First of all thanks to all of you for such a great response on article 3. And second, I am sorry for being so late for the 4th article.
Before we talk of number system, lets discuss the question which I asked in comment #10 on article 3.
The answer is 10%. Let’s see how to get the answer. After explaining how to get the answer, I will give you the logic. 100-85 = 15, 100-80 = 20, 100-75 = 25, 100-70 = 30. Now 15 + 20 + 25 + 30 = 90. This 90 when subtracted from 100 is 10 which is the answer.
Say this line above represents 100% of the girls. The Red ones(upto first ‘|” mark) are the ones who are not fair and therefore the balance i.e. the black ones are fair. Similarly the blue ones(from first ‘|’ mark and upto 2nd ‘|” mark) on the line do not have blue eyes. Therefore the rest i.e. red ones and black ones do have blue eyes. And similarly the yellow ones(from 2nd ‘|’ mark and upto 3rd ‘|” mark) are not tall and therefore the rest i.e. red, blue and black are tall. And similarly the green ones(from 3rd ‘|’ mark and upto 4th ‘|” mark) are not rich and therefore the rest i.e. red, blue and yellow and black, are. See carefully now, these are the black ones who have all the four characteristics. And this will be 10%.
I do not have a solution better than this. Here note that I have kept the ‘Don’t have’ disjoint to arrive at ‘have ‘at least’’. The method is useful only in this type of question. And note that this ques(with diff data) has been asked many times in last 12 CATs and many other exams. Ques: Is this Maths? No. But its common sense.
Number system comprises of rational and irrational numbers, positive and negative numbers, even and odd numbers, prime and composite numbers. It also has Natural numbers, whole numbers, Integers, Perfect numbers, co-prime numbers etc. I am assuming that all of you know all this. If not, then please read any book. Please note you will, almost always find a ques on these in CAT.
So here come a few questions for you. Real CAT type questions.
Q1: 3ab59 = x + y. x and y are natural numbers and x < y. Both x and y are prime. What is x?
Q2: 2^10 = 1024. 1024 = p + q. p and q both are integers. p < q. Both p and q are not even. Both p and q are not odd. None of the two is negative. What is p? What is q?
Q3: How many rational numbers exists between two rational numbers?
Q4: Give one rational number between 1.3333……. and 1.4444…….(Both are recurring decimal numbers).
Q5: How many perfect numbers are there which are greater than 100?
Divisibility rules: If you want to understand divisibility rules of a number, I suggest instead of mugging the things, look into the multiples of a number. You will be able to see a trend/pattern almost always. If you don’t, then keep looking for the pattern, you will for sure find a pattern, almost always. Caution: Not all the numbers have divisibility rules. But these are only few. So few that u could be effected practically. I will talk more about divisibility rules with passage of time and with your feedback.
Q6: If a^b+b^a=100, where a and b are natural numbers, find the number of pairs of (a,b) such that the product a.b is maximum.(Ques by Courtesy of Mr.Rajneesh Tripathi)
Q7. Is X = 42.317317317…….(recurring), a rational number or irrational? If it’s rational, what is it’s p/q form. (Ques by Courtesy of Mr.Rajneesh Tripathi)(I suggest in this ques note the time in which u solved this question).
Q8. X = 0.ababab………(recurring). X is multiplied by Y and the result is an integer. What can Y be?
98 b) 198 c)298 d)398 e) None of these
Q9: 1001 ^ 1001 is expanded and sum of the digits is taken. Now sum of the digits of ‘sum of the digits from previous calculation’ is taken. And so on till we get a single digit. What will be this digit?
Q10. abcde x 4 = edcba. What are a, b, c, d and e respectively. a, b, c, d and e are all distinct.
Only this much for now. I am sure all of you will be able to post the answers within 24 hours. I think that should be enough time for you for you are preparing for a 2.5 hour exam having about 75 questions.
All d best to all of you.
VM (& Rajneesh)
P.S.: Mr.Rajneesh Tripathi is a seasoned CAT trainer, teaching for last 6+ years. He is joining our team now on and will be an invaluable resource to all of you and to us as well.