Here are some clues to a mystery number. • The GCF of 18. 36, and me is 2. I am a multiple of 5. I am greater than 18 and less than 30. What is the mystery number? • The mystery number is
The Correct Answer and Explanation is:
The correct mystery number is 20.
Explanation:
To find the mystery number, each clue must be carefully examined and all conditions met:
Clue 1: “The GCF of 18, 36, and me is 2”
- Begin by listing the factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- The number must share only 2 as the greatest common factor with both 18 and 36.
This implies that the mystery number must be even, but cannot have any other common factors with 18 and 36 except for 2.
Clue 2: “I am a multiple of 5”
- Multiples of 5 between 18 and 30 are: 20 and 25
Clue 3: “I am greater than 18 and less than 30”
- This narrows the possibilities to the numbers: 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29
Now combine the clues:
From clue 2 and 3, only 20 and 25 are multiples of 5 and lie between 18 and 30.
Now test each of these with the GCF clue:
Test 20:
- GCF of 18 and 20 = 2
- GCF of 36 and 20 = 4
- But this fails, because 4 is not acceptable
Wait, this shows a contradiction, so re-evaluate:
Actually:
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors of 18, 36, and 20 = Only 1 and 2, and 2 is the greatest
So GCF(18, 36, 20) = 2 — this satisfies the clue.
Test 25:
- GCF(18, 25) = 1
- GCF(36, 25) = 1
- So the overall GCF would be 1 — this does not meet the clue
Therefore, the only number that fits all three clues is:
The mystery number is 20.
