In each of the following questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern.
625, 5, 125, 25, 25, ?, 5
Answer: C
Correct answer: 125
Two series alternate. The odd places divide by five each time - 625, 125, 25, 5 - and the even places multiply by five - 5, 25, and then \( 25 \times 5 = \mathbf{125} \).
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10, 100, 200, 310, ?
Answer: D
Correct answer: 430
The gaps rise by ten each time: \( 100-10=90 \), \( 200-100=100 \), \( 310-200=110 \). The next gap is 120, giving \[ 310 + 120 = \mathbf{430} \]
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11, 10, ?, 100, 1001, 1000, 10001
Answer: A
Correct answer: 101
The terms come in pairs, each pair one digit longer than the last: 11 and 10, then 101 and 100, then 1001 and 1000, then 10001. The missing term is the first of the second pair.
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2, 7, 27, 107, 427, ?
Answer: B
Correct answer: 1707
Each term is four times the one before, less one: \( 4(2)-1=7 \), \( 4(7)-1=27 \), \( 4(27)-1=107 \), \( 4(107)-1=427 \), so \[ 4 \times 427 - 1 = \mathbf{1707} \]
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2, 15, 4, 12, 6, 7, ?, ?
Answer: B
Let the missing terms of the series be x1 and x2.
Thus, the sequence 2, 15, 4, 12, 6, 7, x1 x2 is a combination of two series :
I. 2, 4, 6, x1 and II. 15, 12, 7, x2I consists of consecutive even numbers.
So, missing term, x1 = 8.
The pattern in II is - 3, - 5,......So, missing term, x2 = 7 - 7 = 0.
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4832, 5840, 6848, ?
Answer: C
Correct answer: 7856
The series rises by a constant 1008: \( 5840-4832=1008 \) and \( 6848-5840=1008 \), so \[ 6848 + 1008 = \mathbf{7856} \]
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5824, 5242, ?, 4247, 3823
Answer: B
Correct answer: 4718
Each term is reduced by the number formed from its own first three digits: \( 5824-582=5242 \), then \( 5242-524=\mathbf{4718} \), and the rule holds on: \( 4718-471=4247 \) and \( 4247-424=3823 \).
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2, 8, 16, 128, ?
Answer: C
Correct answer: 2048
Each term is the product of the two before it: \( 2\times8=16 \), \( 8\times16=128 \), so \[ 16 \times 128 = \mathbf{2048} \]
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4, 9, 25, 49, 121, 169,…
Answer: B
Correct answer: 289
The terms are the squares of the prime numbers: \( 2^2, 3^2, 5^2, 7^2, 11^2, 13^2 \). The next prime is 17, so the next term is \( 17^2 = \mathbf{289} \).
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5, 7, 13, 23, …
Answer: D
Correct answer: 41
Each term is the sum of the two before it plus the next odd number: \[ 5+7+1 = 13,\quad 7+13+3 = 23,\quad 13+23+5 = \mathbf{41} \]
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