Arbitrageur wrote:
An infinite sequence of positive integers is called a perfect
sequence if each term in the sequence is a perfect number,
that is, if each term can be expressed as the sum of its divisors,
excluding itself. For example, 6 is a perfect number, as its
divisors, 1, 2, and 3, sum to 6. Is the infinite sequence S a
perfect sequence?
(1) Exactly one term in S is a prime number.
(2) In sequence S, each term after the first in S has exactly 3 divisors.
The OA is D. I put down A as my answer. For statement 2 I get that a positive integer with 3 divisors will be the square of a prime number (4, 9, 25, 49, etc.). This statement though says that each term AFTER THE FIRST has 3 divisors. So the first term could be a perfect number or not. Maybe I'm missing something here. Any help on this will be helpful.
In the sequence S, if there is even one term which is not a perfect number, the sequence is not a perfect sequence. You need every term of the sequence to be a perfect number for the sequence to be a perfect sequence.
Statement 2 tells you that after the first term, every term is 'non-perfect'. We don't care whether the first term is perfect or not. Since we know that the sequence has non-perfect numbers, the sequence is not perfect. Hence, statement 2 is also sufficient.
Test makers like to add little twists like these "after the first term" to mess with your mind! I am sure you would have had no problems if the second statement were "...each term has exactly 3 divisors"
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Karishma
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