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quant-number system
by satish kumar - Sunday, 20 July 2014, 11:23 AM
  looking easy but taking difficult.
Re: quant-number system
by Raghav Lakhotia - Tuesday, 22 July 2014, 07:09 PM
  480 ?
Re: quant-number system
by satish kumar - Wednesday, 23 July 2014, 08:34 PM
  dunno the answer but how did you do that?
Re: quant-number system
by sai vummenthala - Wednesday, 20 August 2014, 11:16 PM
  numbers are from 31-51, there are few prime nos 31,37,41....these dont have common factors wid any. so lcm cant be so less as given in options...wat say??
Re: quant-number system
by TG Team - Friday, 22 August 2014, 11:20 AM
  The sum of 20 distinct numbers is 801. What is their minimum LCM possible?
Choose one answer.
a. 360
 
b. 840
 
c. 480
 
d. 42


Correct answer is a. 360


We are looking for the smallest number which have 20 or more divisors (as all of the divisors of a number are distinct and also their LCM is same as the number itself) such that sum of 20 of its divisors is 801.

Just check the options and get the answer.


Kamal Lohia

Re: quant-number system
by Avinash Marepalli - Friday, 29 August 2014, 06:25 AM
  sir.please explain how can the product of those 20 numbers be the minimum possible LCM and is the required answer and selecting 20 factors of each of numbers and checking if their sum is 801 takes some time..any other method to find the solution???
Re: quant-number system
by TG Team - Friday, 12 September 2014, 02:40 PM
  Hi Avinash smile

It is LCM and not product of the 20 numbers.

Regarding selecting the 20 factors with sum 801, you can invert the question. Just select the number of divisors which are extra and whose sum is equal to the Total sum of divisors - 801.

For example, in the options we have smallest number as 360 (i.e. 23325) whose number of factors are 24 (i.e. {3 + 1}{2 + 1}{1 + 1}) and whose sum of all the factors is 1170 (i.e. {23 + 22 + 2 + 1}{32 + 3 + 1}{5 + 1}).

So instead of looking for the 20 divisors with sum equal to 801, I'd prefer to look for 4 divisors (i.e. 24 - 20) whose sum is 369 (i.e. 1170 - 801).

And this is pretty easy to do. smile

Two easily available possible set of 4 divisors are: 360, 5, 3, 1 & 360, 6, 2, 1.

Kamal Lohia