If the square root of the product of three distinct positive integers is equal to the largest of the three

both 1 and 2 options are required to ans this question.
for ex, (abc)^1/2=36, So abc= 1296
and a+b+c=17*3=51
so a+b= 51-36=15.............................(i)
ab=1296/36=36............................(ii)

So, a-b= (225-144)^1/2=9

a=12,b=3
so ans is 36
8 years agoHelpfull: Yes(7) No(5)
using only 1
8 years agoHelpfull: Yes(4) No(1)
sry guys I was wrong before...... only 1st option will be enough to solve this
8 years agoHelpfull: Yes(4) No(0)
Only product of the smallest number we need to find................hence only 1st condi is required.....
8 years agoHelpfull: Yes(3) No(0)
let assume c is largest num
a^1/2*b^1/2*c^1/2=c
but given that c=36
ab=36
a+b =15
and after solving a=12 and b=3 so ab=36
8 years agoHelpfull: Yes(2) No(0)
with the help of (1)
8 years agoHelpfull: Yes(1) No(0)
statement (1) only.
8 years agoHelpfull: Yes(1) No(0)
How? Can u briefly explain me?
8 years agoHelpfull: Yes(0) No(0)
using 1st statement only .......
we get the other two numbers....
8 years agoHelpfull: Yes(0) No(0)
let x=36
so, (xyz)^1/2 =36
(yz)^1/2 = 6
yz=36
8 years agoHelpfull: Yes(0) No(0)
both are required to solve this question.
since yz=36
there is unique values of y & z here. but together by using statement 2 we can find the unique valus of y & z =12,3.
8 years agoHelpfull: Yes(0) No(2)
If we use only option 1 then we will have sets of values for a and b. We won't be able to find the exact ans.
8 years agoHelpfull: Yes(0) No(3)
sqrt(x*y*z)=z
z= 36 then solve xy=36
8 years agoHelpfull: Yes(0) No(0)

If the square root of the product of three distinct positive integers is equal to the largest of the three numbers, what is the product of the two smaller numbers?

(1) The largest number of the three distinct numbers is 36
(2) The average (arithmetic mean) of the three numbers is 17