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Questions (16)
ABCD is a quadrilateral with ∠ADC=∠ACD, ∠ACB=∠ABC and CD=7. If triangles ADC and ABC have perimeter 51 and 59,
1 answer
668 views
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that
0 answers
483 views
x,y and z are positive integers such that x<y,x+y=201,z−x=200. What is the maximum value of x+y+z?
2 answers
327 views
A neutral solid conducting cylinder rotates about its axis with angular speed 1600 rad/s. In addition, there is an external
0 answers
508 views
The space shuttle had a top orbital speed of 8000 m/s and orbited in a circular orbit approximately 320 km above the earth's
1 answer
372 views
ABCD is a quadrilateral with ∠ADC=∠ACD, ∠ACB=∠ABC and CD=7. If triangles ADC and ABC have perimeter 51 and 59,
1 answer
672 views
41 different balls are drawn from a bag containing balls labelled 1,2,…,300. The probability that the number of balls drawn
2 answers
488 views
Circles Γ1 and Γ2 intersect at 2 distinct points A and B. A line l through A intersects Γ1 and Γ2 at points C and D,
0 answers
461 views
Find the number of solutions to the equation
1/a+1/b+1/c+1/d=1 where a, b, c, d are positive integers and a≤ b≤ c≤ d.
0 answers
381 views
How many integer values x satisfy the inequality 2<3x−1/6<5 ?
2 answers
1,961 views
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
1 answer
1,828 views
What is the smallest 3-digit positive number whose product of the individual digits is still a 3-digit number
2 answers
454 views
Let N=1!⋅2!⋅3!⋅4!…9!⋅10!. Let 2^k be the largest power of 2 that divides N. What is the value of k?
2 answers
335 views
a,b,c are positive integers such that a:b=7:9 and b:c=12:7. What is the smallest possible value of a?
1 answer
331 views
You and your friend, both of mass 70 kg, are playing catch with a frisbee on frictionless ice. Initially, you are both at rest.
2 answers
526 views
A kayaker paddles due north at 2 m/s. The river the kayaker is paddling in flows towards the east at 1 m/s. After 5 seconds of
1 answer
536 views
