kakz wrote:Line m and line n intersect, forming 4 angles. Does any of these angles measure greater than 120°?
(1) The product of the measures, in degrees, of the four angles is less than 2^10*3^4*5^4
(2) The product of the measures, in degrees, of the four angles is greater than 2^14*5^4
Note that the four angles are nothing but two pairs of opposite angles.
Hence, if one of the angles is x°, then the other three angles are x°, (180 - x)°, and (180 - x)° also 0 < x < 180 and 0 < (180 - x) < 180
Hence, product of the four angles = x²(180 - x)²
Statement 1: x²(180 - x)² < (2^10)*(3^4)*(5^4)
--> x(180 - x) < (2^5)*(3^2)*(5^2) = 7200
--> x² - 180x + 7200 > 0
--> (x - 60)(x - 120) > 0
--> either x < 60 or x > 120
--> either (180 - x) > 120 or (180 - x) < 60
In any case two of the four angles are greater than 120°.
Sufficient
Statement 1: x²(180 - x)² > (2^14)*(5^4)
--> x(180 - x) > (2^7)*(5^2) = 3200
--> x² - 180x + 3200 < 0
--> (x - 20)(x - 160) < 0
--> 20 < x < 160
--> 20 < (180 - x) < 160
The angles may or may not have a value greater than 120°.
NOT sufficient
The correct answer is A.
