For positive integers x, y, and z, the function x ? y ? z means that is an integer, but is not. If x ? 2 ? 144, then which of the following is NOT a possible value of x?
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Took me a second to parse the notation, but once I did it's a clean divisibility question. 705-805 feels about right for the trickiness of the setup though, not the math itself.
Same here, the notation was the hardest part lol
Yeah the actual calculation is fast once you see what it's asking.
Wait, so x ? 2 ? 144 means x^2 divides 144 but x^2 + 1 does not divide 144? Or is it that x^2/144... I'm second-guessing the direction of the fraction.
Wait that doesn't sound right either, 144 is way bigger than most of the answer choices squared.
Got it on the third try. The +1 part is what makes it interesting, you can't just check divisibility of x^2 alone.
Right, that's the whole trap. People stop after the first condition and pick the wrong one.
Is anyone else finding that 2 and 3 both seem to work here? I keep getting two answers that satisfy the conditions and I'm not sure which one the question wants.
I thought so too at first, then realized one of them has the +1 still dividing evenly.
What it tests
Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.
Common trap
Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).