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

neynetr

Quote:

Originally Posted by srikar2097

How are you ruling out 6, just because 16 is not satisfying. There are other possible nos. with 6 as units digit for N<60.

hi.. just got back here....
hey srikar... if by looking at the units digit if srikar (of the question) is able to say that the no is divisible by at least two different primes then of course 16 cannot be the number. So if the units digit is 6 srikar cannot be sure whether the no has at least 2 prime factors.... similarly for last digit 8 also..... so i guess the answer to the original question will be 10 only.... i.e. 1 number....

How ever as per my previous doubt....
arbit only knows that the no of factors to that number is unique in 1 to 60 which leaves us with only 36 (9 factors) but of course as per srikar's statement the last digit can only be 0....

m getting confuesd like anything......

kindly help me out

arbit_rageur

Aarav, for the x,y problem is one of the values for(x,y)=(5,4)....is there any other value?.

DeepBlue.mj23

neynetr......what is the confusion?????....can u be a bit more specific?????

ravishah17

Not able to move ahead in that mindsport 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 each number 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 product xy you have, and I'm sure that you don't know either what sum x+y I have.

arbit_rageur: Oh, then I know what the value of x+y is.

Srikar: Now I also know what xy is.

Assuming that both Srikar and arbit_rageur speak truthfully and to the best of their knowledge, what is x and y here?

The numbers are less than 20, so numbers can be 1,2,3,4,..19
Srikar knows sum i.e. x+y
Assuming the numbers to be same,
sums are
2,3,4,5,...38
Products are
1,2,3,4,5,6,7,8,9,....361

Aarav, please help...

m2shines

unit digit can be 1,2,3...9,0

if we take 1 as unit digit... 11,21,31,41,51
here 21 and 51 are divisible by 2 primes while 31,41, 51 are not-> so srikar cant conclude the fact that its divisble by 2 primes

if we take 2 as unit digit 12,22,32,42,52
here 12,22,42 are divisible by 2 primes -> so srikar cant conclude.

in same way we can conclude that only 0 can be the unit digit since if only unit digit is 0 then only srikar can tell that N is divisible by 2 primes.

so possible no.s 10,20,30,40,50
no of divisors of 10 = 4
20 = 6
30 = 8
40 = 8
50 = 6

so 10 can only be the value of N

pjg123

Quantitative Question # 049
my estimated answer is:
b.) 1

srikar tells that the no is divisible by at least 2 primes.
From the units digit, we can only gauge if the no is divisible by 2 or 5.
For divisibility by 3, we require the full number. Similarly, divisibility by 7 also cannot be found from only the last digit.

Thus, if the number is divisible by both 2 n 5, the units digit has to be 0.
So now, shrikar knows that the possibilities are 10, 20, 30, 40, 50.
After shrikar gives out this info, arbit understands that the possibilities are 10, 20, 30, 40, 50.
He calculates the no of divisors of each of the above:
10 - 4 divisors
20 - 6 divisors
30 - 8 divisors
40 - 8 divisors
50 - 6 divisors
But he already knows wat is the actual no of divisors.
But when he says that he knows the answer means that it is a unique no of divisors that he has. Thus 30, 40 each with 8 divisors is ruled out.
Similarly, 20,50 each with 6 divisors is also ruled out.
This leaves us with only 1 unique answer that is 10.
Thus the answer is b.)1

slam

Quote:

Originally Posted by Aarav

This is an easy question but interesting.

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

Good to be back. Albeit a bit late, I am posting my approach to this problem:

Since srikar is able to ascertain that the number has two different prime factors only by seeing the units digit, the units digit comes out to be '0' (double checked by considering numbers with units digit 1,2,.. for numbers less than 60, that this is the only possibility).
So, he knows that the number is one of 10,20,30,40,50.

When he tells arbit this, arbit is able to narrow down to one number. Which means that the number has to be 10 (which has 4 factors, while 20 and 50 have 6 factors, 30 and 40 have 8 factors)

Working backwards, we can now say that arbit already knew that N had four factors, hence had a list of such numbers with him.
When srikar gave him additional information, he understood that the number must be one of 10,20,30,40,50. The only number in both sets would be 10 and hence the answer.

neynetr

Quote:

Originally Posted by DeepBlue.mj23

neynetr......what is the confusion?????....can u be a bit more specific?????

ok... ill try to make my confusion as clear as possible....!!!

first lets talk about srikar... by the units digit information he has concluded that the last last digit is 0... so the number is 10 20 30 40 50.... i think evrything is clear till now...

now we come to arbit.... what is the information he has...???
he knows its no of factors...(lets assume its 4 as 10 is the answer that has come up).... but what is the other information that srikar goves arbit..... srikar says that this number has at least two prime factors....
but arbit doesnt know that srikar has concluded this information by knowing the unit digits of the number... so now... after srikar has made his statement.... arbit will have many options.. i.e. all the numbers from 1 to 60 for which the no of prime factors is at least 2....
e.g. 6, 10, 12, 14, 15, 18, 21..... etc...etc...

so we see... for 10, 14, 15 and 21 also the no of factors is 4....

so how can arbit conclude the number to be 10....???

to conclude 10 arbit needs to have this necessary piece of information that srikar has come to this conclusion by the knowledge of its units digit....

am i clear now...??

shivam_01

Here is my appraoch
sine the unit digit alone is able to tell that the number has two or more prime divisors hence the
unit digit equals to 0 can be possible as 0 can not be the number and rest others have two or more prime divisors
unit digit equals to 1 is not possible as 31,41 are prime them selves
unit digit equals to 2 is also not possible as 32 has only one prime divisor 2
unit digit equals to 3 is not possible as 43 is prime and has one prime divisor
unit digit equals to 4 is also not possible 4 can also be the number and that has only one prime divisor
unit digit equals to 5 is also not possible 5,25 can also be the number and that has only one prime divisor
unit digit equals to 6 is also not possible 16 has only one prime divisor
unit digit equals to 7 is also not possible 17 has only one prime divisor
unit digit equals to 8 is also not possible 8 can also be the number and that has only one prime divisor
unit digit equals to 9 is also not possible 19 has only one prime divisor.

so options left are 10,20,30,40,50
but 10 has 4 factors, 20 has 6 factors,30 has 8 factors,40 has 8 factors, 50 has 6 factors
unique value is number having 4 factors (number 10).

hence option (b) 1

correct me if i am wrong.........

arbit_rageur

I assumed that N is a two digit number<60,...but since in the question, nowehere does it state that N is a two digit number, I guess I am wrong....

Answer should be 10 as already found out by many puys.