Skill: 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:

$$3,\ 6,\ 8,\ 9$$

The number is:

• greater than $5$,
• even,
• less than $8$.

Step 1: Use “greater than $5$.”

Cross out $3$, because $3$ is not greater than $5$.

Possible numbers:

$$6,\ 8,\ 9$$

Step 2: Use “even.”

An even number can be split into two equal groups. Cross out $9$, because $9$ is odd.

Possible numbers:

$$6,\ 8$$

Step 3: Use “less than $8$.”

Cross out $8$, because $8$ is not less than $8$.

Only $6$ remains.

$$\boxed{6}$$

The secret number must be $6$ because every other choice was ruled out by a clue.