@amresh_maverick said:1> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 75% , the no of factors is decreased by 33.33%. Min value of N ?
2^5*3^4 hoga...OA kya hai??
@amresh_maverick said:1> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 75% , the no of factors is decreased by 33.33%. Min value of N ?
OA : N= 2^5 *3^4
1> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?
2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
1> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?
2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
For smallest number took ...2^a*3^b..
1st case..
a+1 * b+ 1 = a *b+2
...
b+1 = a
2nd case
:
(a-1 * b+1)/(a+1 * b+1)= 2/3
a= 5
b=4
@amresh_maverick said:1> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 75% , the no of factors is decreased by 33.33%. Min value of N ?
N = 2^a+1 * 3^a... no fo factors = (a+2)*(a+1)
thus, 3N/2 = 2^a * 3^a+1...... no of factors = (a+1)*(a+2)
so for N/4 = 2^a-1 * 3^a .... no of factors = (a+1)*a
as no of factors reduce by 1/3..
so (a+2)*(a+1) / (a+1)*a ==> 3/2
which gives a=4..
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
2> 2^3*3^2 ??
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?
95, 119, 125, 143 I am getting...
Edit: took 25 instead of 31. Resolving.
Edit 2: 716. And I see @saurav205 has already got that...
regards
scrabbler
@amresh_maverick said:
2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
2^3*3^2 ?
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
Numbers will be
a^3
or ab
a^3 = 5^3
as 1+5+25 =31
if its a*b then a+b+1 =31
a+b =30
a,b will have to be co-pimes..
so ,
a=7 b =23
a=11 b =19
a=13 b =17
I guess these are the only numbers possible...
so,
125+ 161 + 209 + 221 = 716..
OA kya hai??
a^3
or ab
a^3 = 5^3
as 1+5+25 =31
if its a*b then a+b+1 =31
a+b =30
a,b will have to be co-pimes..
so ,
a=7 b =23
a=11 b =19
a=13 b =17
I guess these are the only numbers possible...
so,
125+ 161 + 209 + 221 = 716..
OA kya hai??
@scrabbler said:482 hai kya?95, 119, 125, 143 I am getting...regardsscrabbler
yaar sum of 4 factors excluding the no ya sum of 3 factors excluding the no...
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
1) 4 numbers???
no. can be of the form ab or a^3
for a^3 = 1 + a + a^2 = 31 --> a = 5 (should be a prime number only)
for ab = 1 + a + b = 31 --> a + b = 30
a = 11, b = 19, a = 23 , b = 7 , a = 13 , b = 17, so 4 numbers///
sum of such no. = 125 + 209 + 161 + 221 = 716
2) 2^3*3^2
@scrabbler said:482 hai kya?95, 119, 125, 143 I am getting...regardsscrabbler
sir jee
119 = 17*7
sum of factors 17+7+1 = 25 aayega....not 31..
baaki bhi check kar lo ek baar...
Me getting...
125 , 161,209 and 221..
Did I miss something here kya?/
Correct me if I got it wrong...
@saurav205 said:sir jee 119 = 17*7sum of factors 17+7+1 = 25 aayega....not 31..baaki bhi check kar lo ek baar...Me getting...125 , 161,209 and 221..Did I miss something here kya?/Correct me if I got it wrong...
ye sahi lag rha h..
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?
1 - 716 ?
@saurav205 said:sir jee 119 = 17*7sum of factors 17+7+1 = 25 aayega....not 31..baaki bhi check kar lo ek baar...Me getting...125 , 161,209 and 221..Did I miss something here kya?/Correct me if I got it wrong...
Nahin maine galat kiya tha. Did sum as 25 instead of 33. 
edited
regards
scrabbler
editedregards
scrabbler
@saurav205 said:Numbers will bea^3or aba^3 = 5^3as 1+5+25 =31if its a*b then a+b+1 =31a+b =30a,b will have to be co-pimes..so ,a=7 b =23a=11 b =19a=13 b =17I guess these are the only numbers possible...so,125+ 161 + 209 + 221 = 716..OA kya hai??
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
OA :
1> 716 -- refer above for detail soln
2> N=2^3 *b^2
1> 716 -- refer above for detail soln
2> N=2^3 *b^2
@amresh_maverick said:OA :1> 716 -- refer above for detail soln2> N=2^3 *b^2
is the OA for the 2nd one correct? most of us are gettin 2592..
@amresh_maverick said:OA : N= 2^5 *3^41> A +ve no has a total of 4 factors and the sum of 4 factors excluding the no itself is 31. what is the sum of all such nos ?2> A no N when increased by 50% has its no of factors as unchanged . But when decreased by 25% , the no of factors is decreased by 33.33%. Min value of N ?
1> 716
#iSolve@turtleSpeed! 😞
#iSolve@turtleSpeed! 😞
@Narci said:is the OA for the 2nd one correct? most of us are gettin 2592..
yeh diff. question hai....dec by 25%...usme 75% dec tha...
1> A 3 digit no xyz is a perfect square. No of factors is also a perfect suqare. If x+y+z is also a perfect square , what is the no of factors of 6 digit no xyzxyz ?
@Narci said:is the OA for the 2nd one correct? most of us are gettin 2592..
woh dossre question ka hia..this one is changed thoda sa,....