Difficulty: Easy
Correct Answer: 4690
Explanation:
Introduction / Context:
This problem is a classic example of numerical simplification that appears frequently in aptitude tests. The candidate must carry out addition and subtraction for relatively large four digit numbers without making place value errors. Even though the calculation is straightforward, carelessness can easily lead to a wrong answer, so a systematic approach is important.
Given Data / Assumptions:
We need to simplify the expression 1234 + 2345 - 3456 + 4567.
All quantities are integers and the operations are standard addition and subtraction.
Concept / Approach:
We simply apply integer arithmetic, but we can choose an order that reduces mental effort. Grouping positive terms together and negative terms together, or pairing terms that almost cancel, can help. The result must be computed exactly, since options are close to one another and a small mistake in one digit can lead to choosing the wrong option.
Step-by-Step Solution:
Start with 1234 + 2345 = 3579.
Now compute 3579 - 3456. This gives 123.
Then add the final term: 123 + 4567 = 4690.
So the overall value of the expression is 4690.
Verification / Alternative check:
As a cross check, we can regroup terms differently. Combine 2345 and 4567 first: 2345 + 4567 = 6912. Now compute 1234 - 3456 = -2222. Finally add: 6912 - 2222 = 4690, which matches the earlier result. Using two different routes yet arriving at the same answer gives strong confidence that 4690 is correct.
Why Other Options Are Wrong:
Option 4680 and 4670 are very close to the correct answer and likely represent errors of ten or twenty due to misaligned subtraction. Option 4590 reflects a larger mistake while carrying or borrowing. Option 4700 may come from rounding or incomplete subtraction. Since we have carefully verified the exact sum, only 4690 satisfies the expression.
Common Pitfalls:
The main pitfalls include incorrectly subtracting 3456, mixing up hundreds and tens, or failing to carry over digits correctly. Another issue is rushing without checking the result with an alternative grouping. Always rewrite long expressions clearly and perform operations step by step, checking intermediate totals as needed.
Final Answer:
The correctly simplified value of the expression is 4690.
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