Terry and Sandra both found the sum of two 4-digit numbers, but their results were not the same. If Terry made an error of addition by one in the thousands column and Sandra's result was correct, what was the difference between the larger result and the smaller result?
A. 1000.
B. 1.
C. 100.
D. 10.
1000
Its 1000
1000
To find the difference between the larger result and the smaller result, we need to determine the difference in the thousands column.
Let's say the two 4-digit numbers are represented as ABCD and EFGH.
Terry's error in the thousands column means that the actual sum of the numbers should be (A+1)BCD + EFGH.
Sandra's correct result is ABCD + EFGH.
The difference between Terry's result and Sandra's result is:
((A+1)BCD + EFGH) - (ABCD + EFGH)
This simplifies to:
(A+1)BCD - ABCD
Since the only difference is in the thousands column, the difference is determined by (A+1) - A.
Let's examine the answer choices:
A. 1000: This would be the difference if Terry's error was in the thousands column and he added one thousand instead of one. However, we are given that Terry made an error of addition by one in the thousands column, not by adding an extra thousand. So, option A is incorrect.
B. 1: This is the correct answer because the error made by Terry in the thousands column only results in a difference of one in the thousands place. The error is only in the thousands place, not affecting the other digits. Therefore, option B is the correct answer.
C. 100: This would be the difference if Terry's error was in the hundreds column and he added one hundred instead of one. However, we are given that Terry made an error of addition by one in the thousands column, not by adding one hundred. So, option C is incorrect.
D. 10: This would be the difference if Terry's error was in the tens column and he added ten instead of one. However, we are given that Terry made an error of addition by one in the thousands column, not by adding ten. So, option D is incorrect.
Therefore, the correct answer is B. 1.