Which of the four options will replace the question mark (?) in the following series? UE 88, VG 84, WI 80, XK76, ?

Correct — D. Each of the three tracks runs its own arithmetic, so split the term and read them separately.

First letter: U, V, W, X — a step of +1, so the next is Y.
Second letter: E, G, I, K — a step of +2, so the next is M.
Number: 88, 84, 80, 76 — a step of −4, so the next is 72.

Reassembling the three tracks gives YM72, option (d).

Why the others are wrong

• (a)
  ZM72 — Z is two places past X, not one. The second letter and the number are both right, which is exactly what makes this the option a rushed candidate marks.
• (b)
  ZN71 — All three tracks are wrong: Z is +2 from X, N is +3 from K where the gap has been +2, and 71 is −5 from 76 where the gap has been −4.
• (c)
  YN73 — The first letter is right, but N is +3 from K and 73 is −3 from 76. Two tracks moved by the wrong amount in the same step.

An alpha-numeric series hides two or three independent progressions inside one printed term. The letters do not interact with the number and the two letters do not interact with each other.

The reliable method is to write the term out as columns, convert the letters to their alphabet positions, and find the common difference in each column on its own.

Once all three differences are known, the missing term is built rather than guessed.

Key facts

• On the standard scale A is 1 and Z is 26, so U is 21, V is 22, W is 23, X is 24 and Y is 25.
• The second track E, G, I, K, M is the odd-numbered letters, a chain of +2.
• The numeric track 88, 84, 80, 76, 72 is an arithmetic progression with common difference −4.

Common traps

• Verifying only the number track, which is the easiest to see, and then picking the first option that matches it
• Miscounting the alphabet under time pressure, most often between W and Y
• Assuming both letters must move by the same amount

No directly related past PYQ was found.