CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions

[pallaviagrawal]

Originally Posted by Aarav

Let me try to test more on this.

OK -> Assume, the number is a 2 digit and N < 100. Can we now have a unique N?

then we should have 2 values,10 and 48.

[kk_sonam]

hey aarav but single digit 4 doesnt satisfy the condition

[Aarav]

Originally Posted by kk_sonam

hey aarav but single digit 4 doesnt satisfy the condition

That's OK Sonam, I was trying to grill him more. The problem statement has been twisted a bit and also a new problem added. Read again. Try all these in tandem, will teach number theory at very basic levels.

[kk_sonam]

hey where's the new question.. n what has been added

[nbangalorekar]

Originally Posted by Aarav

Let me try to test more on this.

OK -> Assume, the number is a 2 digit and N < 100. Can we now have a unique N?

I will go a step further and talk about a famous problem.

Two budding MBAs who are also mathematicians, Srikar and arbit_rageur, play a game. The computer selects two secret positive integer x, y such that x, y < 20 (both Srikar and arbit_rageur know that , but that they don't know what the value of N is). The computer tells Srikar the sum x+y, and it tells arbit_rageur the number xy . Then, Srikar and arbit_rageur have the following dialogue:

Srikar: I don't know what N is, and I'm sure that you don't know either.

arbit_rageur: Oh, then I know what the value of N is.

Srikar: Now I also know what N is.

Assuming that both Srikar and arbit_rageur speak truthfully and to the best of their knowledge, how many possible values of N are there?

Aarav this problem is too complicated... i guess it also appeared in mind sport... am i correct?
for the other qn we just have to findout the last digit of the powers of primes less than 100 with their powers too less than 100. i will talk abt exceptions: if last digit :
2-32
3-13
4-64
5-25
6-16
7-47
8-no exception
9-49
so we check for 8:
for 48 (10 divisors), 88 (8 divisors) we get unique divisors.
so we get 3 values of the answer:
10,48 n 88
il try to attempt the advanced level qn too in sum time.

[Aarav]

Originally Posted by nbangalorekar

Aarav this problem is too complicated... i guess it also appeared in mind sport... am i correct?

You are right, it did appear in Mindsport 1st in 1995 Your answer for today's problem is spot on -> some one who had seen the sum and product problem would have cracked today's QQAD in a good time. Well done and keep it up!

[utsavbhatt]

With atleast two prime nos... we have 10, 20, 30, 40, 50 as options...
If Arbit tells that he knows the no. and then Srikar also says the same then the only possible value is 10 because N would have only and only two distinct prime divisors... which are 2 & 5
So, the answer is (b) 1

[kk_sonam]

Originally Posted by nbangalorekar

Aarav this problem is too complicated... i guess it also appeared in mind sport... am i correct?
for the other qn we just have to findout the last digit of the powers of primes less than 100 with their powers too less than 100. i will talk abt exceptions: if last digit :
2-32
3-13
4-64
5-25
6-16
7-47
8-no exception
9-49
so we check for 8:
for 48 (10 divisors), 88 (8 divisors) we get unique divisors.
so we get 3 values of the answer:
10,48 n 88
il try to attempt the advanced level qn too in sum time.

please can u explain me

[nbangalorekar]

Originally Posted by Aarav

You are right, it did appear in Mindsport 1st in 1995 Your answer for today's problem is spot on -> some one who had seen the sum and product problem would have cracked today's QQAD in a good time. Well done and keep it up!

I used to luv mind sport (tho very rarely cud i crack the problems that appeared in it). the questions have been archived on the site. some are real beauties

[kk_sonam]

Originally Posted by nbangalorekar

I used to luv mind sport (tho very rarely cud i crack the problems that appeared in it). the questions have been archived on the site. some are real beauties

please write some explanation