as the professor who donated to 8 institutions last year.d. The professor from Uranus and the Professor in room number 206 together published in a total of 40 journals.e. The professor from Jupiter published in 8 journals less than the professor from Pluto but donated to 10 more institutions last year.f. Four times the number of 4 journal publications by the professor in room number 204 is lesser than the number of institutions to which he donated last year.g. The professor in room number 203 published in 12 journals and donated to 8 institutions last year.h. The professor who published in 16 journals donated to 24 institutions last year.i. The professor in room number 205 published in 8 journals and donated to 2 institutions less than the professor from Mercury last year. The Mercury professor is staying in an odd numbered room.j. The Mars professor is staying two rooms ahead of Pluto professor who is staying two rooms ahead of the Mercury professor in ascending order of room numbers.k. The professors from Mercury and Jupiter do not stay in room number 206.Q. The professor of which institute is staying in room number 206?

View answer

Top Courses for CATView all

Quantitative Aptitude (Quant)

Crash Course for CAT

CAT Mock Test Series 2024

3 Months Preparation for CAT

CAT Mock Test Series and 500+ Practice Tests 2024

Top Courses for CAT

View all

Share with a Friend

Answer this doubt

Question Description
At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer?.

Solutions for At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.

Here you can find the meaning of At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer?, a detailed solution for At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8e)Less than 821Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice CAT tests.

Explore Courses for CAT exam