Asked by ethan
im a multiple of 20 three digits. i have 3 digits. my hundreds digit and tens add to make 10. half of me is less than 100
All Answers 1
Answered by
GPT-5 mini
AI
No such number exists.
Reasoning:
- A three-digit multiple of 20 must end with 00, 20, 40, 60 or 80, so the tens digit t is one of {0,2,4,6,8}.
- If the hundreds digit h and the tens digit add to 10, h = 10 − t, so the possible (h,t) pairs are (8,2), (6,4), (4,6), (2,8) (t = 0 gives h = 10, which is impossible).
- Those give the candidate numbers 820, 640, 460 and 280.
- Half of those are 410, 320, 230 and 140 respectively — all ≥ 100, so none satisfies “half of me is less than 100.”
Also, any number whose half is < 100 must be < 200, so the only three-digit multiples of 20 that could work are 100, 120, 140, 160 and 180 — none of which have hundreds digit + tens digit = 10.
Therefore there is no three-digit multiple of 20 meeting all three conditions.
Reasoning:
- A three-digit multiple of 20 must end with 00, 20, 40, 60 or 80, so the tens digit t is one of {0,2,4,6,8}.
- If the hundreds digit h and the tens digit add to 10, h = 10 − t, so the possible (h,t) pairs are (8,2), (6,4), (4,6), (2,8) (t = 0 gives h = 10, which is impossible).
- Those give the candidate numbers 820, 640, 460 and 280.
- Half of those are 410, 320, 230 and 140 respectively — all ≥ 100, so none satisfies “half of me is less than 100.”
Also, any number whose half is < 100 must be < 200, so the only three-digit multiples of 20 that could work are 100, 120, 140, 160 and 180 — none of which have hundreds digit + tens digit = 10.
Therefore there is no three-digit multiple of 20 meeting all three conditions.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.