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Use logical elimination

Logical elimination involves identifying a limited set of possible numbers, shapes, arrangements, or solutions and ruling out each possibility that conflicts with a given condition, using the remaining information to determine what must be true. The reasoning connects numerical relationships, place value, operations, and attributes such as size or position; it does not include formal symbolic logic or generalized systems with large or unrestricted sets.

Detailed Explanation: Use logical elimination

When there are only a few possible answers, make a list. Then use each clue to cross out answers that cannot work. The answer left must be correct.

Example:
A secret number is one of these cards:

3, 6, 8, 93,\ 6,\ 8,\ 9

The number is:

  • greater than 55,
  • even,
  • less than 88.

Step 1: Use “greater than 55.”

Cross out 33, because 33 is not greater than 55.

Possible numbers:

6, 8, 96,\ 8,\ 9

Step 2: Use “even.”

An even number can be split into two equal groups. Cross out 99, because 99 is odd.

Possible numbers:

6, 86,\ 8

Step 3: Use “less than 88.”

Cross out 88, because 88 is not less than 88.

Only 66 remains.

6\boxed{6}

The secret number must be 66 because every other choice was ruled out by a clue.

Learn by doing: Use logical elimination

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Competition Math - Grade 6


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