60-second revision
- k-th from the right in a series of n elements = (n - k + 1)th from the left.
- 'a-th to the right of b-th from the left' = (b + a)th from the left; 'to the left' = (b - a)th.
- Vowels are A, E, I, O, U; every other letter is a consonant.
- Read 'immediately preceded by X' as 'the element just before is X' and 'followed by Y' as 'the element just after is Y'.
- After removing elements, renumber the series before counting positions.
- Letter positions: E 5, J 10, O 15, T 20, Y 25 (EJOTY).
- Letter-pair questions: compare the gap in the word with the gap in the alphabet, both forward and backward.
What these sets look like
A row of 20–30 elements mixing letters, digits and symbols is given, followed by questions on positions and on elements that satisfy conditions. Related questions ask you to rearrange digits of a number, letters of a word or a set of numbers. The skills are careful counting and a fixed scanning routine.
Position arithmetic
| Asked | Convert to | Example (n = 24) |
|---|---|---|
| k-th from the right | (n - k + 1)th from the left | 7th from right = 18th from left |
| a-th to the right of b-th from the left | (b + a)th from the left | 5th right of 10th = 15th |
| a-th to the left of b-th from the left | (b - a)th from the left | 4th left of 10th = 6th |
| a-th to the left of b-th from the right | (b + a)th from the right | 3rd left of 6th from right = 9th from right |
| a-th to the right of b-th from the right | (b - a)th from the right | 2nd right of 6th from right = 4th from right |
Condition-counting scans
For 'how many symbols are immediately preceded by a digit and immediately followed by a letter', do not scan the whole condition at once. First mark every element of the type asked (here, symbols). Then check the neighbour before each one, and only for survivors check the neighbour after. Write the qualifying triplets in the margin so you can recount them.
Worked example: in 5 K # 2 @ M 8 % A 4 & 3, the symbols are #, @, %, &. # is preceded by K (letter) — out. @ is preceded by 2 and followed by M — counts. % is preceded by 8 and followed by A — counts. & is preceded by 4 and followed by 3 — out. Answer: 2.
Removing elements
When a question says 'if all the symbols are removed' or 'if all the vowels are dropped', rewrite the shortened series first. All positions change, so count only on the rewritten line.
Rearranging digits and letters
- Write the original and the rearranged forms one above the other and compare column by column.
- For numbers, 'ascending' runs from the smallest digit to the largest; 'descending' the other way.
- For words, arrange the letters in dictionary order and compare letter by letter.
- When digits of each number are swapped or changed, write the new numbers first, then answer the comparison asked.
Worked example: digits of 5813 in ascending order give 1358. Comparing 5813 with 1358, no digit stays in place. In descending order (8531), again none stays in place.
Letter pairs in a word
For each pair of letters in the word, find the number of letters between them in the word and in the alphabet. They form a valid pair when the two numbers are equal. 'Both forward and backward' means the order of the two letters in the word may match or reverse the alphabet order. Check every pair systematically: first letter with each later letter, then the second letter with each later letter, and so on.
| Letter | Position | Opposite letter |
|---|---|---|
| A | 1 | Z |
| E | 5 | V |
| J | 10 | Q |
| M | 13 | N |
| O | 15 | L |
| T | 20 | G |
| Y | 25 | B |
Modified alphabet questions
Some questions reverse part of the alphabet or write it backwards. Write the modified order for the stretch you need (no need to write all 26) and count positions on it. For a fully reversed alphabet, the n-th letter is the (27 - n)th letter of the normal alphabet.
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