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
Updated On: Jul 15, 2026
- 10
- 11
- 12
- 13
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The Correct Option is A
Approach Solution - 1
The correct option is (A): 10.
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Approach Solution -2
The series lists number pairs: (1, 3), (4, 6), (7, 9), (?, 12). To find the missing number, notice that within each pair, the second number is always exactly 2 more than the first: 3 minus 1 = 2, 6 minus 4 = 2, 9 minus 7 = 2. This constant gap of 2 should also hold for the last pair. Let's check each option against this rule, and cross-verify using the pattern formed by the first numbers of each pair (1, 4, 7, ...), which increases by 3 each time.
- 10: If the missing number is 10, the pair becomes (10, 12), and 12 minus 10 = 2, matching the constant gap seen in every other pair. Also, the sequence of first numbers becomes 1, 4, 7, 10, each increasing by exactly 3, consistent with the earlier pairs. Both checks confirm 10.
- 11: This would make the pair (11, 12), giving a gap of only 1, which breaks the constant +2 gap rule. It also does not fit the +3 pattern of first numbers (7 to 11 would be +4).
- 12: This would make the pair (12, 12), giving a gap of 0, which does not match the required +2 gap, and would mean the first number equals the previous pair's second number, which never happens elsewhere in the series.
- 13: This would make the pair (13, 12), where the first number is larger than the second, giving a negative gap. Every earlier pair increases from first to second number, so a decreasing pair breaks the pattern entirely.
Only the value 10 satisfies both the constant within-pair gap of 2 and the steady +3 growth of the first numbers across pairs.
Therefore, the correct answer is 10.
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Approach Solution -3
The sequence is written as four pairs: (1, 3), (4, 6), (7, 9), (?, 12). Instead of checking gaps by eye, we can build an explicit formula for the first number of the n-th pair and test it against every option. Numbering the pairs n = 1, 2, 3, 4, the first numbers so far are 1, 4, 7, an arithmetic progression with a common difference of 3 and a first term of 1, giving the general formula \( a_n = 3n - 2 \).
- 10: Substituting n = 4 into \( a_n = 3n - 2 \) gives \( a_4 = 3(4) - 2 = 10 \). This matches the derived formula exactly, and pairing 10 with 12 keeps the second number 2 more than the first, just like every earlier pair.
- 11: The formula predicts \( a_4 = 10 \), not 11, so this value does not satisfy the arithmetic progression governing the first numbers of each pair. Forcing 11 into the formula would require the common difference to jump from 3 to 4 between the third and fourth pairs, which nothing in the earlier pairs supports.
- 12: This value would make the first and second numbers of the last pair identical (12 and 12), which fails both the derived formula \( a_4 = 10 \) and the constant +2 gap seen in every prior pair.
- 13: This exceeds even the formula's next term and would put the first number of the pair above its second number (13 and 12), reversing the increasing pattern present in every one of the first three pairs.
The explicit formula \( a_n = 3n - 2 \), built directly from the first three pairs, predicts exactly one value for the missing term.
Therefore, the correct answer is 10.
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