What is the rightmost digit (units place) of the sum 65776759 + 54697467?

Introduction / Context:
This question focuses on finding the units digit of the sum of two large numbers. In many competitive exams, you do not need the entire sum; only the last digit is required. Recognising that only the units digits affect the units digit of the sum is a quick and efficient trick that saves time and avoids big calculations.

Given Data / Assumptions:

• Two large integers are given: 65776759 and 54697467.
• We need only the rightmost digit (units digit) of their sum.
• All standard addition rules of decimal arithmetic apply.
• We do not need to compute the full sum explicitly.

Concept / Approach:
The units digit of a sum depends only on the units digits of the addends. When we add two numbers, carry from the tens place does not change which pair of units digits we initially add; instead it influences higher places. So to get the final units digit, we just add the units digits of each number and then take the units digit of that small sum. This method is very fast and works for any size of integers.

Step-by-Step Solution:
Step 1: Identify the units digit of each number.Step 2: For 65776759, the units digit is 9.Step 3: For 54697467, the units digit is 7.Step 4: Add the units digits: 9 + 7 = 16.Step 5: The units digit of 16 is 6.Step 6: Therefore, the units digit of the sum 65776759 + 54697467 is 6.

Verification / Alternative check:
If you wish, you can perform the full addition to verify. 65776759 + 54697467 = 120474226. The last digit of 120474226 is 6, which matches the units digit we found using the shortcut. However, for exam speed, computing the entire sum is unnecessary. The simple method using only units digits is more efficient and less error prone.

Why Other Options Are Wrong:
Option 4: This might arise from incorrect addition of 9 and 7, for example mistaking 9 + 7 as 14 and then misreading the units digit.Option 9: May come from mistakenly copying one of the original units digits instead of summing them.Option 0: Would require the units digits of the addends to sum to a multiple of 10, which is not the case here (9 + 7 = 16, not 10 or 20).Option 2: Could result from a miscalculation during mental arithmetic.

Common Pitfalls:
Students sometimes try to add the full numbers and may make mistakes in the higher place values, which can then incorrectly influence their confidence in the units digit. Others might misread the question and compute something different, like the tens digit. Always read carefully and remember that for the units digit of a sum, only the units digits of the addends matter. Simple mental addition is sufficient.

Final Answer:
The rightmost digit (units place) of the sum is 6.