Number Series Questions and Answers

Answer: C

Correct answer: 59

The gaps run 4, 2, 4, 6 and settle into no pattern at all, so no arithmetic step will fit. The terms are the prime numbers in order, each having no divisor but itself and one. The next prime after 53 is 59. As a check, every number between 53 and the answer has a divisor other than itself and one, so none of them could be the next term. A number is prime when it has no divisor but itself and one, so each candidate can be tested directly rather than recalled.

Answer: D

Correct answer: -25

Setting the signs aside, the magnitudes run 5, 9, 13, 17, 21 and rise by a constant 4. The signs alternate between positive and negative. The next magnitude is 25 and the alternation makes it -25. As a check, the answer has the opposite sign to 21, the term before it, which the alternation requires. Splitting a signed series into its magnitudes and its signs turns one problem into two, each of them simple.

Answer: A

Correct answer: -33

Setting the signs aside, the magnitudes run 3, 9, 15, 21, 27 and rise by a constant 6. The signs alternate between positive and negative. The next magnitude is 33 and the alternation makes it -33. As a check, the answer has the opposite sign to 27, the term before it, which the alternation requires. The sign of a term depends only on its position, so it can be settled independently of the arithmetic.

Answer: B

Correct answer: -32

Setting the signs aside, the magnitudes run 7, 12, 17, 22, 27 and rise by a constant 5. The signs alternate between positive and negative. The next magnitude is 32 and the alternation makes it -32. As a check, the answer has the opposite sign to 27, the term before it, which the alternation requires. An alternating sign is a common decoration and rarely carries the substance of the pattern.

Answer: C

Correct answer: 95

Neither a constant difference nor a constant ratio fits, since the gaps run 3, 6, 12, 24. Each term is the previous one multiplied by 2 and then increased by 1: 2 times 2 plus 1 is 5, and 5 times 2 plus 1 is 11. Applying it once more, 47 times 2 plus 1 is 95. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 47, the last term shown. A rule that multiplies and then adds produces differences that themselves grow geometrically, which is how the family is identified.

Answer: D

Correct answer: 485

Neither a constant difference nor a constant ratio fits, since the gaps run 4, 12, 36, 108. Each term is the previous one multiplied by 3 and then increased by 2: 1 times 3 plus 2 is 5, and 5 times 3 plus 2 is 17. Applying it once more, 161 times 3 plus 2 is 485. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 161, the last term shown. Two-part rules are found by asking how the differences grow rather than by how the terms grow.

Answer: A

Correct answer: 220

Neither a constant difference nor a constant ratio fits, since the gaps run 7, 14, 28, 56. Each term is the previous one multiplied by 2 and then increased by 4: 3 times 2 plus 4 is 10, and 10 times 2 plus 4 is 24. Applying it once more, 108 times 2 plus 4 is 220. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 108, the last term shown. Testing a candidate rule against the first pair as well as the last is what exposes a rule that happens to fit only the recent terms.

Answer: B

Correct answer: 597

Neither a constant difference nor a constant ratio fits, since the gaps run 7, 28, 112. Each term is the previous one multiplied by 4 and then increased by 1: 2 times 4 plus 1 is 9, and 9 times 4 plus 1 is 37. Applying it once more, 149 times 4 plus 1 is 597. As a check, reversing the rule on the answer -- subtracting the constant and dividing -- returns 149, the last term shown. The multiplier can be recovered by dividing one difference by the previous one, after which the added constant follows.

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.