Thread: problem i need to solve

The first digit of a 4 digit number is 7 and the last digit is 4. If the first and last digits are swapped, then the new number would be:
a)made larger by 2997
b)made smaller by 2997
c)made larger by 3003
d)not enough information

Originally Posted by kl050196

The first digit of a 4 digit number is 7 and the last digit is 4. If the first and last digits are swapped, then the new number would be:
a)made larger by 2997
b)made smaller by 2997
c)made larger by 3003
d)not enough information

7xy4 = 7*10^3 + x*10^2 + y*10 + 4...............1

4xy7 = 4*10^3 + x*10^2 + y*10 +7...................2

1-2

= 3*10^3 -3

= 2997

Hello, kl050196!

The first digit of a four- digit number is 7 and the last digit is 4.
If the first and last digits are swapped, then the new number would be:

(a) made larger by 2997
(b) made smaller by 2997
(c) made larger by 3003
(d) not enough information

Set up the subtraction problem . . .


The number has the form: .

The new number would be: .

Obviously, the number becomes smaller . . . Eliminate choices (a) and (c).


Then we have: .

The last (rightmost) digit is 7.
The next digit is 9 . . . [Think about it!]
The next digit is 9.
And the leftmost digit is 2.

The difference is 2997 . . . answer (b).