ardz24 wrote:If n is an integer, is the prime number y equal to 5 ?
(1) y = n² + 1
(2) y = n³ - 3
Statement 1:
If n=1, then y = 1² + 1 = 2.
In this case, prime number y is NOT equal to 5.
If n=2, then y = 2² + 1 = 5.
In this case, prime number y IS equal to 5.
INSUFFICIENT.
Statement 2:
If n=2, then y = 2³ - 3 = 5.
In this case, prime number y IS equal to 5.
If n=4, then y = 4³ - 3 = 61.
In this case, prime number y is NOT equal to 5.
Statements combined:
Since y =
n² + 1 and y =
n³ - 3, the expressions in blue are EQUAL:
n³ - 3 = n² + 1
n³ - n² = 4
n²(n-1) = 4.
A quick test of easy values (1, 2, 3, etc.) reveals that n=2.
Thus:
y = n² + 1 = 2² + 1 = 5.
The answer to the question stem is YES.
SUFFICIENT.
The correct answer is
C.
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