There is a math teacher in a school whose favorite number is a positive integer (let's call it \(x).\) She told her 5 students--Alice, Beatrice, Candice, Denise, Eunice--the number \(x,\) and the following conversation took place:
Alice: "\(x+1\) is not divisible by 5."
Beatrice: "\(x+2\) is not divisible by 5."
Candice: "\(x+3\) is not divisible by 5."
Denise: "\(x+4\) is not divisible by 5."
Eunice: "\(x+5\) is not divisible by 5."
Without knowing \(x\), can we guarantee that at least one of these 5 students is lying?
by
Pi Han Goh
What is the surface area of a cube with a 10-meter space diagonal?
Give your answer in square meters.
by
Brilliant Member
James arrived home after a party and realized that he had forgot to turn off the knob of the gas line. There is a strong smell of liquefied petroleum gas in his apartment.
What should he do to avoid any accidents?
- Turn off the knob of the gas line.
- Open all the windows.
- Turn on the exhaust fan.
- Turn off all the electrical appliances.
by
Rohit Gupta
Evaluate \[ \frac{ 63^4 - 37^4 } { 63^2 + 37^2 }. \]
Hint: Use the difference of two squares identity.
by
Chung Kevin
A car is driving at \(100\text{ mph}\) down a straight road. What is the speed at the point on the tire where the wheel touches the ground?
Note: Assume that the tires are not slipping or skidding.
by
Zach Abueg