In the four digit number series 6834, 6151, 5536, 4983, x, each new term is obtained by subtracting a specific three digit number from the previous term. Which option correctly gives the next term x?

Introduction / Context:
This question involves a series of four digit numbers. The values decrease but not by a constant amount, which suggests that each step uses a rule based on the digits themselves rather than on a fixed difference. Recognising how the subtracted quantities relate to the digits of the current term is the key to predicting the next number in the series.

Given Data / Assumptions:

• The series is: 6834, 6151, 5536, 4983, x.
• We must determine the value of x.
• Each term is obtained from the previous term by subtracting a three digit number.
• The three digit number being subtracted is likely derived from the digits of the current term.

Concept / Approach:
We calculate the differences between consecutive terms and then examine these differences as separate three digit numbers. If these differences are formed from the leading digits of the earlier term (for example, by concatenating the first three digits), this provides a simple, digit based rule for constructing each new term. Once we confirm this pattern, we apply it to the last known term to obtain x.

Step-by-Step Solution:
Step 1: Compute the differences between consecutive terms as positive three digit numbers. 6834 - 6151 = 683. 6151 - 5536 = 615. 5536 - 4983 = 553. Step 2: Express each number explicitly with its digits: First term: 6834 → leading three digits are 6, 8, 3, forming 683. Second term: 6151 → leading three digits are 6, 1, 5, forming 615. Third term: 5536 → leading three digits are 5, 5, 3, forming 553. Step 3: Observe that each difference equals the three digit number formed by the first three digits of the previous term. 6834 - 683 = 6151. 6151 - 615 = 5536. 5536 - 553 = 4983. Step 4: Apply the same rule to obtain the next term from 4983. Form the three digit number from the first three digits of 4983: that is 4, 9, 8 → 498. Step 5: Subtract this value from 4983. Compute 4983 - 498 = 4485. Step 6: Therefore, x = 4485.

Verification / Alternative check:
We can summarise the rule: each new term = current term minus the three digit number composed of the current term's first three digits. Starting from 6834, this gives 6834 - 683 = 6151; then 6151 - 615 = 5536; 5536 - 553 = 4983; 4983 - 498 = 4485. There is no inconsistency in this process, and the relationship holds at every step, strongly confirming that 4485 is the correct next term.

Why Other Options Are Wrong:
Values such as 4467, 4538 or 4184 do not equal 4983 minus 498. To obtain those, one would need to subtract different three digit numbers that do not match the pattern derived from the leading digits. Thus, they break the digit based subtraction rule that matches all earlier transitions in the series. Only 4485 preserves this structure.

Common Pitfalls:
It is easy to focus on numerical differences alone without relating them to the digits of the terms. Another frequent mistake is to search for constant or linearly changing differences, which do not appear here. The important insight is that the subtracted values are not arbitrary but exactly mirror the first three digits of each term. Once this is seen, predicting the next term becomes straightforward.

Final Answer:
Using the rule of subtracting the three digit number formed by the first three digits of each term, the next term in the series is 4485.