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?

What is the surface area of a cube with a 10-meter space diagonal?

Give your answer in square meters.

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.

Evaluate \[ \frac{ 63^4 - 37^4 } { 63^2 + 37^2 }. \]

**Hint:** Use the difference of two squares identity.

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.

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