SSC CGL Reasoning · Coding-Decoding
Position Values and Sums
Letters become numbers: each letter is written as its place in the alphabet (from the front or from the back, sometimes changed by a fixed rule), the places are added into one number, or the code depends only on how many letters the word has.
Why this matters
Sixty questions in the bank: thirty-two code each letter as a number, nineteen add the letters into a single number, and nine use only the word's length or a number system. Twenty-seven are MODERATE, more than on any other page of this chapter, because a rule has to be found and then tested on a second example.
Concept 1 of 3: Each letter written as a number
Definition
- Forward position: A = 1 to Z = 26 (anchors E 5, J 10, O 15, T 20, Y 25).
- Reverse position: A = 26 to Z = 1. It equals 27 minus the forward position, which is the forward position of the opposite letter: H is 8, so its reverse position is 19 (S).
- Usual changes: position plus or minus a fixed number, twice the position, the square of the position, or a change for vowels only or consonants only.
- Reading a joined code: one- and two-digit numbers run together (DOLL is 4, 15, 12, 12, written 4151212). Split it from the left using the letters you know, never by guessing.
- Two different reversals: the word read backwards (TOP as P, O, T gives 161520) is not the same as the digits reversed (201516 reversed is 615102). Test both on the example.
- Fast route: work out the first and last letters' numbers only; they usually leave one option.
Reverse position of a letter
Worked example
Practice this conceptself-check · 4 quick reps
The same idea in a real exam question:
Example 1 · Coding-Decoding · Position Values and Sums
Splitting a joined code the wrong way
Reversing the digits when the letters were reversed
Concept 2 of 3: Adding the letters into one number
Definition
1. Add the forward positions. Compare with the code: equal, total plus a number, total times a number, total times the number of letters, or total divided by the number of letters. 2. If nothing fits, add the reverse positions and compare again. 3. Shortcut: for a word of n letters, reverse sum = 27n minus forward sum. Work out one sum and you have both. 4. Test the step on both examples. +10 and times 2 can both fit one word. 5. Fast route: look at the options' last digits, or which options are multiples of the letter count; often only one can be right.
Reverse sum of a word
- the number of letters in the word
Worked example
Practice this conceptself-check · 4 quick reps
The same idea in a real exam question:
Example 2 · Coding-Decoding · Position Values and Sums
Trusting a step that fits one example
Counting a repeated letter once
Concept 3 of 3: Codes from the number of letters, and number systems
Definition
- Count the letters, n. Try n squared, n cubed, 2n, 7n, n minus 1. A square (16, 25, 36) or a cube (27, 64, 125) is a strong hint.
- If two words of the same length but different letters have the same code, the letters do not matter.
- Two-sign number systems are binary: one sign stands for 0, the other for 1. Write the number as a sum of 64, 32, 16, 8, 4, 2, 1 and put 1 for each value used, 0 for each one skipped.
- Remainder codes: a number coded by its remainders on division by 3, 7 and 11. A number leaving the same remainder r on all three is r more than a multiple of 3 times 7 times 11, which is 231.
Binary place values
Worked example
Practice this conceptself-check · 4 quick reps
The same idea in a real exam question:
Example 3 · Coding-Decoding · Position Values and Sums
Adding letters when only the length matters
Dropping the zeros in binary
Summary — formulas & gotchas at a glance
A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.
Formulas (3)
- Each letter written as a number
Reverse position of a letter
- Adding the letters into one number
Reverse sum of a word
- Codes from the number of letters, and number systems
Binary place values
Watch out for (6)
- Splitting a joined code the wrong way→ Each letter written as a number
- Reversing the digits when the letters were reversed→ Each letter written as a number
- Trusting a step that fits one example→ Adding the letters into one number
- Counting a repeated letter once→ Adding the letters into one number
- Adding letters when only the length matters→ Codes from the number of letters, and number systems
- Dropping the zeros in binary→ Codes from the number of letters, and number systems
Test yourself on Coding-Decoding
20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.