Quantitative Aptitude Quiz 32

ABCD is a square of area 4 with diagonals AC and BD, dividing square into 4 congruent triangles. Figure looks like four non-over lapping triangles. Then the sum of the perimeters of the triangles is

A certain city has a circular wall around it, and the wall has four gates pointing north, south, east and west. A house stands outside the city, three kms north of the north gate, and it can just be seen from a point nine kms east of the South Gate. What is the diameter of the wall that surrounds the city?

Consider the set . How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?