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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?
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What is the surface area of a cube with a 10-meter space diagonal?
Give your answer in square meters.
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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?
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A car is driving at 100 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.
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