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

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- Mar 20th 2009, 03:31 AMkl050196problem 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 - Mar 20th 2009, 03:41 AMADARSH
- Mar 20th 2009, 03:54 AMSoroban
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:

(a) made larger by 2997

(b) made smaller by 2997

(c) made larger by 3003

(d) not enough information

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 . . . [Think about it!]

The next digit is 9.

And the leftmost digit is 2.

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