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Addition / Difference Code

Introduction

Addition / Difference Code problems convert letters or digits into numbers by using sums or differences - for example the sum of letter positions, difference between extremes, or sum/difference of digit pairs. These are common in reasoning sections because they test basic arithmetic applied to symbolic inputs.

This pattern is important because it trains you to spot simple numeric transforms quickly and to verify them with a quick arithmetic check.

Pattern: Addition / Difference Code

Pattern

The key concept is: the code is produced by adding or subtracting relevant numeric values derived from the input (letters → A=1…Z=26, digits → numeric digits). Typical rules: sum of letter positions, difference between highest and lowest digit/position, sum of outer letters, or (sum of letters) ± constant.

Common transforms to test:

  • Sum of positions: WORD → Σ(letter positions). (e.g., CAT → 3+1+20 = 24)
  • Sum of first & last: WORD → first_pos + last_pos (e.g., BAD → 2+4=6).
  • Difference of extremes: digits → max - min or letters → max_pos - min_pos.
  • Sum ± constant: Σ(positions) ± k (check small constant offsets).
  • Digit-based: For two-digit numbers, use (a+b) or (a-b) or (a×b) then add/subtract a constant.

Step-by-Step Example

Question

If CAT = 24 and DOG = 26 using A=1…Z=26, what is BAT?

Solution

  1. Step 1: Check possible rules

    CAT → C(3)+A(1)+T(20)=24. DOG → D(4)+O(15)+G(7)=26. Both examples equal the sum of letter positions.

  2. Step 2: Apply the rule to BAT

    B(2)+A(1)+T(20)=2+1+20 = 23.

  3. Final Answer:

    23

  4. Quick Check:

    Recompute CAT: 3+1+20=24; DOG: 4+15+7=26. BAT: 2+1+20=23 ✅

Quick Variations

1. Use first+last letters only (fast check).

2. Use difference: highest position - lowest position (good for digit inputs).

3. Sum of digits for numeric inputs (e.g., 47 → 4+7=11).

4. Combine sum with constant offset (Σ ± k) - identify k by comparing examples.

5. Weighted sum (e.g., 2×first + last) - check for scaling factors if sums don't match exactly.

Trick to Always Use

  • Step 1: Compute simple sums first (whole-word Σ or first+last).
  • Step 2: If sums don't match, try difference of extremes or check for a constant offset.
  • Step 3: Verify by applying the inferred rule to all given examples before answering.

Summary

Summary

  • Addition/Difference codes use sums or differences of numeric representations (A=1…Z=26 or digits).
  • Always test sum-of-positions, sum of first+last, and difference of extremes first - they are the most common.
  • Confirm the rule across all examples; perform a quick reverse-check to avoid arithmetic slips.

Practice

(1/5)
1. If the code of MOP is found by summing alphabetical positions (A=1…Z=26), what is the code for MOP?
easy
A. 44
B. 42
C. 46
D. 40

Solution

  1. Step 1: Identify the rule

    Rule = sum of letter positions (A=1…Z=26).

  2. Step 2: Compute positions

    M = 13, O = 15, P = 16 → Sum = 13 + 15 + 16 = 44.

  3. Final Answer:

    44 → Option A

  4. Quick Check:

    Recalculate: 13+15+16 = 44 ✅
Hint: When words map to moderate integers, try summing alphabetical positions first.
Common Mistakes: Forgetting correct alphabetical values (e.g., P = 16).
2. If 71 → 6 and 84 → 4 using the rule (absolute difference of digits), what is the code for 95?
easy
A. 3
B. 4
C. 5
D. 6

Solution

  1. Step 1: Identify the rule

    Rule = absolute difference of the two digits: |first - second|.

  2. Step 2: Apply the rule to 95

    |9 - 5| = 4 → 4.

  3. Final Answer:

    4 → Option B

  4. Quick Check:

    Check examples: |7-1|=6, |8-4|=4 → rule consistent. 95 → |9-5|=4 ✅
Hint: Use absolute value to avoid sign mistakes when subtracting digits.
Common Mistakes: Subtracting smaller from larger without absolute value or reversing digits.
3. If a code uses the sum of all letter positions, what is the code for BOX?
easy
A. 41
B. 39
C. 43
D. 37

Solution

  1. Step 1: Identify the rule

    Rule = sum of alphabetical positions (A=1…Z=26).

  2. Step 2: Compute positions

    B = 2, O = 15, X = 24 → Sum = 2 + 15 + 24 = 41.

  3. Final Answer:

    41 → Option A

  4. Quick Check:

    2+15+24 = 41 - matches Option A ✅
Hint: Try the position-sum quickly for short words (3-4 letters).
Common Mistakes: Using wrong letter values or skipping a letter in the sum.
4. If 'MOON' = (sum of letter positions) - 2 and 'SUN' = (sum of positions) - 2, what is the code for STAR?
medium
A. 58
B. 54
C. 56
D. 60

Solution

  1. Step 1: Deduce the rule

    Given rule: code = (sum of alphabetical positions) - 2.

  2. Step 2: Compute STAR

    S=19, T=20, A=1, R=18 → Sum = 19+20+1+18 = 58. Apply rule: 58 - 2 = 56.

  3. Final Answer:

    56 → Option C

  4. Quick Check:

    Example check: MOON (13+15+15+14=57) → 57-2=55; SUN (19+21+14=54) → 54-2=52 - rule applied consistently. STAR → 58-2=56 ✅
Hint: If sums are off by a small constant, test sum ± k patterns.
Common Mistakes: Forgetting to apply the -2 offset after summing positions.
5. If a two-digit code is formed by multiplying its digits (product rule): 23 → 6, 34 → 12, 45 → 20, what is the code for 67?
medium
A. 36
B. 42
C. 13
D. 48

Solution

  1. Step 1: Identify the rule

    Rule = product of the two digits (first × second): 2×3=6, 3×4=12, 4×5=20.

  2. Step 2: Apply to 67

    6 × 7 = 42.

  3. Final Answer:

    42 → Option B

  4. Quick Check:

    Pattern holds for examples; 6×7=42 ✅
Hint: For two-digit inputs, test product of digits if sums don't fit.
Common Mistakes: Using digit-sum instead of product.

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