Question

Find the greatest 4 digits number which when divided by 18,24,30 and 36 leaves a remainder 17 (in each case).

Answer 1

a=18q+17
a=24k+17
a=30p+17

so
30|a-17
24|a-17
18|a-17

so
[24,18,30]|a-17

Answer 2

I need a way by which I can calculate answer to such question in 1-2 mins time. This type of questions appears in admission exam for MS(CS).

Answer 3

no offense but @amoodarya I got no clue what you did back there. A little explanation please ?

Answer 4

that notation for the second one is 30 divides a -17
similarly 24 divides a-17 and 18 divides 1-17

Answer 5

Let \(a\) = required number

Notice that \(a-17\) is divisible by each of the given integers, therefore \(a-17\) must also be divisible by their lcm, \(360\) :

\[a-17 = 360k\]

Answer 6

[30,24,18]=[5.3.2, 2.2.2.3, 3.3.2]=2.2.2.3.3.5=\[2^3*3^2*5=360\\a-17=360k\\a=360k+17\\a_\min=360*3+17=1080+17\]

Answer 7

@ganeshie8 and others thank you!

Answer 8

when did k =3 for the last line? just wondering. unless we have k = 3 because it's the lcm of 18,24,30, and 36.

Answer 9

Lol I think @amoodarya assumed k = 3 :P

Answer 10

:S there is always a reason to let k = 3. isn't it?

Answer 11

I can't think of any reasons to do so :| cause 3 isn't given in the question

Answer 12

the only thing I can think of is that 3 is the lcm of 18.24.30.36.. not to mention that's part of the 3 x table
3 x 6 =18
3 x 8 = 24
3 x 10 = 30
3 x 12 = 36

3 x 3 x 2 = 18
3 x 2 x 2 x 2 = 24
3 x 2 x 5 = 30
3 x 3 x 2 x 2
Each of them has at least 1 3

Answer 13

yup thats true

Answer 14

@amoodarya it'll be less confusing if you just type down a few words explaining the problem like ganeshie8 did. Thanks

Answer 15

\[a=360k+17 \ge 1000\\360k \ge 1000-17\\k \ge \frac{1000-17}{360}\\k \space is \space integer \\k \ge 3\]

Answer 16

where did you get the 1000 from?

Answer 17

largest 4 digit number is 9999
Man Imma cry now seriously

Answer 18

@amoodarya you're not helping sir rather you are making it more confusing and complex :|

Answer 19

yeah this is how my adviser would do... just be like ok this this this the end.

Answer 20

LOL I hate such kind of teachers >:|
Teacher's job is to explain the whole process....

Answer 21

yeah I got a B- for absolutely knowing 5.5 out of 8 chapters in Passage to Advanced Mathematics book

Answer 22

oh . sorry
i had a little mistake
i wrote it for smallest 4 digits
so you do it for the greatest , like that

Answer 23

@ganeshie8 can you make things simple its seriously frying my brain :|

Answer 24

wow I wish my retired professor was on here. He was awesome.

Answer 25

spoonfeeding is not good always, it would be more fun if you try and solve the problem on your own based on the given hints

Answer 26

\[a \leq 9999\\360k+17 \leq 9999\\k \leq \frac{9999-17}{360}\]

Answer 27

well what if the person made so many attempts and then got fed up?

Answer 28

where are the "many" attempts ?

Answer 29

^ yes that's what I am doing for last 1 hour :|

Answer 30

k is less than or equal to 27.7222222222 something seems legit

Answer 31

"many" attempts? lol like using every theorem out there

Answer 32

teaching is not easy... there is no way for a teacher to know what the student has already tried right

Answer 33

showing off like what my professor did to me a while back doesn't help me understand either -_-

Answer 34

^

Answer 35

try this :

teach me how to multiply 3*5

Answer 36

ummm let's see. it's like writing 3 5 times and adding them up

Answer 37

3*5 = 15 simple enough :O

Answer 38

how do you know i know addition ?

Answer 39

omg! take 3 rocks that's 1 batch
then 3 rocks 3 rocks 3 rocks 3 rocks... add them all up

Answer 40

alright I'll solve it myself .... no more arguments

Answer 41

where do i find rocks ?
your explanation is confusing me

Answer 42

you find rocks outside!