Difficulty: Easy
Correct Answer: 41
Explanation:
Introduction / Context:
This question features a short numeric sequence with alternating increases and decreases. Very often such patterns have two operations applied alternately, for example adding a fixed number and then subtracting another fixed number. The task is to discover the alternating rule and use it to find x.
Given Data / Assumptions:
Concept / Approach:
When a series moves up and down, it is often best to examine the differences between adjacent terms and check if these differences alternate between two fixed values. Once this alternating pattern is detected, extending it to the next step becomes straightforward.
Step-by-Step Solution:
Step 1: Compute the differences: 40 - 33 = 7, 37 - 40 = -3, 44 - 37 = 7.Step 2: We see an alternating pattern: +7, -3, +7.Step 3: The natural continuation of this alternating rule is another -3 after the last +7.Step 4: Starting from 44, subtract 3 to get x: 44 - 3 = 41.
Verification / Alternative check:
Write the pattern explicitly: 33 + 7 = 40, 40 - 3 = 37, 37 + 7 = 44, 44 - 3 = 41. Every step now consistently follows the rule of adding 7 and then subtracting 3 in alternation. No other value for x maintains this simple and clear pattern.
Why Other Options Are Wrong:
Values like 31, 42, 39 or 45 would correspond to subtractions or additions that do not match the established alternation of +7 and -3. For example, 42 gives a difference of -2 from 44, which contradicts the required -3 step.
Common Pitfalls:
Some learners try to force a single uniform pattern such as always adding or always subtracting, which does not match the observed behaviour here. It is important to notice alternation, particularly in shorter series where simple alternating rules are very common.
Final Answer:
The value of x that correctly continues the alternating pattern is 41.
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