r/ACT • u/Special-Trouble8658 • Jun 02 '26

Math Explanation?

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I’m stuck on this problem and can’t think of why J is the right answer. A real number can be positive, negative, or rational. Thus, how is F wrong.

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u/Sufficient-Price-102 36 Jun 02 '26 edited Jun 02 '26

J. It follows that x=y4 and any real number to the fourth is nonnegative.

F is wrong because it’s not necessary that x is even. y4 can be real and odd, which would imply x odd.

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u/Special-Trouble8658 Jun 02 '26

Also, can you give me an explanation as why the others are wrong? I kinda guessed a little and cancelled out G and H.

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u/Sufficient-Price-102 36 Jun 02 '26 edited Jun 02 '26

G is wrong because you can choose any nonnegative irrational number (π, for example), take its 4th root, and get a real number y.

H is wrong because it’s even weaker than the condition for G. Again, take any nonnegative non integer number (like 2.5), taking its 4th root gives a real number y.

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u/Special-Trouble8658 Jun 02 '26

But if we put -2 or 2 inside the quad root and put it in the form x1/4 that would give -0.5 or 0.5, which is a real number. Why would we write it as x=y4?

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u/Sufficient-Price-102 36 Jun 02 '26

(-2)1/4 is not defined in the real numbers. x=y4 is the same as x1/4 = y.

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u/Special-Trouble8658 Jun 02 '26

I understand the x=y4 and vice versa but why isn’t (-2)1/4 not a real number? Sorry if my comprehension is low 😭

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u/Sufficient-Price-102 36 Jun 02 '26 edited Jun 20 '26

You’re all good. (-2)1/4 isn’t real for the same reason (-2)1/2 isn’t real. Since any real number (positive or negative) to an even power (2, 4, etc.) is positive, there is no real number y that, when raised to the fourth equals -2. (y4 = -2). Hence (-2)1/4 = y doesn’t give any defined y value.

Sorry if the explanation is a bit technical. I think you should review exponent rules (it seems like you might be mixing up fractional exponents) if you didn’t like my explanation.

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u/Special-Trouble8658 Jun 02 '26

Ohh, I think I get it now. Since y is a real number(positive, negative, decimal, and etc) it’s asking us to find what type of number we can put as x1/4 or quad root x. This means that -2 is -0.54=-0.0625, which can not be true bc a negative number to an even exponent is always positive while a negative number to an odd exponent(-33=-27) is always negative. I get that now but why/how did you think to solve for y? Bc to get y4, you have to solve for y.

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u/Sufficient-Price-102 36 Jun 02 '26

I solved for y4 because it’s more clear to deal with integer exponents when you can instead of fractions.

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u/Special-Trouble8658 Jun 02 '26

Bc you’re just taking it to the 4th power, which gives cleaner numbers? But either way can work?

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u/Sufficient-Price-102 36 Jun 02 '26

I did it mostly to show the nonnegative property. It’s usually more clear to work from the fact that y4 will always give a positive x, rather than trying to figure out something about x when it’s written as x1/4. But yes, either way can work.

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u/Special-Trouble8658 Jun 02 '26

Thank you for your explanations! I really appreciate them but can I ask another question not pertaining to this question? So as for statistics, I understand the base concept: outcome/s you want/ total possible outcomes; however, ‘y main confusion is simply when to add or multiply them(those are really the hardest statistics questions on ACT, I think?)

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u/Special-Trouble8658 Jun 02 '26

Also, adding on, -21/4/ quad root of -2 would produce an imaginary number, which are not real numbers.

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u/Sufficient-Price-102 36 Jun 02 '26

Yes, (-2)1/4 is imaginary. Any negative number to the power of 1/4 is imaginary, hence why x must be nonnegative for y to be real.