Combo
Alg
Geo
NT
100
Marvin has a deck of 9 cards. Two of the cards have the number 2, three have the number 3, and four have the number 4. If he arranges the 9 cards in a random order, what is the probability that he arranges the cards in nondecreasing order?
1/1260
100
Suppose that x and y are nonzero real numbers such that 3x + 2y = 17xy and 2x + 3y = 18xy What is the value of x/y?
3/4
100
An equilateral hexagon ABCDEF of side length 1 has angle measures: ∠A = ∠C = ∠E = 90 , ∠B = ∠D = ∠F = 150 . What is the area of this hexagon?
(3+sqrt3)/2
100
How many ordered pairs of positive integers (m, n) satisfy the equation m2 + mn = 144?
7
200
Alex picks a real number r uniformly at random between 0 and 10. What is the probability that |r − 2| < |r − 7|?
9/20
200
Petunia's flower garden contains red, blue, and green flowers. On Monday, 
of the flowers were red. The day after that, the number of green flowers doubled, while the number of the rest of the flowers stayed the same, and 
of the flowers were red. What fraction of the flowers were blue on Monday?
14/36
200
In trapezoid ABCD, CD is parallel to AB, and CD = 3, BC = 6, AB = 7. A and D are right angles. Let point P be on BC be such that AP is perpendicular to BC. What is the length of segment AP?
7sqrt5/3
200
What is the remainder when 112123123412345 is divided by 90?
35
300
Joy flips a coin ten times. Among the first five coin flips, there are more heads than tails. Given this information, what is the probability that, among all ten coin flips, there are more tails than heads?
65/512
300
Let 
be a real number for which 
. There exists a unique real number 
for which:
What is the value of ?
110
300
A rectangle ABCD with side lengths AB = 12 and BC = 10 has points E on segment AB and F on segment CD such that AE = 4 and DF = 3. Let AF and DE intersect at Q and let BF and CE intersect at R. Suppose line QR intersects AD at point P and intersects BC at S. The ratio PQ : QR : RS can be written as x : y : z, where x, y, and z are positive integers and gcd(x, y, z) = 1. What is x + y + z?
119
300
A positive integer 
is chosen between 
and 
, inclusive. The probability that
may be expressed as 
for relatively prime positive integers 
and 
. What is 
?
61