Alphabet Series — PPSC previous year questions

UNDERTAKING has 11 letters: U, N, D, E, R, T, A, K, I, N, G. Arranged alphabetically they read A, D, E, G, I, K, N, N, R, T, U. With 11 letters the middle one is the 6th, which is K.

Note the character just before every 3. The first 3 has nothing before it. Then come A3 and U3 (vowels), S3, T3 (from TT3) and J3 (from JJ3). After that 53 (a digit), X3 (from DX3), Z3 (from XZ3) and T3. > consonants before 3: S, T, J, X, Z, T = 6 So there are 6 consonants.

Each group is built as (n)(n-1)(n+1) around consecutive middle letters: P-O-Q around P, S-R-T around S, V-U-W around V, with first letters advancing by 3 (P, S, V, Y). Next group centres on Y: Y-X-Z, i.e., YXZ.

The row is 3 9 2 1 8 1 2 6 8 6 3 6 4 2 5 2 8 5 2 6 4 5 1 4 9 4 7 3 2 7 2 5 9. Find each 2 that comes just after a digit of 5 or more: 9-2 (3rd place), 5-2 (16th), 5-2 (19th) and 7-2 (31st). The other 2's come after 1, 4 and 3. So there are four such 2's — more than three.

Removing the even digits (2, 4, 6, 8) from 392181268636425285264514947327259 leaves 3 9 1 1 3 5 5 5 1 9 7 3 7 5 9 — fifteen digits. Tenth from the right end is the (15 − 10 + 1) = 6th from the left, which is 5.

Seventh to the left of the 14th digit from the left end is the (14 − 7) = 7th digit from the left. Counting in 3 9 2 1 8 1 2 6 8 6 …, the 7th digit is 2.

Each letter is repeated one more time than the previous one: A twice, B three times, C four times, D five times, then E. > A A | B B B | C C C C | D D D D D | E E … The blanks are B and D.

Count pairs, in either direction, whose gap in the word equals their gap in the alphabet. > CASTRAPHONE: S–T, T–O, T–N, R–P, H–E, O–N = 6 pairs > EXPERIENCED: P–R, I–E, I–D, E–C, E–D = 5 pairs CASTRAPHONE has 6 — neither fewer than 5 nor more than 7. EXPERIENCED has 5, which is more than 4.

Take each letter position separately. The third letters run I, J, K, L, M, N, so the missing term ends in L. The first and second letters follow two interleaved series: odd terms W, X, Y and Z, A, B; even terms E, ?, G and H, ?, J. > 1st letter: E → F → G > 2nd letter: H → I → J > 3rd letter: K → L → M The missing term is FIL.

In the reversed alphabet Z, Y, X, …, A, count from the left: Z=1, Y=2, …, P=11, O=12. So the 12th letter is O. Move four places to the right: N, M, L, K. Shortcut: the 12th letter from the left of the reversed series is the 12th from the right of the normal series, which is O. Four to its right in the reversed order is the 16th letter from the right of the normal series, i.e. the 11th from the left — K.