billzhao wrote:If k is a positive integer, is k the square of an integer?
(1) k is divisible by 4
(2) k is divisible by exactly four different prime numbers
1) 20 is divisible by 4, but is not the square of an integer. 36 is divisible by 4, and is the square of an integer. INSUFFICIENT.
2) 210 (2*3*5*7) has four different prime factors, and is not the square of an integer. 210^2 also has four different prime factors (the same ones), and is the square of an integer. INSUFFICIENT.
1) + 2) together:
210^2 has four different prime factors, is a multiple of four, and is the square of an integer.
210 * 2 has four different prime factors, is a multiple of four, and is not the square of an integer. INSUFFICIENT
So it's E.
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