- What is the maximum possible area of a quadrilateral with sidelengths 15, 19, 33, and 35?
A) 432 B) 512 C) 576 D) 672
- How many 2-digit positive integers are there which are divisible by the sum of their digits?
A) 14 B) 15 C) 23 D)25
- How many 2-digit positive integers are there which are divisible by the product of their digits?
A) 3 B) 4 C) 5 D)6
- A point P moves in such a way that the average of squares of its distances from two fixed points
on a line l differs by the square of its distance from the line l by a constant. The path traced out by
P is
A) parallel lines B) an ellipse C) a parabola D) a hyperbola
- A point P moves in such a way that the average of squares of its distances from two fixed points
on a line l differs by the square of its distance from another line parallel to the line l by a constant. The path traced out by
P is
A) parallel lines B) an ellipse C) a parabola D) a hyperbola
- A point P moves in such a way that the sum of squares of its distances from two fixed points
on a line l differs by the square of its distance from the line l by a constant. The path traced out by
P is
A) parallel lines B) an ellipse C) a parabola D) a hyperbola
- The year is 2605 B.C. King Neterikhet (Dzoser) of the Third Dynasty (Old Kingdom) asked his
architect Imhotep of Ankhtowë to build him a pyramid 400 cubits high and with a square base 600
cubits on each side. Imhotep ordered 2.072 million hekats of stone to be quarried. However after
using all the stone he had ordered he found his pyramid to be incomplete. Each trapezoidal side had
area 2.4 times that of the square top. How many more thousands of hekats of stone would he need to
complete the pyramid?
A) 125 B) 216 C) 432 D) 576
- ABC is an isosceles triangle with AB = AC = 36 and BC = 24. A point
D lies on AC such that BC = BD. E and F are midpoints of the sides
BC and CD respectively. If the lines AE and BF intersect at G, the ratio
of the lengths BG : GF is
A) 7 : 9 B) 9 : 7 C) 11 : 5 D) 17 : 7
- Harry and Billy went to a casino where there was a new game going on. You bet some money and if
you win you square your money, i.e. if you bet $5 and win you get $25 back altogether and if you do not win
you lose your $5. Harry felt lucky but he had no money so he borrowed all that Billy had and bet the
entire amount and won. He returned Billy all that he had borrowed. With a lot of money in his wallet
Harry bought many boxes of chocolates priced at $10, $15, $25 each and spent all his money. Billy
bought some cheaper quality chocolates at $5 a box, as many boxes he could with his smaller amount and
still had a little money left. How much did he have left?
A) $1 B) $2 C) $3 D) $4
- Four friends went to the same casino (see Q. 9) and each played the same game once. They had
different amounts of money with them but altogether n dollars. Each of them bet all she had and won.
They came out in pairs. Ann and Betty found they had $2005 together and when Chris and Debbie came
out they found they too had $2005 together. What is n ?
A) 115 B) 120 C) 125 D) 130
