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?

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

Step-by-step 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

It is 23