Problem Analysis and Solution
The task involves solving number analogies, where you need to identify the pattern or rule governing the sequence of numbers and determine the missing number. Let's solve each question step by step.
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Question 1:
Sequence: 10, 12, 14, 16, 18, 20, ?
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Pattern: The sequence increases by 2 each time.
- \( 10 + 2 = 12 \)
- \( 12 + 2 = 14 \)
- \( 14 + 2 = 16 \)
- \( 16 + 2 = 18 \)
- \( 18 + 2 = 20 \)
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Next number: \( 20 + 2 = 22 \)
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Answer: D (22)
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Question 2:
Sequence: 20, 23, 19, 22, 18, 21, ?
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Pattern: The sequence alternates between adding 3 and subtracting 4.
- \( 20 + 3 = 23 \)
- \( 23 - 4 = 19 \)
- \( 19 + 3 = 22 \)
- \( 22 - 4 = 18 \)
- \( 18 + 3 = 21 \)
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Next number: \( 21 - 4 = 17 \)
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Answer: A (17)
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Question 3:
Sequence: 20, 19, 17, 16, 14, ?
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Pattern: The sequence alternates between subtracting 1 and subtracting 2.
- \( 20 - 1 = 19 \)
- \( 19 - 2 = 17 \)
- \( 17 - 1 = 16 \)
- \( 16 - 2 = 14 \)
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Next number: \( 14 - 1 = 13 \)
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Answer: A (13)
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Question 4:
Sequence: 53, 62, 71, 80, 89, 98, ?
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Pattern: The sequence increases by 9 each time.
- \( 53 + 9 = 62 \)
- \( 62 + 9 = 71 \)
- \( 71 + 9 = 80 \)
- \( 80 + 9 = 89 \)
- \( 89 + 9 = 98 \)
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Next number: \( 98 + 9 = 107 \)
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Answer: B (107)
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Question 5:
Sequence: 64, 63, 62, 60, 59, ?
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Pattern: The sequence decreases by 1, then by 2, then by 1, and so on.
- \( 64 - 1 = 63 \)
- \( 63 - 1 = 62 \)
- \( 62 - 2 = 60 \)
- \( 60 - 1 = 59 \)
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Next number: \( 59 - 2 = 57 \)
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Note: The correct answer is not listed in the options. However, based on the pattern, the next number should be 57. If we must choose from the given options, none are correct.
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Question 6:
Sequence: 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, ?
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Pattern: The sequence increases by 1 each time.
- \( 1.5 + 1 = 2.5 \)
- \( 2.5 + 1 = 3.5 \)
- \( 3.5 + 1 = 4.5 \)
- \( 4.5 + 1 = 5.5 \)
- \( 5.5 + 1 = 6.5 \)
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Next number: \( 6.5 + 1 = 7.5 \)
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Answer: C (7.5)
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Question 7:
Sequence: 3, 4, 6, 7, 9, 10, ?
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Pattern: The sequence alternates between adding 1 and adding 2.
- \( 3 + 1 = 4 \)
- \( 4 + 2 = 6 \)
- \( 6 + 1 = 7 \)
- \( 7 + 2 = 9 \)
- \( 9 + 1 = 10 \)
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Next number: \( 10 + 2 = 12 \)
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Answer: D (12)
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Final Answers:
1.
D (22)
2.
A (17)
3.
A (13)
4.
B (107)
5.
None of the options are correct.
6.
C (7.5)
7.
D (12)
If you have any further questions or need clarification, feel free to ask!
Final Answer Boxed:
\[
\boxed{D, A, A, B, \text{None}, C, D}
\]
Parent Tip: Review the logic above to help your child master the concept of number analogies worksheet.