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

Ash_CAT08

Quote:

Originally Posted by Aarav

All variants of sum/product problem can be found here.
http://www.math.uni-bielefeld.de/~si...ic_sum_product

Dear Aarav,

I think the answer for the question is 30.. if urs is 10 then its wrong i guess..

ravishah17 · 03:57 PM

Quote:

Originally Posted by Ash_CAT08

Dear Aarav,

I think the answer for the question is 30.. if urs is 10 then its wrong i guess..

Dude,

According to your logic, What are the number of factors of "2"??
I suppose it would be only one which is 2

But actually number of factors of "2" is two i.e. 1,2

According to your logic, What are number of factors of "10"?
I suppose it would be only two which are 2,5

but actually number of factors of "10" are four viz 1,2,5,10

Similarly number of factors of 30 are 1,2,3,5,6,10,15,30 i.e. "eight"

===>It comes from the a theorem, I suppose Fermant's or Euler's

If a number N can be represented by its prime factors, p,q,r..... as below:-

N=(p^a)(q^b)(r^c)....

Then the number of factors will be product (a+1)(b+1)(c+1)...

Example---

30 = 2.3.5=(2^1) (3^1)(5^1)

Number of factors will be (1+1) (1+1) (1+1)=8

I hope I am clear..

Ash_CAT08

Well.. Well.. Well...

There is no major calculation required in this question..
Zero has to be the last digit..
Hence possible No. are - 10,20,30,40,50

If we talk in terms of No. of Divisors then

10 has 4 Divisors
20 has 6 "
30 has 8 "
40 has 8 "
50 has 6 "

Had the computer told Arbit 6 or 8.. he would not have been able to tell the no. confidently..

But computer actually told him that the no. has 4 divisors.. and 10 having unique no. of divisors.. confirmed that the no. can only be 10..

Hence N is 10 and the option is (b)

Initially i thought that the computer told Arbit no of PRIME divisors.. in that case the answer would have been 30.. but it(computer) told him no. of divisors..

Ash_CAT08

Quote:

Originally Posted by madhulikasambit

hello sir,
according to question N<60
now as srikant knows the unit digit it has to be unique
now he also know it is divisible by atleast 2 prime numbers.
now as arbit says he knows it ,so there have to be 2 prime divisors along with 1 and itself..
now considering prime nos<60 we have 2,3,5,7,11,13,17,19,23,29
as rest values on multiplication give a result >60
now the product of each of these primes will yield 6-26-46;14-34;
38-58;21-51;15-55,10,22,33,39,57 and rest values >60 which can be discarded.
if we look at the number pairs we find they have common unit digit hence for conditions given it is not unique. but the nos 10,22,33,39,57 have unique unit digit which says the no is <60 and also with two distinct prime factors.therefore there are 5 possible values of n

please help me if i am wrong in interpreting the question

Well.. Well.. Well...

There is no major calculation required in this question..
Zero has to be the last digit..
Hence possible No. are - 10,20,30,40,50

If we talk in terms of No. of Divisors then

10 has 4 Divisors
20 has 6 "
30 has 8 "
40 has 8 "
50 has 6 "

Had the computer told Arbit 6 or 8.. he would not have been able to tell the no. confidently..

But computer actually told him that the no. has 4 divisors.. and 10 having unique no. of divisors.. confirmed that the no. can only be 10..

Hence N is 10 and the option is (b)

Initially i thought that the computer told Arbit no of PRIME divisors.. in that case the answer would have been 30.. but it(computer) actually told him no. of divisors..

Aarav · 04:25 PM

Hello All,

People who are also seeing last year questions in the NL will realise that we took a hint from the suggestion given by past QQAD students and made QQAD slightly easier. The polling of 200 people indicate that we are on the right track, but however if you feel we are going over the board in toughness or delivering too easy problems then please feel free to speak your mind.

Please note that I'm travelling today and hence wouldn't be able to access NL software to put the names of people who solve QQAD 049 after now. You will get the NL tomorrow on time and I will join you for the discussions tomorrow afternoon.

The 2nd practice Test will be delivered on July 1st.

pnvishal

QQAD 49

When srikar says that number is divisible by ATLEAST two prime number then unit digit has to be Zero, as all other digit 1 2,3,4,5,6,7,8 and 9 will not give information about the number of prime factors of number.

e.g. six can be obtained by 2^4 as well as 2X3.

So unit digit is fix. Second guy can know the number exactly if the unit digit is 0 and he knows the total number of factor.

Possible number can be

2*5 = 10, 4*5 =20, 2*5*3=30, 8*5 = 40 and 25*2 = 50 with total factor as 4,6,8,8,and 6 respectively. Now Srikar can determine the number uniqly only if the number of factor known by second guy is unique. that has to be 4

Hence the number is N =10 and there is only one possible number.

option (B)

pnvishal

Post was delayed due to problem in NET

themystique

aarav bhai,
long ago when there was problem with the NL, u had posted this,
none of us had solved it.. (as far as i know )
guess it was conveniently forgotten!

pray do give me the solution...

Set 3:

Problem 1:

14 coins were presented in court of evidence. The judge knows that exactly 7 of these are counterfeit and weigh less than the genuine coins. A lawyer claims to know which coins are counterfeit and which one are genuine, and she is required to prove it. How can she accomplish in only 3 weighings?
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deepakraam

My ans for the above q is option C)3

The numbers cud be 20,30 & 50.Since both the guys know that the last is 0 and the no.of factors is also 6 they cud nt come to a conclusion

20 = 5*2^2 (6)
30 = 5*3*2 (6)
50 = 5^2*2 (6)

But the clue given by Srikar -I know that N is divisible by at least two different primes(means the no is also divisible by more than 2 primes).So Arbit comes to the conclusion that the number must be 30.30 is divisible by 3 primes (2,3 & 5).

-Deepak.

deepakraam

There was a mistake in my previous post in the no.of factors

30 will have 8 factors and not 6 as I said.So there will 2 8 factor nos(30 and 40) and 2 6 factor nos(20 and 50)-there arises a confusion.But the clue given by sridhar will clearly point the number to 30.So the no.of possibilities is only one.

My final ans for the q is only one and the number is 30.

-Deepak.