# Probability

Jasmine  flipped a fair coin five times. In the fi rst three flips, the coin came up heads exactly twice. In the last three flips, the coin also came up heads exactly twice. What is the probability that the third flip was heads?

In a group of friends, every friend sends a gift to every other friend on Diwali. After the last Diwali, some more friends get included in the group and the number of gifts increases by 46 this Diwali.

Out of the following , what can be the number of friends in the group this year ?

A. 11
B. 12
C. 13
D. 23

# Algebra

How many real numbers x are solutions to the following equation ?
|x − 1| = |x − 2| + |x − 3|

# A Serial Killer

What is the next number in the sequence : 1, 4, 5, 6 , 7, 9, 11 , ……

# Geometry

An icosidodecahedron is a convex polyhedron with 20 triangular faces and 12 pentagonal faces. How many vertices does it have?

# 25 Horses

There are 25 horses. What is the minimum of race needed so you can identify the fastest 3 horses ? You can race up to 5 horses at a time , but you do not have a watch.

# Geometry

Triangle ABC is given in the plane. Let AD be the angle bisector of ∠BAC; let BE be the altitude from B to AD, and let F be the midpoint of AB. Given that AB = 28, BC = 33, CA = 37, what is the length of EF ?

# The Confabulating Liar

Hrithik is a strange liar. He lies on six days of the week, but on the seventh day he always tells the truth. He made the following statements on three successive days:

Day 1: “I lie on Monday and Tuesday.”
Day 2: “Today, it’s Thursday, Saturday, or Sunday.”
Day 3: “I lie on Wednesday and Friday.”

On which day does Hrithik tell the truth?

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