1. 18

Triangle ABD and triangle ECD are similar triangles (share the same angle)

Hence EC = 3 (3,4,5 triangle)

Also triangle AEF and ECD are similar triangles, since they are formed by parallel lines cut by a line (transversal as math geeks would call it)

Infact these traingles are equal since AE = ED = 5

Area of the quadrilateral = 1/2 (4) (3+6) = 18

2. C (It will not pass), assuming that each of the L's vote YES on the bill, Otherwise it is E.

From #1 we get total L's who vote = (55/100)*400*(85/100) = 187 (But we don't know about Rs and Ds.

From #2 we know that none of the Rs or Ds vote.

Hence total votes = 187 < 189. Hence C. (or E if we don't know each one will vote YES or NO)

3. 11 (div by 78) + 9 (div by 91) = 20.

78*10 = 780 (including 78 there are 10 numbers. Excluding 78 there are 9 of them)

78+78*2 = 936 < 1000. So 2 more available.

Hence No divisible by 78 =9+2 = 11

Similarly for 91 there are 10-1 = 9

Total = 20.

OA's please?

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