Question

In a 4-digit number, ABCD, none of the digits (A, B, C, or D) is greater than 6. A new 4-digit number, WXYZ, is to be constructed by keeping the digits in the same order as ABCD and increasing exactly 2 of the digits. One digit is to be increased by 2, the other by 3. What is the smallest amount by which the new number can exceed the original number?

Answer 1

It is 23

Explanation:

Answer 2

The smallest amount by which the new number can exceed the original number is 23

Explanation:

First, is necessary to identify that in a number ABCD, there are A thousands, B hundreds, C tens and D units, so the smallest number WXYZ that we obtain when we increasing exactly 2 digits by 2 and 3, is when we increase units by 3 and tens by 2. Then every digit of the the smallest number WXYZ would be:

W=A

X=B

Y=C+2

Z=D+3

Taking into account that A, B, C and D doesn't exceed the number 6, W,X,Y or Z does not exceed number 9. So the smallest WXYZ minus ABCD is:

_ A B C+2 D+3

A B C D

0 0 2 3

Finally, the smallest amount by which the new number can exceed the original number is 23