GRE Exam Numerical Ability Geometry

All the sides of a hexagon become three times the original length. Find the ratio of areas of the new and old hexagons.

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GRE Other Question

If the group of students eats 2 cookies, 3 sandwiches and drinks 2 cokes, the bill amounts to $74. If the group of students eats 5 cookies, 6 sandwiches and drinks 4 coke, the bill amounts to $128. If the group of students eats 3 cookies, 3 sandwiches and drinks 2 coke, then what should the group pay? Two machines S and T produce 1000 and 2000 items every day. Machine S produce 10 defective items machine T produces 40 defective items. On particular day the supervisor of the shop floor picked up an item and found it was defective. Find the probability that it came from machine S.