ISI-2008

find out a four digit number M such that N=4xM
and N has the following properties :
i) it is also a four digit no.
ii) the digits of N are in reverse order of those in M.

8 Answers

62
Lokesh Verma ·

M<=2499

First digit of M is 1 or 2

so the last digit of N has to be 1 or 2 (ButN is a multiple of 4 so it has to be 2)

Now can you solve it?

first digit of M becomes 2
last digit is either between 3 or 8

Now can you try some more?

1
skygirl ·

cant we take the no as abcd.
i mean M=abcd
then N=dcba

and, N= 4 M

so, 4000Xa + 400Xb + 40Xc +4Xd = 1000d+100c+10b+a

but then i am geting 4a=d and 4d=a.

so, a=d !

can this be an approach ?

24
eureka123 ·

sorry to disturb everyone...........

but sky are u giving ISI ?????

1
skygirl ·

yeah.

1
palani ............... ·

no. is 2178

postin soln soon

1
palani ............... ·

let m be 1000w+100x +10y+z

z,w≠0

m<2500
so w=1or 2

since n is a multiple of 4 w=2 →z=8

m looks like 2 x y 8

since n=4m

writin dem in eq leads to

332z+20y=1333w+130x
sub w & z

eq bcomz

2y-1=13x ---1

since n is div by 4 last 2 digit must be div by 4

10y+2/4

y can b 1,3,5,7,9

4m 1

y belongs to I

satisfied by 7 only

d no. is 2178

1
skygirl ·

yep i got it jus now.. 2178 .. btw, good work :)

11
Devil ·

Palani and the others forgot that there exists a much simpler soln....
If number is abcd, then only possible value of a is 2....
Meaning d=8....(it can't be 9)....
Only possible values of b={3,1,9}....
Easy to check only 1 is consistent with corresponding c's.....
Done!

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