GRE Alfa-Numeric
GRE Alphanumeric Concepts
In alphanumeric puzzles, digits are often replaced with letters or symbols, and the objective is to solve the puzzle using logical inferences. Below are some important principles related to digit sums and carries:
[i] Sum of two digits in two numbers has a hundreds digit that is always 1.
This condition implies that the sum of two numbers results in a value that extends beyond the hundred place. Typically, this happens when the sum exceeds 99, causing a carry over into the hundreds place.
Example:
57 + 63 = 120
Here, the hundreds digit of the sum is 1, as required.
[ii] Sum of two single digits has a carry of 1 or 0.
When adding two single-digit numbers (between 0 and 9), the possible sums range from 0 to 18. If the sum is less than 10, there will be no carry (carry = 0). If the sum is 10 or more, there will be a carry of 1.
Examples:
- 5 + 4 = 9 → No carry (carry = 0).
- 7 + 5 = 12 → Carry of 1 (carry = 1).
[iii] Sum of three single digits has a carry of 0, 1, or 2.
When adding three single-digit numbers, the sum can range from 0 to 27. The possible carry values are:
- Sum less than 10: Carry = 0.
- Sum between 10 and 19: Carry = 1.
- Sum between 20 and 27: Carry = 2.
Examples:
- 3 + 4 + 2 = 9 → Carry = 0.
- 6 + 7 + 8 = 21 → Carry = 2.
[iv] If A + B = A, then B must be zero.
If the sum of two numbers results in one of the numbers itself, the other number must be zero.
Example:
If A = 7 and B = 0, then 7 + 0 = 7, which satisfies the equation.
These principles are often used in puzzles that involve deciphering missing digits or letters in alphanumeric formats. Understanding the relationship between digits and carries is key to solving these problems efficiently in exams like the GRE.