@sunnychopra89 said:N = 55^3 + 17^3 - 72^3 is divisible by?
N= - 2^3 * 3^3 * 5 * 11 * 17
How many of the first 1000 positive integers can be expressed in the form [2x]+[4x]+[6x]+[8x]
,
where x is a real number, and [x] denotes the greatest integer less than or equal to x ?
,
where x is a real number, and [x] denotes the greatest integer less than or equal to x ?
@ishu1991 said:How many of the first 1000 positive integers can be expressed in the form [2x]+[4x]+[6x]+[8x],where x is a real number, and [x] denotes the greatest integer less than or equal to x ?
???????
Number of positive integer valued pairs(x,y) satisfying 4x - 17y = 1 and x
@sunnychopra89 said:How did u get this?
N=17^3 - (72^3 - 55^3)
=17^3-{(72-55)^3 + 3.72.55(72-55)}
=17^3 - 17^3 - 3.72.55.17= -2^3*3^3*5*11*17
=17^3-{(72-55)^3 + 3.72.55(72-55)}
=17^3 - 17^3 - 3.72.55.17= -2^3*3^3*5*11*17
@sunnychopra89 said:Number of positive integer valued pairs(x,y) satisfying 4x - 17y = 1 and x
59
4x = 17y + 1
x = (17y + 1)/4
y = 3, x = 13
x = 13,30,47,..., 999
So (999-13)/17 + 1 = 986/17 + 1 = 59
4x = 17y + 1
x = (17y + 1)/4
y = 3, x = 13
x = 13,30,47,..., 999
So (999-13)/17 + 1 = 986/17 + 1 = 59
@sunnychopra89 said:N = 55^3 + 17^3 - 72^3 is divisible by?
Then use options no? will be easier.
N / 17 = Rem (4^3 +0 -4^3 ) / 17 = 0 so divisible by 17
and n / 3 = ( rem1^3 + 2^3 -0) / 3 = Rem ( 1+ 8 ) / 3 = 0 so divisible by 3
N / 17 = Rem (4^3 +0 -4^3 ) / 17 = 0 so divisible by 17
and n / 3 = ( rem1^3 + 2^3 -0) / 3 = Rem ( 1+ 8 ) / 3 = 0 so divisible by 3
@sunnychopra89 said:Number of positive integer valued pairs(x,y) satisfying 4x - 17y = 1 and x
59?
x=1+17y/4
x=3...y=13
x=7...y=30
....
....
till y=999
(999-13)/17+1=59
@ishu1991 said:How many of the first 1000 positive integers can be expressed in the form [2x]+[4x]+[6x]+[8x],where x is a real number, and [x] denotes the greatest integer less than or equal to x ?
take LCM of 2,4,6,8. one gets 24.
so if x=1/24, N=0
for x=2/24, N=0
for x=3/24, N=1
for x=4/24, N=2
for x=5/24, N=2
for x=6/24, N=4
for x=7/24, N=4
for x=8/24, N=5
for x=9/24, N=6
for x=10/24, N=6
for x=11/24, N=6
for x=12/24, N=10
for x=13/24, N=10
for x=14/24, N=10
for x=15/24, N=11
for x=16/24, N=12
for x=17/24, N=12
for x=18/24, N=14
for x=19/24, N=14
for x=20/24, N=15
for x=21/24, N=16
for x=22/24, N=16
for x=23/24, N=16
for x=24/24, N=20
So for 1/24So for 1000 nos we will get 50*13=650 integers.
Ans?
so if x=1/24, N=0
for x=2/24, N=0
for x=3/24, N=1
for x=4/24, N=2
for x=5/24, N=2
for x=6/24, N=4
for x=7/24, N=4
for x=8/24, N=5
for x=9/24, N=6
for x=10/24, N=6
for x=11/24, N=6
for x=12/24, N=10
for x=13/24, N=10
for x=14/24, N=10
for x=15/24, N=11
for x=16/24, N=12
for x=17/24, N=12
for x=18/24, N=14
for x=19/24, N=14
for x=20/24, N=15
for x=21/24, N=16
for x=22/24, N=16
for x=23/24, N=16
for x=24/24, N=20
So for 1/24So for 1000 nos we will get 50*13=650 integers.
Ans?
@x2maverickc said:take LCM of 2,4,6,8. one gets 24.so if x=1/24, N=0for x=2/24, N=0for x=3/24, N=1for x=4/24, N=2for x=5/24, N=2for x=6/24, N=4for x=7/24, N=4for x=8/24, N=5for x=9/24, N=6for x=10/24, N=6for x=11/24, N=6for x=12/24, N=10for x=13/24, N=10for x=14/24, N=10for x=15/24, N=11for x=16/24, N=12for x=17/24, N=12for x=18/24, N=14for x=19/24, N=14for x=20/24, N=15for x=21/24, N=16for x=22/24, N=16for x=23/24, N=16for x=24/24, N=20So for 1/24So for 1000 nos we will get 50*13=650 integers.Ans?
__/\__
Sir we get a total of 12 integers.
N = 20 of this set is N = 0 of the next.
12 * 50 = 600
Sir we get a total of 12 integers.
N = 20 of this set is N = 0 of the next.
12 * 50 = 600
@sunnychopra89 said:Number of positive integer valued pairs(x,y) satisfying 4x - 17y = 1 and x
for this the solns for x will have a c.d of 17.
starting from x=13.
total values = 13+(n-1)17=999=> n=59
starting from x=13.
total values = 13+(n-1)17=999=> n=59
@sunnychopra89 said:Number of positive integer valued pairs(x,y) satisfying 4x - 17y = 1 and x
for this the solns for x will have a c.d of 17.
starting from x=13.
total values = 13+(n-1)17=999=> n=59
starting from x=13.
total values = 13+(n-1)17=999=> n=59
@ishu1991 said:@x2maverickcu ar getting 12 integers not 13 chck again 50*12=600
@grkkrg said:__/\__Sir we get a total of 12 integers.N = 20 of this set is N = 0 of the next.12 * 50 = 600
"To a solution having milk and water in the ration of 2:3, 15 lts of water is added and then 15 lts of the solution is drawn out. This operation is done a total of three times. If the ration of milk and water is not 25:231, find the volume of the original solution"
is there an easier way to solve this question rather, than taking 2x/5 and 3x/5 as the original quantities?
Of 128 boxes of Oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least ?