Geo
In triangle ABC, AB = AC. Point P lies on AB such that CP = BC. If Angle APC = 115 degrees, what is angle ACP in degrees?
What is 15 degrees?
The numbers 3, 5, 7, a, and b have an average (arithmetic mean) of 15. What is the average of a and b?
What is 30?
There are two ducks in front of a duck, two ducks behind a duck, and a duck in the middle. How many ducks are there?
What is Three?
Two of the exterior angles of a triangle are 158 degrees and 99 degrees. Find the third exterior angle, in degrees.
What is 103 degrees?
John has a 4 x 6 index card. If she shortens the length of one side of this card by 1 inch, the card would have an area of 18 square inches. What would the area of the card be in square inches if instead, she shortens the length of the other side by 1 inch?
What is 20?
Jack is looking at Anne. Anne is looking at George. Jack is married, George is not, and we don’t know if Anne is married. Is a married person looking at an unmarried person?
What is Yes?
Three circles are drawn so that each circle is externally tangent to the other two circles. Each circle has a radius of 2. A triangle is then constructed such that each side of the triangle is tangent to two circles, as shown below. Find the perimeter of the Triangle.
Integers x and y with x>y>0 satisfy x+y+xy=80. What is x?
What is 26?
A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are out and he is completely in the dark. How many socks must he take out to make 100 percent certain he has at least one pair of black socks?
Two tangents PA and PB are drawn to a circle, where P lies outside the circle, and A and B lie on the circle. The length of PA is 12, and the circle has a radius of 9. Find the length AB.
What is 72/5 or 14.4?
The zeros of the function f(x) = x^2-ax+2a are integers. What is the sum of the possible values of a?
What is 16?
A bad guy is playing Russian roulette with a six-shooter revolver. He puts in one bullet, spins the chambers and fires at you, but no bullet comes out. He gives you the choice of whether or not he should spin the chambers again before firing a second time. Should he spin again?
A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point P on the edge of the table has a distance of 6 from one wall, and a distance of 27 from the other wall. Find the radius of the table.
What is 51?
For some positivie integers P, there is a quadrilateral ABCD with positive integer side lengths, perimeter P, right angles at B and C, AB = 2, and CD = AD. How many different values of p<2015 are possible?
What is 31?
There are three people (Alex, Ben and Sam), one of whom is a knight, one a knave, and one a spy. The knight always tells the truth, the knave always lies, and the spy can either lie or tell the truth. Alex says: “Sam is a knave.” Ben says: “Alex is a knight.” Sam says: “I am the spy.” Who is the knight, who the knave, and who the spy?
What is Ben is the spy?