Letter and Symbol Series Questions and Answers

Answer: A

Correct answer: L

The series runs backwards in steps of three: X(24), U(21), R(18), O(15). Three below 15 is position 12, which is L. Working backwards is where most errors creep in, so it helps to convert to positions first and subtract. M at 13 is only two below O and would fit a step of two, which the series has never taken. A useful habit with any descending series is to read it backwards first: L, O, R, U, X climbs by three, which is far easier to confirm than the same series read the other way.

Answer: B

Correct answer: Q

The letters descend two places at a time: Y(25), W(23), U(21), S(19). Two below 19 is position 17, giving Q. The run picks out alternate letters going backwards from Y, so it is the odd-numbered positions in reverse. R at 18 is the immediately preceding letter and is what a single backward step would give. Alternate letters are among the easiest patterns to spot, and the direction is the only thing that has to be settled before answering.

Answer: C

Correct answer: G

Each term is four places back from the one before: W(23), S(19), O(15), K(11). Four below 11 is position 7, which is G. Because the step is large and backwards, converting to positions is far safer than counting letters on the fingers. H at 8 is a three-step and F at 6 a five-step, the two neighbouring errors. Read in reverse the series is G, K, O, S, W, a four-step climb, which is the quickest way to confirm the answer once it has been found.

Answer: D

Correct answer: D

The series falls by four places each time: T(20), P(16), L(12), H(8). Four below 8 is position 4, which is D. The run would end there for practical purposes, since a further four would take it off the front of the alphabet. C at 3 and E at 5 sit either side and are the usual off-by-one answers. Because the step is four and the series has reached position 8, only one more term is possible before the alphabet is exhausted, which is a useful sanity check on the answer.

Answer: A

Correct answer: P

The gaps themselves grow by one each time: A to B is +1, B to D is +2, D to G is +3, G to K is +4. The next gap must be +5, and five beyond K(11) is position 16, which is P. Series of this kind are recognised by the differences rather than by the terms, so writing the gaps underneath is the first move. Assuming a constant gap of four would give O and is the commonest mistake.

Answer: B

Correct answer: Q

The differences increase by one at every step: B to C is +1, C to E is +2, E to H is +3, H to L is +4, so the next must be +5. Five beyond L(12) is position 17, giving Q. Note that the terms are at positions 2, 3, 5, 8, 12, 17 - each is the previous plus the running count. P at 16 would follow from repeating the +4 step instead of increasing it. The running total of the gaps is 1, 3, 6, 10, 15 - the triangular numbers - so the position of the nth term is always the starting position plus a triangular number.

Answer: C

Correct answer: K

The series moves backwards by a growing amount: Z to Y is -1, Y to W is -2, W to T is -3, T to P is -4. The next step is -5, and five below P(16) is position 11, which is K. Growing gaps in reverse are the hardest of these to read, because the letters accelerate away from the end of the alphabet; converting to positions removes the difficulty entirely.

Answer: D

Correct answer: Y

The positions are 1, 4, 9, 16 - the perfect squares. The next square is 25, and position 25 is Y. Reading this as a letter series with growing gaps also works, since the differences are 3, 5, 7 and then 9, but recognising the squares is quicker and leaves no room for a miscount. Z at 26 is the natural guess for anyone who assumes the series ends at the alphabet's close. Squares grow quickly, so a series of this shape gives at most five terms before it passes Z, and recognising that limit is often enough to identify the rule.

Answer: A

Correct answer: R

The gaps widen by one each time: C to D is +1, D to F is +2, F to I is +3, I to M is +4. The next gap is +5, so from M(13) the series reaches position 18, which is R. The pattern is the same as several others of this family but started from a different letter, so the answer cannot be recalled - it has to be counted. Q at 17 results from repeating the previous gap rather than extending it.

Answer: B

Correct answer: X

The steps backwards grow by one: M to L is -1, L to J is -2, J to G is -3, G to C is -4. The next step is -5, and five below C(3) is position -2, which wraps round to X at position 24. Wrapping is what makes this one hard: the series runs off the front of the alphabet and continues from the back. B at 2 is what a single further step would give and is the answer most often chosen. Whenever a series with growing backward steps starts below the middle of the alphabet, a wrap is almost certain, and it is worth checking for one before rejecting the pattern.