# problem i need to solve

• Mar 20th 2009, 03:31 AM
kl050196
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:
d)not enough information
• Mar 20th 2009, 03:41 AM
Quote:

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:
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
• Mar 20th 2009, 03:54 AM
Soroban
Hello, kl050196!

Quote:

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:

(d) not enough information

Set up the subtraction problem . . .

The number has the form: .$\displaystyle 7\,a\,b\,4$

The new number would be: .$\displaystyle 4\,a\,b\,7$

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

Then we have: .$\displaystyle \begin{array}{ccccc}& 7 & a & b & 4 \\ - & 4 & a & b & 7 \\ \hline & ? & ? & ? & ? \end{array}$

The last (rightmost) digit is 7.
The next digit is 9 . . .