Answers

Hi All.

Good news for all of you is that I am back in India and the bad news associated with it is, BSNL is taking hell lot of time in activating broadband at my home.

Anyways. Here are the long awaited answers. I am not answering individual comments as that will be too long a post for all to read.

Here the answers go.

1. Both x and y are prime. All primes except 2 are odd. 3ab59 is odd. So 1 of x and y has to be even and other odd. The only even prime we know is 2 and thats smallest as well. Since x < y, x has to be 2.

2. Here the ‘click’ point should be ‘None of the 2 is -ve’. If you start from that you can easily figure out that p and q both are non -ve i.e. 0 and +ve. Hence p = 0 and q = 1024.

3. Answer is infinite. Most of you are correct.

4. I am asking what’s your dad’s name. You are telling me how many uncles you have. I am asking you to tell me 1 rational no. between the 2 given rational no. and am not asking how many between the 2. Simplest answer as per me is (1.3333….. + 1.444…..)/2. Yes answers of many are correct. I better suggest revise 9th class NCERT funda of inserting n rational numbers between 2 given rational numbers.
Say 1.333… = a and 1.444… = b and I ask you to tell me 2 rationals between a and b. Then let d = (b-a)/3. 1st rational number will be a + d and 2nd will be a + 2d. I hope this is enough for you to recollect the basics.

5. opinionated and all others, please note only a finite number of perfect numbers are known so far. If i can recall from my ‘getting older’ memory, there are 46 perfect numbers known and 2 of them are less then 100. so the answer should be 44. Howzz that??

6. Its the coolest one. Answer is 2 such pair and those are (1,99) and (99,1). Do u still need an explaination??

7. Ans is (42317-42)/99= 42275/99. Max 3 seconds job after u have read the ques. Please note in short i have also explained the process.

8. Ans is b. See the explaination of 7.

9. Ans is 5. This was a 15 sec question. Logic is 1001 ^ 1001 divided by 9, whatever is the remainder is the answer. Why – because thats the concept. To know more of the concept I need a face to face class cant explain by writing.

10. a= 2, b= 1, c = 9, d = 7 and e = 8. This involves more of logic and less of NUMBERS. All u guys do a little brain storm. Its difficult for me to explain this by writing. By the way this was an old CAT actual question. and there were 5 ques. I solved this in 3 minutes 15 sec. which I think is worth 5 ques.

Here comes a ques based on the last set of questions. Lets see how fast I get a reply.

Q1. 3p5q7 = x + y. x and y are natural numbers and x < y. Both x and y are prime. What is x?

Q2. Give one rational number between 1.9999……. and 2.0.

All d best.
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