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

[arbit_rageur]

Answer is b)1 and the number is 30.

From the fact that srikar knows that the number is divisible by atleast 2 numbers,we can deduce that the last digit of the number must be either 4,8 or 0.

So possible number at this stage is 14,18,20,24,34,28,30,38,44,40,48,50,54,58.

Now from this the only ones with unique number of divisors are 48 and 30.

But if the number is 48, arbit_rageur(not me,the one in the question :P) wouldn't need to know even the unit's digit to guess as no other number below 60 would have 10 divisors....so it must be 30 only.

[DeepBlue.mj23]

The answer is (b) 1.

The only possible value is 10....

Explanation will soon follow....

[arbit_rageur]

But Aarav, srikar knows the last digit while we don't know and arbit knows the number of divisors while we don't...so even if arbit and srikar decipher n, it does not mean that we would be able to decipher n...

let's assume that in a different problem, that two values 18, 93 are two potential values after arbit_rageur's statement, then the fact that srikar knows the last digit will help him decipher n, while we still can't.

Correct me if I am wrong.

Originally Posted by Aarav

Originally Posted by selebratinglife (CAT 2008: Quantitative Questions a Day 1 to 50 - The discussions)
I have a fundamental doubt here aarav,
If arbit and srikar claims they know N, does it mean that they deciphered uniquely what 'N' is? Then the question of how many possible values of 'N' are there doesn't hold good..

Pardon my ignorance and please clarify..
You have a valid point -> the answer will be choice (b) only but we have to find that value of N here as N is unique.

[DeepBlue.mj23]

oops....the only possible value is 30 not 10....just a correction

[abhishek24]

hey send me the questions of quant and also the verbel if u have

[DeepBlue.mj23]

nope...it's 10 for sure.....sorry for the confusion

[ravishah17]

*Two budding MBAs who are also mathematicians, Srikar and arbit_rageur, play a game. The computer selects some secret positive integer N < 60 (both Srikar and arbit_rageur know that , but that they don't know what the value of N is). The computer tells Srikar the unit digit of N, and it tells arbit_rageur the number of divisors of N. 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. However, I know that N is divisible by at least two different primes.

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?

(a)0 (b) 1 (c) 2 (d) 3 (e) none of these


Unit's digit can be 0,1,2,3,4,5,6,7,8,9
Primes- 2,3,5,7,11....

From units digit itself, if number is known then it ll be "0"

Now, numbers can be 10,20,30,40,50(N<60)

Number of divisors of
10 will be 4
20 will be 6
30 will be 8
40 will be 8
50 will be 6

As arbit can uniquely identify it, the number must be "10"

So there is 1 possible value of N---> answer is (b)1

[arbit_rageur]

I din't account for 40 and 24 also having 8 divisors.

The best option then is 48, although in this case, no other number <60 would have 10 divisors, so arbit wouldn't need to know srikar's statement to even know the number....but i suppose the question doesn't mention anything of that sort( that arbit doesn't know the number before srikar's staement).

So the answer is b)1 and number is 48 i think.

[swati1606]

lets look at the unit's digit issue
1: not possible(np) eg.31(prime itself)
2: np eg.32(only one prime divisor)
3: np eg.43
4: np eg.4
similarly,no digit from 0-9 fulfills the "only two prime divisors" criterion except 0

hence,we're left with 10,20,30,40,50

10-4 factors
20-6 factors
30-8 factors
40-8 factors
50-6 factors

hence uniquely determinable value is only and only 4 factors which corresponds to the number 10.

hence,my answer----> option (b) 1

[DeepBlue.mj23]

And Now the explanation...
Srikar - says that the number has 'atleast' 2 prime divisors (taking into consideration that he knows the units digit)....
The keyword here is 'atleast'....
Now taking all the units digit into consideration....
Numbers ending with 'odd' units digit can be prime....Hence 1,3,5,7,9 are ruled out....
We are left with 0,2,4,6,8....
Among these numbers, those ending with 2,4,6,8 have a possibility of having just 1 prime divisor or exactly 2 divisors.....

That leaves us with the possibility of only '0' as the units digit....

'Arbit' pretty well knows this fact.....Hence he'll take all the numbers ending with 0....viz...10,20,30,40,50 and compare it with the number of divisors he has.....Had 'A' had either 6 or 8...that wud have left him with 2 options...(20,50 for 6) and (30,40 for ......But 'A' says he knows the number...which implies the number of divisors told to him is '4'....leaving him only one option - 10....
Now 'S' also does a minor calculation with this and comes to the conclusion that '10' is the number...