Letter and Symbol Series Questions and Answers

Answer: C

Correct answer: E4

The letters advance one place at a time while the numbers are halved at each step: 64, 32, 16, 8. Half of 8 is 4, so the term is E4. Halving series are read most easily from the right-hand end, where the numbers are small and the relationship is obvious. E6 comes from subtracting a constant, which fits no pair in the series. Halving series are read most easily from the small end, where 8, 4 and 2 make the relationship plain even if the larger terms do not.

Answer: D

Correct answer: T81

The letters advance one place at a time - P, Q, R, S - while the numbers are multiplied by three: 1, 3, 9, 27. Three times 27 is 81, so the term is T81. T54 comes from doubling and adding, a rule that fits no adjacent pair here; checking a candidate against the first pair as well as the last is what exposes it. Powers of three grow quickly, and writing them as 3 to the power 0, 1, 2 and 3 makes the next term immediate without repeated multiplication.

Answer: A

Correct answer: G162

The letters step forward one place at a time. The numbers are tripled at each step: 2, 6, 18, 54. Three times 54 is 162, giving G162. The arithmetic is the only real difficulty, and it is worth doing in two parts - three fifties is 150 and three fours is 12. G108 doubles instead of tripling, which agrees with none of the earlier steps. Tripling is easier to check than to perform: 162 divided by 3 is 54, which restores the previous term exactly.

Answer: B

Correct answer: P120

The letters advance one place at a time. The numbers are multiplied by a growing factor: 1 times 2 is 2, 2 times 3 is 6, 6 times 4 is 24, so the next is 24 times 5, which is 120. The term is P120. These are the factorials, 1! through 5!, which is the quicker way to see it. P96 quadruples again instead of increasing the multiplier. Factorials appear rarely in letter series, but the giveaway is a multiplier that grows by one each time rather than staying fixed.

Answer: C

Correct answer: E80

The letters climb one place at a time and the numbers double: 5, 10, 20, 40. Twice 40 is 80, so the term is E80. E60 treats the numbers as growing by a constant 20, which fits only the last step; the earlier steps of 5 and 10 rule it out immediately, which is why every gap should be checked rather than just the most recent. Doubling and adding a constant agree at one step and diverge at every other, so a rule should always be tested against the first pair as well as the last.

Answer: D

Correct answer: U

These are the vowels in alphabetical order: A, E, I, O. The next and last is U. The series looks like a letter-gap pattern at first because the steps are 4, 4 and 6, but the gaps are not constant and no arithmetic rule fits. When the differences refuse to settle, the answer usually lies in a property of the letters themselves rather than in their positions. When the differences between terms refuse to settle into a pattern, the rule usually depends on a property of the letters rather than on their positions.

Answer: A

Correct answer: G

The series lists the consonants in order: B, C, D, then F - E is skipped because it is a vowel. The next consonant after F is G. The single irregular gap between D and F is the clue; a series that advances by one throughout and then jumps once is usually omitting something on a rule of its own. E is the tempting answer precisely because it is the letter that was left out. The single irregular gap is the whole clue: a series that steps by one throughout and jumps exactly once is almost always omitting letters on a rule of its own.

Answer: B

Correct answer: R

The letters descend two places at a time from the end of the alphabet: Z(26), X(24), V(22), T(20). Two below 20 is position 18, which is R. Equivalently the series picks out alternate letters running backwards from Z. S at 19 is the immediately preceding letter and is what a single backward step gives. Reading the series in reverse gives R, T, V, X, Z, a forward two-step, which confirms the answer from the other direction.

Answer: C

Correct answer: A

The vowels in reverse order: U, O, I, E and then A. Reading the series forwards gives A, E, I, O, U, which is the familiar sequence, so recognising it depends on being willing to read a series from either end. Y is sometimes counted as a vowel but never appears in this position, and it would in any case belong at the far end of the forward sequence. Reading a series from either end is a habit worth forming, since a pattern that looks obscure forwards is often obvious backwards.

Answer: D

Correct answer: E^

Two strands run in parallel. The letters advance A, B, C, D one place at a time, so the next is E. The symbols are the shifted number keys in order - shift-2 gives @, shift-3 gives #, shift-4 gives $, shift-5 gives % - so the next is shift-6, which is ^. The term is E^. E& skips a key, taking shift-7 instead of shift-6. The symbols advance one key at a time along the number row, so the answer depends on counting keys rather than on any property of the characters themselves.