Question

how many three-digits integers can be divided y 4 to produce a new integer with the same ten' digit as the original integer?

Answer 1

Maybe it will help to know that there are 225 numbers from 100-999 that are divisible by 4?
4*25 = 100
4*249 = 996

Answer 2

not that i know a concrete way to figure this out, just throwing stuff out.

Answer 3

which numbers?

Answer 4

128 /4 = 32
those dont have the same tens digit.

Answer 5

512/4 = 128, those also dont have the same tens digit.

Answer 6

136/4 = 34, thats a match.
So is 132/4 = 33

Answer 7

hey joemath come to twiddla we r gonna find a real method to solve it

Answer 8

http://www.twiddla.com/584034

Answer 9

im down, im very curious as to a method other than guess and check lol

Answer 10

We know that ,
N = Dq + R
According to question,
100x+10y+z = 4(10y +z) +0
=> 100x = 30y + 3 z = 3(10y+z)
clearly Multiple of 100

Answer 11

right

Answer 12

like 300,303...

Answer 13

no

Answer 14

let me think again

Answer 15

i think you are assuming the numbers will have the same ones digit.
100x+10y+z is the number xyz
and 10y+z is the number yz

Answer 16

yes .that is wrong.it should have same tens digit

Answer 17

do we have more examples ...

Answer 18

for the problem

Answer 19

now 132 is one because 4*3 =12 and the first two term is 13
similarly in 200s 260 as 4*6 =24 and first two terms is 26

Answer 20

nvm, im retarded

Answer 21

and sleepy. i found some more numbers though.
260/4 = 65
264/4 = 66
268/4 = 67

Answer 22

im sorta thinking about it like this:
counting by ones, it takes 10 ones digit to change the tens digit.
counting by 4's, it about 2 or 3 multiples to change the tens digit.
think of this problem like "one guy completes a lap in 10 mins, the other one completes a lap in 2-3 mins, how many times with they meet on the track"

Answer 23

the first time we hit a 3 digit number that satisfies this condition is 132:
132/4 = 33
the LCM of 10 and 3 is 30, so approximately around 33+30 i should find the next solution:
63* 4 = 252 nope
64*4 = 256 nope
65*4 = 260 bingo
66*4 = 264 bingo
67*4 = 268 bingo

Answer 24

Adding another 30 to get in the general area again:
67+30 = 97
97*4 = 388 nope
98*4 = 392 bingo
99*4 = 396 bingo

Do you guys see it yet?

Answer 25

3 digit numbers divisible by 4 have their last 2 digits divisible by 4.

Answer 26

I think there should 12 integers like this upto 408

Answer 27

see thats the thing I was talking about

Answer 28

4*3 =12
and we need some three digit number

then as tens should be same ...which is only possible for 130s

then we go to 4*4 =16 but not possible then 4*5 =20 which is not possible again
but when we go into 4*6 =24

We get possibilities in 260s

Now in every whether its 130s or 260s only 3 cases are possible
then similar goes until 390 as 3*9 =36..and now 400 /4 =100
here also 3 cases are possible

with totaling 12 upto 410