Letter and Symbol Series Questions and Answers

Answer: D

The missing cluster is T G 40.

First letters: E (5), H (8), M (13), ?, C. The gaps are +3, +5, +7, +9, so the missing letter is \(13 + 7 = 20\), T, and then \(20 + 9 = 29\), which wraps round to 3, C, as given.

Second letters are the opposites of the first (letters whose positions add to 27): E-V, H-S, M-N, so T pairs with G. Numbers are twice the first letter's position: 10, 16, 26, so T gives 40, and C (29 on the wrap) gives 58, as given.

T H and S G break the letter rule, and 36 breaks the number rule.

Answer: C

The missing letters are z y z x y.

Filling them in gives: yyzzx xxyyz zzxxy yyzzx. The series is made of blocks of five letters; each block has two of one letter, two of the next and one of the third, and each block starts with the letter its predecessor ended on: yyzzx, then xxyyz, then zzxxy, then yyzzx again.

Each of the other options breaks this pattern in at least one block; for instance x y z y x leaves the first block as yyzxx.

Answer: A

The series adds the next letter of the alphabet at each step: a, then ab, then abc, then abcd, then abcde. So the next term adds f to give abcdef. The option abcdfe has the last two letters in the wrong order, and Abcfed and Abcdef start with a capital letter while every term of the series is in small letters, so they do not continue the pattern. The answer is abcdef, option A.

Answer: D

The missing term is UQ120. Take the three parts of each term separately. The first letters A, C, G, M move by 2, 4 and 6 places, so the next move is 8 places, giving U. The second letters G, H, J, M move by 1, 2 and 3 places, so the next move is 4 places, giving Q. The numbers 48, 63, 80, 99 differ by 15, 17 and 19, so the next difference is 21 and the number is 99 + 21 = 120. The options VR122, VS124 and UQ112 each fail on at least one of the three parts, and only UQ120 satisfies all of them.

Answer: B

In each term the first letter moves three places forward, the second moves three places back and the number is the next prime: F P 11, I M 13, L J 17, then O G 19, and R D 23 follows.

\[ L+3=O,\ J-3=G,\ \text{next prime after } 17 = 19 \]

The missing term is O G 19. The options with 21 break the prime sequence, and P H or P G shift the first letter by four places.

Answer: D

The blanks are filled with a, a, b, c, a, c, b, d, c, d (option D). The series is the seven-letter block abbcade repeated. Writing the given series with the blanks filled in this way gives abbcade abbcade abbcade abbcade abbcade, and every printed letter agrees with it: the first blank takes a to start the block, the second takes a, and so on through the string.

Option A starts with c, which would make the first block cbbc..., not matching the b b c after it, and options B and C fail at the first or second blank in the same way, because the letters after each blank (b b c, d e a) fix the block abbcade. Only the sequence a, a, b, c, a, c, b, d, c, d completes all five repeats.

Answer: D

DOWN-NODW-OWND follows the same logic. In CHIP-PHCI-HIPC the first step takes letters 4, 2, 1, 3 of CHIP to make PHCI (P, H, C, I). The second step takes letters 2, 4, 1, 3 of PHCI to make HIPC (H, I, P, C).

Apply the same two steps to DOWN. Letters 4, 2, 1, 3 give N, O, D, W, which is NODW. Letters 2, 4, 1, 3 of NODW give O, W, N, D, which is OWND, exactly as printed. In the other triads at least one of the two steps uses a different rearrangement: for example HAIR gives AIRH in the first step, which is not the 4, 2, 1, 3 pattern.

Answer: A

The series is the block aaz bby ccx repeated. Placing abcabxzyabc in the 11 blanks in order gives a(a)zb(b)yc(c)x(a)az(b)bycc(x)aa(z)bb(y)ccx(a)az(b)by(c)cx, which reads aaz bby ccx aaz bby ccx aaz bby ccx aaz bby ccx without a break.

The other options put a letter other than the required one in an early blank. For example, acbacxzyabc makes the second block read bcy instead of bby, so the repeating pattern breaks.

A quick test of the key is that every third letter in the completed string runs z, y, x, then repeats, with the first letters running a, b, c in pairs.

Answer: A

The letters go B, F, J, N, R, which move four places each time, so the next letter is V. The numbers 113, 125, 142, 164 and 191 differ by 12, 17, 22 and 27, which rise by 5 each time, so the next difference is 32 and the next number is 191 + 32 = 223. The missing term is therefore V-223, option (A). The options beginning with U break the four-place step in the letters, and V-221 does not follow the number pattern, since it would need a difference of 30.

Answer: D

Go through the string 1 3 @ $ 5 6 & 5 % $ # 1 2 # % # 2 * 5 3 @ 4 $ & * and check each symbol for a number before it and a symbol after it. The @ after 3 is followed by $, so it counts. The % after the second 5 is followed by $, so it counts. The # after 2 is followed by %, so it counts. The $ after 4 is followed by &, so it counts. The other symbols fail: $ after @ and the # after $ follow symbols, the & after 6 and the * after 2 are followed by numbers, and the @ after 3 is followed by 4. There are 4 such symbols, option (D).