Question:
Identify the missing number:
1 and 3, 4 and 6, 7 and 9, …. and 12
Identify the missing number:
1 and 3, 4 and 6, 7 and 9, …. and 12
1 and 3, 4 and 6, 7 and 9, …. and 12
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In pattern problems, first check the difference between numbers in the same position in each pair. Then extend that pattern to predict the next number.
Updated On: Jul 15, 2026
- 10
- 11
- 12
- 13
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The Correct Option is A
Approach Solution - 1
This is a numerical pattern problem. Let's analyze the pattern step by step.
- The first number in each pair increases by 3: - 1 and 3
- 4 and 6
- 7 and 9
Thus, the next pair should start at 10. The second number in each pair is 2 more than the first number: - 10 and 12
Therefore, the missing number is 10. The correct answer is (A).
- The first number in each pair increases by 3: - 1 and 3
- 4 and 6
- 7 and 9
Thus, the next pair should start at 10. The second number in each pair is 2 more than the first number: - 10 and 12
Therefore, the missing number is 10. The correct answer is (A).
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Approach Solution -2
The question gives pairs of numbers, (1, 3), (4, 6), (7, 9), and (blank, 12), and asks for the missing first number of the last pair. Instead of just extending the pattern, let's check each of the four given options against the full pattern to confirm which one fits.
- 10: Look at only the second number of each pair: 3, 6, 9, 12. Each is 3 more than the one before, so 12 is exactly the expected fourth term of this sequence, confirming the last pair belongs at this position. Now look at the first numbers: 1, 4, 7, and this candidate, 10. Each of these also increases by exactly 3 from the one before. Additionally, within every pair the second number is exactly 2 more than the first: 3 minus 1 is 2, 6 minus 4 is 2, 9 minus 7 is 2, and 12 minus 10 is 2. All three checks line up perfectly.
- 11: If the first number were 11, the gap to the previous first number, 7, would be 4, breaking the consistent step of 3 seen between every other pair of first numbers. It also gives a gap of only 1 within the pair, unlike the steady gap of 2 seen in every other pair.
- 12: This would make the gap from 7 to 12 equal to 5, again breaking the step of 3, and would make the pair's internal difference 0, which matches no other pair in the list.
- 13: This would make the first number bigger than the second number in its own pair, 13 and 12, which breaks the pattern seen in every prior pair, where the first number is always smaller than the second.
Only 10 satisfies the steady step of 3 in both the first and second numbers of each pair, as well as the constant gap of 2 within every pair.
Therefore, the correct answer is 10.
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Approach Solution -3
The pairs given are (1, 3), (4, 6), (7, 9), and (missing, 12). Let's find a general formula for the first number of the nth pair and use it to test each option, rather than just extending the pattern by eye.
- Setting up the formula: The first numbers of the first three pairs are 1, 4, 7, increasing by 3 each time, so the first number of the nth pair is \( a_n = 3n - 2 \). Checking: \( a_1 = 3(1) - 2 = 1 \), \( a_2 = 3(2) - 2 = 4 \), \( a_3 = 3(3) - 2 = 7 \), all matching the given values. The second number of each pair is always 2 more than the first, so the second number is \( a_n + 2 \). For the fourth pair, the second number is given as 12, so \( a_4 + 2 = 12 \), giving \( a_4 = 10 \). The formula independently gives \( a_4 = 3(4) - 2 = 10 \) as well, confirming the same value two different ways.
- 10: Matches \( a_4 = 3(4) - 2 = 10 \) exactly, and also satisfies \( a_4 + 2 = 12 \). Both checks agree.
- 11: Substituting \( n = 4 \) into \( 3n - 2 \) gives 10, not 11, so this value fails the formula. It also gives a pair-gap of only 1 (12 minus 11), not the constant gap of 2 seen elsewhere.
- 12: Also fails the formula, since \( 3(4) - 2 = 10 \), not 12. Using 12 here would additionally make the pair-gap 0, unlike any other pair.
- 13: Fails the formula for the same reason, and makes the first number larger than the second in that pair, which contradicts every other pair, where the first number is always smaller.
Only 10 satisfies both the general formula for the first number of each pair and the constant gap of 2 within each pair.
Therefore, the correct answer is 10.
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