Answer:
1800
Step-by-step explanation:
Let us solve this question by Modular Airthmatic.
Let the lowest 4 digit number be X.
X= 1 (mod 5)
X =2 (mod 5)
X=3 (mod 5)
X =4 (mod 5)
X=1+5 t where t is any integer.
1+5 t=2 (mod 5)
5 t=1 (mod 5 )
5 is the Modular Inverse of modulo 5
t=1 (mod 5)
t =1+5 u : u= any integer.
X becomes 1+ 5 (1+5u )=6+25 u
6+25u =3 (mod 5)
25 u= -3 (mod 5)=2 (mod 5)
25 is Modular Inverse of Modulo 5
u=2 (mod 5)
u =2+5 v : v= any integer.
X becomes 6 +25 (2+5 v)=56+125 v .
56 +125 v=4 (mod 5)
125 v=-52 (mod 5)=3 (mod 5)
125 is Modular Inverse of modulo 5
v = 3 (mod 5)
v =3 +5 w where w is any integer.
For lowest 4 digit number, take
w=200
X=1003 : Lowest 4 digit number.
Take w=201
X=208 : Next number.
For 4 digit largest number, take
w=1995
X= 9978 : Largest number.
No. of Numbers =(1995 - 200 )+1=1800 □Ans.
