hi crak.gmat,
1) the key here is in the words "pair of consecutive terms", not consecutive numbers.
the goal is to find as many pairs where the product of the two consecutive terms results in a negative number.
we are given 1, -3, 2, 5, -4, -6. so the pairs are:
1 * -3 = -3
-3 * 2 = -6
5 * -4 = -20
note: -4 * -6 = +24 so this is not a pair.
thus, we have 3 pairs.
now, if the problem had said consecutive "numbers", then we would order the numbers given from lowest to highest, and then perform the same operation. in that case, this is what it would look like -
-6, -4, -3, 1, 2, 5
so the pairs could be:
-3 * 1 = -3
-6 * 5 = -30
2) Now, the PRO angle = 35, so due to the inscribed triangle rule, this angle is double i.e. 70 degrees at the center.
Thus the arc PO is 70.
Now, since PQ and OR are parallel, anglePRO = angle QPR = 35. This angle becomes double at the center due to the above rule.
Thus, arc QR is 70.
So, to find the degrees in arc PQ: OR is the diameter, it divides the circle into half, so arc OR = 180.
Thus arc PQ = 360 - 180 - 70 - 70 = 40
Now since the diameter is 18, the radius = 9. Using the circumference formula and equating it with the measure of our arc:
2Pir * 40/360
2Pi9 * 40/360
Pi9 * 40/180
Pi * 40/20
= 2Pi
