Four-digit number

George is thinking of a four-digit number and gives us the following clues:

a) Its digit sum equals one hundredth of the number obtained by rounding the mystery number to the nearest hundred.
b) Its last digit is 1 more than the second-to-last digit.
c) The sum of its last two digits equals its second digit.

What number is George thinking of?

Final Answer:

x =  4000

Step-by-step explanation:

x = 1000a+100b+10c+d  a+b+c+d = (1000a+100b)/100 d=c+1 c+d=b  b>5  a+b+c+d = (1000a+100(b+1))/100 d=c+1 c+d=b  b = c+d = c+c+1 = 2c+1  100(a+b+c+d) = 1000a+100b+100  100(a+b+c+c+1) = 1000a+100b+100  100(a+2c+1+c+c+1) = 1000a+100(2c+1)+100  a=2 c=9  b=2 c+1=2 9+1=19 d=c+1=9+1=10  x=1000 a+100 b+10 c+d=1000 2+100 19+10 9+10=4000



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