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ACT Exam  >  ACT Questions  >  If X, Y, and Z are real numbers, and XYZ = 1,... Start Learning for Free
If X, Y, and Z are real numbers, and XYZ = 1, then which of the following conditions must be true?
  • a)
    XZ = 1/Y
  • b)
    X, Y, and Z > 0
  • c)
    Either X = 1, Y = 1, or Z = 1
  • d)
    Either X = 0, Y = 0, or Z = 0
  • e)
    Either X < 1, Y < 1, or Z < 1
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If X, Y, and Z are real numbers, and XYZ = 1, then which of the follow...
Understanding the Condition XYZ = 1
When we have the condition XYZ = 1, we need to analyze the implications of this equation. Let’s break down each option to see why option A is correct.
Option A: XZ = 1/Y
- This can be derived directly from the equation XYZ = 1.
- By rearranging, we get XZ = 1/Y.
- Hence, this condition must always be true when XYZ = 1.
Option B: X, Y, and Z > 0
- This is not necessarily true.
- X, Y, and Z can take negative values as long as their product equals 1. For example, X = -1, Y = -1, and Z = 1 also satisfies XYZ = 1.
Option C: Either X = 1, Y = 1, or Z = 1
- This is also not a requirement.
- For instance, if X = 2, Y = 0.5, and Z = 1, all are not equal to 1, yet their product is still 1.
Option D: Either X = 0, Y = 0, or Z = 0
- This cannot be true since the product of any number with 0 is 0, not 1. Thus, none of X, Y, or Z can be 0.
Option E: Either X < 1,="" y="" />< 1,="" or="" z="" />< />
- This condition is not necessarily true either.
- All three variables can be greater than 1 while still satisfying XYZ = 1. For example, X = 2, Y = 0.5, Z = 1.
Conclusion
- The only condition that must always hold true from the given options is option A: XZ = 1/Y. This is a direct consequence of the original equation XYZ = 1.
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Community Answer
If X, Y, and Z are real numbers, and XYZ = 1, then which of the follow...
If XYZ = 1, then Z cannot equal 0. If Z (or X or Y, for that matter) were 0, then XYZ would equal 0. Both sides of the equation can be divided by Y, which gives you XZ = 1/Y, answer choice A. Answer choice B is incorrect because two of the values could be −1. Answer choice C is incorrect because two of the values could be fractions and the third value could be a whole number, that, when multiplied by the fractions give you 1. Answer choices D and E are incorrect because you have already determined that none of the values can be equal to zero.
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If X, Y, and Z are real numbers, and XYZ = 1, then which of the following conditions must be true?a)XZ = 1/Yb)X, Y, and Z > 0c)Either X = 1, Y = 1, or Z = 1d)Either X = 0, Y = 0, or Z = 0e)Either X < 1, Y < 1, or Z < 1Correct answer is option 'A'. Can you explain this answer?
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If X, Y, and Z are real numbers, and XYZ = 1, then which of the following conditions must be true?a)XZ = 1/Yb)X, Y, and Z > 0c)Either X = 1, Y = 1, or Z = 1d)Either X = 0, Y = 0, or Z = 0e)Either X < 1, Y < 1, or Z < 1Correct answer is option 'A'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If X, Y, and Z are real numbers, and XYZ = 1, then which of the following conditions must be true?a)XZ = 1/Yb)X, Y, and Z > 0c)Either X = 1, Y = 1, or Z = 1d)Either X = 0, Y = 0, or Z = 0e)Either X < 1, Y < 1, or Z < 1Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If X, Y, and Z are real numbers, and XYZ = 1, then which of the following conditions must be true?a)XZ = 1/Yb)X, Y, and Z > 0c)Either X = 1, Y = 1, or Z = 1d)Either X = 0, Y = 0, or Z = 0e)Either X < 1, Y < 1, or Z < 1Correct answer is option 'A'. Can you explain this answer?.
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