It’s easy to think that statement (1) is sufficient by thinking, “Well, I can figure out quickly that 20 has six factors (1, 2, 4, 5, 10, 20), and if k is a new prime number, then 20k will have six MORE factors than 20 has, because we can just take the new prime number and multiply it by each of the original six factors. For instance, if k were 3, then the factors of 20k would be each of the six factors of 20 PLUS six new ones - 3, 6, 12, 15, 30, 60. So statement (1) is sufficient.”
Statement (1) is a trap, however, because we aren’t told that k is a NEW prime number!!! It may be a prime that is ALREADY a factor of 20 – i.e., k could be 2 or 5. Suppose k were 2. If that were the case, then the factors of 20k would be 1, 2, 4, 5, 8, 10, 20 and 40 – i.e., we would be adding only two new factors, 8 and 40, to the original list of six. Statement (1) is therefore insufficient.
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