If x, y, and z are integers greater than 1, and (327)(3510)(z) = (58)(710)(914)(xy), then what is the value of x?
(1) z is prime
(2) x is prime
(1) z is prime
(2) x is prime
Are you sure you've entered this correctly? It doesn't appear to have a solution.RiyaR wrote:If x, y, and z are integers greater than 1, and (327)(3510)(z) = (58)(710)(914)(xy), then what is the value of x?
(1) z is prime
(2) x is prime
Let's start by simplifying the original equation:
327 * 3510 * z = 58 * 710 * 914 * xy
Now let's try to factor each number.
327 = 3 * 109
3510 = 10 * 351 = 2 * 5 * 3 * 117 = 2 * 5 * 3 * 3 * 39 = 2 * 5 * 3 * 3 * 3 * 13
So 327 * 3510 is really 2 * 3� * 5 * 13 * 109
58 = 2 * 29
710 = 71 * 2 * 5
914 = 2 * 457
So 58 * 710 * 914 is really 2³ * 5 * 29 * 71 * 457
Setting the two equations equal to each other, we have
2 * 3� * 5 * 13 * 109 * z = 2³ * 5 * 29 * 71 * 457 * xy
which reduces (barely) to
3� * 13 * 109 * z = 2² * 29 * 71 * 457 * xy
Unfortunately, S1 is impossible. If z is prime, the LHS and the RHS cannot be equal, since the LHS needs to have ALL of the prime factors on the RHS, so z must be a multiple of 4, 29, 71, AND 457. Since S1 cannot be evaluated, the question can't be answered.
