From the given set of numbers 519, 328, 746, 495 and 837, if half of the second highest number is subtracted from the third highest number, what will be the resulting value?

Introduction / Context:
This question tests ordering of numbers and basic arithmetic operations. You must first rank the given numbers, then correctly identify the second highest and third highest values, and finally perform a subtraction involving half of one of these numbers. Such questions check attention to detail and simple numerical reasoning.

Given Data / Assumptions:
The five numbers are 519, 328, 746, 495 and 837.We must find the second highest and third highest numbers in this set.We then subtract half of the second highest from the third highest.All numbers are positive integers.

Concept / Approach:
The steps are straightforward: sort the numbers from smallest to largest, identify the required positions, and then compute half of the second highest. Finally, subtract that half from the third highest. It is important not to confuse the ordering positions and to handle the division by 2 correctly.

Step-by-Step Solution:
Step 1: Order the numbers ascending: 328, 495, 519, 746, 837.Step 2: Identify the highest numbers: highest is 837, second highest is 746 and third highest is 519.Step 3: Compute half of the second highest number: half of 746 is 746 / 2 = 373.Step 4: Subtract this half from the third highest: 519 − 373.Step 5: Calculate the difference: 519 − 373 = 146.Step 6: Therefore the required result is 146.

Verification / Alternative check:
We can double check the ordering and arithmetic. Reconfirm that 837 is the largest, 746 the second largest and 519 the third largest. Recalculate half of 746 as 373. Using basic subtraction, 519 minus 300 is 219, and 219 minus 73 is 146. This confirms that there was no mistake in arithmetic.

Why Other Options Are Wrong:
The value 203 could appear if someone subtracts half of the wrong number or miscomputes 519 − 316 instead of 373. The value 345 might arise from subtracting 201 or confusing positions entirely. The value 96 is too small and suggests a serious arithmetic or ordering error. None of these match the correctly computed result.

Common Pitfalls:
Common mistakes include misordering the numbers (for example, accidentally placing 519 below 495), forgetting that half of 746 is 373 and not 372 or 374, or subtracting from the wrong base number. Writing the numbers in a clear list from smallest to largest before proceeding helps avoid these errors.

Final Answer:
The required value is 146.