@amresh_maverick said:When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil's son will be six years older than the age of Sunil at present. The sum of the ages of Sunil's father and Sunil is 85 years at present. What is the sum of the ages of Sunil's son and Sunil at present?
@amresh_maverick said:One day u will be awarded Noble prize for Environment (if this is ever instituted) for saving trees (paper) as u solve most of the q's orally ,P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19?
0?
@amresh_maverick said:One day u will be awarded Noble prize for Environment (if this is ever instituted) for saving trees (paper) as u solve most of the q's orally ,P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19?
N = 19^2 * 2^5 * 3^5 * 5^2
So total = 2^(3-1) = 2^2 = 4 ways
@rnishant231 said:41 seems to be correct@scrabbler Sir, how do you manage it orally.. ?
Explained thought process below in that post (edited) 😃 Need to be able to hold 3-4 numbers in the head simultaneously, everything else can be managed then. Doesn't always work (some embarrassing mistakes happen! 
), but it is a good thing to try, focus sharpens a lot.
regards
scrabbler
), but it is a good thing to try, focus sharpens a lot.regards
scrabbler
@scrabbler said:N will be 19^2 * 2^x *3^y * 5^z so the 2s, 3s and 5s can be distributed in 2^(3-1) = 4 ways?regardsscrabbler
bro N should be 30^30*30! if i am not wrong.. highest power of 19 will be 1.. please tell me where am i going wrong
@iLoveTorres said:bro N should be 30^30*30! if i am not wrong.. highest power of 19 will be 1.. please tell me where am i going wrong
N is the no of factors of 30!*30^30
@amresh_maverick said:When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil's son will be six years older than the age of Sunil at present. The sum of the ages of Sunil's father and Sunil is 85 years at present. What is the sum of the ages of Sunil's son and Sunil at present?
Name Present Future
Sunil y 5x
Father 5x
Son x y+6
5x+y=85 and 5x-y=y+6-x
solving these 2 equations , x=11 and y=30
sum of sunil's son and sunil =x+y= 41 :)
Team BV-- Pratik Gauri
@scrabbler said:N will be 19^2 * 2^x *3^y * 5^z so the 2s, 3s and 5s can be distributed in 2^(3-1) = 4 ways?regardsscrabbler
How did you come to know that N contains only 2, 3 and 5?? 
I had to solve to get N with its prime factorization!
I had to solve to get N with its prime factorization!@iLoveTorres said:bro N should be 30^30*30! if i am not wrong.. highest power of 19 will be 1.. please tell me where am i going wrong
P is the product of first 30 multiples of 30. N is the total number of factors of P.
So P is 30^30 * 30! and not N.
P becomes 2^56 * 3^44 * 5^37 * 7^4 * 11^2 * 13^2 8 17 *19 * 23 *29
And hence N = 57 * 45 * 38 * 5 * 3^2 * 2^4 = 19^2 * 5^2 *3^5 * 2^5.
regards
scrabbler
So P is 30^30 * 30! and not N.
P becomes 2^56 * 3^44 * 5^37 * 7^4 * 11^2 * 13^2 8 17 *19 * 23 *29
And hence N = 57 * 45 * 38 * 5 * 3^2 * 2^4 = 19^2 * 5^2 *3^5 * 2^5.
regards
scrabbler
@ScareCrow28 said:How did you come to know that N contains only 2, 3 and 5?? I had to solve to get N with its prime factorization!
So did I 😃 just didn't write out the whole thing, noted only what different factors came (paid for it eventually as I had to work out the full details anyway to answer @iLoveTorres query :D
regards
scrabbler
regards
scrabbler
@scrabbler said:So did I just didn't write out the whole thing, noted only what different factors came (paid for it eventually as I had to work out the full details anyway to answer @iLoveTorresquery regardsscrabbler
Chalo atleast i am bringing about a change :P
@scrabbler said:So did I just didn't write out the whole thing, noted only what different factors came (paid for it eventually as I had to work out the full details anyway to answer @iLoveTorresquery regardsscrabbler
I thought koi aur method lagadia apne jiski bhanak tak nahi mje 😛 I was pondering over it for 10 minutes last me jaake puch he lia! @iLoveTorres said:Chalo atleast i am bringing about a change
Keep it up bro! :P
@amresh_maverick said:One day u will be awarded Noble prize for Environment (if this is ever instituted) for saving trees (paper) as u solve most of the q's orally ,P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19?
OA : 4 ways
Shor cut given is : ans will always be a power of 2 and the options were
3
4
5
6
Shor cut given is : ans will always be a power of 2 and the options were
3
4
5
6
g(P) represents the product of all the digits of P, e.g. g(45) = 4 — 5.
What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?
What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?
@amresh_maverick said:g(P) represents the product of all the digits of P, e.g. g(45) = 4 — 5.What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?
1281 ?
(6 + 9*10/2 ) * (7 + 8 + 9) + 45 + 2 + 4 + 6 = 1281
Edited: Silliness personified
@amresh_maverick said:g(P) represents the product of all the digits of P, e.g. g(45) = 4 — 5.What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?
6*(7+8+9) + 7*45+8*45+9*45+0+1*45+6*2 = 1281?
@ScareCrow28 said:1280 ?(6 + 9*10/2 ) * (7 + 8 + 9) + 44 + 2 + 4 + 6 = 1280 .. Susceptible to silliness
options are :
a 1381
b 1281
c 1481
d None of these
Q>
78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid is
PS: @ChirpiBird , kaun si movie dekhi aaj ?
a 1381
b 1281
c 1481
d None of these
Q>
78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid is
PS: @ChirpiBird , kaun si movie dekhi aaj ?
@amresh_maverick said:g(P) represents the product of all the digits of P, e.g. g(45) = 4 — 5.What is the value of g(67) + g(68) + g(69) + ..... + g(122) + g(123)?
42+48+54[for 67-69] + (7+8+9)*(9*10)/2[for 70-99] + 0[for 100 - 110] + 45[for 111 - 119] + 12[for 120-123] = 1281..
@amresh_maverick said:options are : a 1381 b 1281 c 1481 d None of theseQ>78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid isPS: @ChirpiBird , kaun si movie dekhi aaj ?
2...
13*3*2 cuboid
regards
scrabbler
13*3*2 cuboid
regards
scrabbler
@amresh_maverick said:options are : a 1381 b 1281 c 1481 d None of theseQ>78 identical cubes each with 2 cm edge are joined together to form a cuboid. If the perimeter of the base of the cuboid is 64 cm, then the number of cubes along the height of the cuboid isPS: @ChirpiBird , kaun si movie dekhi aaj ?
x*(16-x)*y = 2*3*13
y = 2 = cubes in height
P.S. Either my brain is faster than I think OR My keyboard needs hospitalization ( Silly mistakes)..