In the preceding list of numbers, what two numbers can be written in the blanks so that the difference between each pair of consecutive numbers is constant? 19, , , 43

Rationale

27 and 35 can be written in the blanks to maintain a constant difference between consecutive numbers.

To find the two missing numbers between 19 and 43 that maintain a constant difference, we first determine the total difference: 43 - 19 = 24. This difference must be evenly distributed across the three gaps, resulting in a common difference of 8. Therefore, the sequence is 19, 27, 35, 43.

A (25, 31) YOUR ANSWER

If we substitute 25 and 31 into the sequence, we get 19, 25, 31, and 43. The differences would be 6 (25 - 19), 6 (31 - 25), and 12 (43 - 31), which are not constant. Thus, this choice fails to satisfy the condition.

B (26, 36) YOUR ANSWER

Using 26 and 36 results in the sequence 19, 26, 36, and 43. The differences here are 7 (26 - 19), 10 (36 - 26), and 7 (43 - 36). Again, these differences are not consistent, which disqualifies this option.

C (27, 35) CORRECT

By inserting 27 and 35, we have 19, 27, 35, and 43. The differences are 8 (27 - 19), 8 (35 - 27), and 8 (43 - 35), which are all equal. This option successfully maintains a constant difference of 8, making it the correct answer.

D (28, 37) YOUR ANSWER

Inserting 28 and 37 gives us the sequence 19, 28, 37, and 43. The differences calculated are 9 (28 - 19), 9 (37 - 28), and 6 (43 - 37). Since these differences are not uniform, this choice does not fulfill the requirement for a constant difference.

Conclusion

To establish a consistent difference between consecutive numbers, the sequence must maintain equal spacing. The combination of 27 and 35 achieves this with an even difference of 8, while all other options fail to provide a uniform difference among the numbers. Therefore, 27 and 35 are the only valid solutions to the problem.

In the preceding list of numbers, what two numbers can be written in the blanks so that the difference between each pair of consecutive numbers is constant? 19, __, __, 43

27 and 35 can be written in the blanks to maintain a constant difference between consecutive numbers.

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In the preceding list of numbers, what two numbers can be written in the blanks so that the difference between each pair of consecutive numbers is constant? 19, , , 43