The statements about the Rocky Mountains that are true are:
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They are taller than the Appalachian Mountains. The Rocky Mountains are significantly taller than the Appalachian Mountains, with many peaks exceeding 14,000 feet, while the highest peak in the Appalachians, Mount Mitchell, is about 6,684 feet.
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They are younger than the Appalachian Mountains. The Rocky Mountains are generally considered younger than the Appalachian Mountains, which were formed about 480 million years ago, while the major uplift of the Rockies occurred approximately 70 million years ago during the Laramide orogeny.
The other statements ("They are shorter than Apple bottom pounds" and "They are older than the Appalachian Mountains") are false. Also, "Apple bottom pounds" seems to be a non-relevant comparison, as it appears to refer to a brand associated with fashion rather than a geographical feature.