Number Series Questions and Answers

Answer: C

Correct answer: 253

Neither a constant difference nor a constant ratio fits, since the gaps run 8, 16, 32, 64. Each term is the previous one multiplied by 2 and then increased by 3: 5 times 2 plus 3 is 13, and 13 times 2 plus 3 is 29. Applying it once more, 125 times 2 plus 3 is 253. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 125, the last term shown. A series of four terms admits many rules in principle, but only one that is simple enough to be intended.

Answer: D

Correct answer: 781

Neither a constant difference nor a constant ratio fits, since the gaps run 5, 25, 125. Each term is the previous one multiplied by 5 and then increased by 1: 1 times 5 plus 1 is 6, and 6 times 5 plus 1 is 31. Applying it once more, 156 times 5 plus 1 is 781. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 156, the last term shown. Substituting the answer back and regenerating the series is the only check that catches both rule and arithmetic errors.

Answer: A

Correct answer: 100

The gaps are 13, 15, 17, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of a whole number, the numbers running consecutively: position 6 gives 36 and position 9 gives 81. The next position is 10, which gives 100. As a check, the same rule applied to the earlier positions reproduces 36, 49, 64, 81 exactly, so it accounts for every term shown and not merely the last. The position of a term in the series is as much a part of the data as its value.

Answer: B

Correct answer: 169

The gaps are 19, 21, 23, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of a whole number, the numbers running consecutively: position 9 gives 81 and position 12 gives 144. The next position is 13, which gives 169. As a check, the same rule applied to the earlier positions reproduces 81, 100, 121, 144 exactly, so it accounts for every term shown and not merely the last. Growth that accelerates points to multiplication; growth that is steady points to addition.

Answer: C

Correct answer: 225

The gaps are 23, 25, 27, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the square of a whole number, the numbers running consecutively: position 11 gives 121 and position 14 gives 196. The next position is 15, which gives 225. As a check, the same rule applied to the earlier positions reproduces 121, 144, 169, 196 exactly, so it accounts for every term shown and not merely the last. An unexpected sign change is almost always a deliberate feature rather than a typographical accident.

Answer: D

Correct answer: 343

The gaps are 37, 61, 91, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the cube of a whole number, the numbers running consecutively: position 3 gives 27 and position 6 gives 216. The next position is 7, which gives 343. As a check, the same rule applied to the earlier positions reproduces 27, 64, 125, 216 exactly, so it accounts for every term shown and not merely the last. The four options are constructed to be equally plausible until the rule is identified, so guessing gains nothing.

Answer: A

Correct answer: 729

The gaps are 91, 127, 169, which follow no constant pattern, so the rule lies in the terms rather than in the steps between them. Each term is the cube of a whole number, the numbers running consecutively: position 5 gives 125 and position 8 gives 512. The next position is 9, which gives 729. As a check, the same rule applied to the earlier positions reproduces 125, 216, 343, 512 exactly, so it accounts for every term shown and not merely the last. Where the terms are all multiples of a common number, dividing through often simplifies the pattern.

Answer: B

Correct answer: 78

Every gap is the same: the differences run 16, 16, 16, so the common difference is 16. Applying it once more to the final term, 62 + 16 gives 78. As a check, subtracting 16 from the answer returns 62, the term before it, and repeating that recovers the whole series. A series and its differences can both be regular, and identifying which is regular decides the family.

Answer: C

Correct answer: -7

Every gap is the same: the differences run -8, -8, -8, -8, so the common difference is -8. Applying it once more to the final term, 1 - 8 gives -7. As a check, subtracting -8 from the answer returns 1, the term before it, and repeating that recovers the whole series. The intended rule is the one that a reader could state in a single sentence.

Answer: D

Correct answer: 192

The terms are multiplied rather than added to. Dividing each by its predecessor gives the same result throughout: 24 over 12 is 2, and 48 over 24 is 2, so the ratio is 2. Multiplying the last term, 96 times 2 is 192. As a check, dividing the answer by 2 returns 96, which is the last term shown. Every question in this topic can be answered from the terms shown, with no outside knowledge required.