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y>x>0
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08 Oct 2025, 01:16
08 Oct 2025, 01:16
Expert Reply
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Question Stats:
50% (01:00) correct
50% (01:21) wrong based on 2 sessions
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\(y>x>0\)
Quantity A |
Quantity B |
\(\frac{y}{x} \) |
\(\frac{x}{y} \) |
- Part of the project: PrepClub Daily GRE Quant Questions: Arithmetic, Algebra, Geometry & DA
- Also replying to the unanswered questions
Re: y>x>0
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31 Oct 2025, 11:42
31 Oct 2025, 11:42
Expert Reply
The given constraint is:
$$
\(y>x>0\)
$$
Since both $x$ and $y$ are positive, we know that $y$ is the larger number and $x$ is the smaller number.
Analysis of Quantities
Quantity A
$$
\(\frac{y}{x}\)
$$
This is the ratio of the larger positive number $(y)$ to the smaller positive number $(x)$. Since $\(y>x\)$, the result of this division must be greater than $\(\mathbf{1}\)$.
Example: If $\(y=4\)$ and $\(x=2\)$, then $\(\frac{y}{x}=\frac{4}{2}=2\)$.
Quantity B
$$
\(\frac{x}{y}\)
$$
This is the ratio of the smaller positive number ( $x$ ) to the larger positive number ( $y$ ). Since $x<y$, the result of this division must be a positive fraction that is less than 1 .
Example: If $\(y=4\)$ and $\(x=2\)$, then $\(\frac{x}{y}=\frac{2}{4}=\frac{1}{2}=0.5\)$.
Conclusion
Since Quantity $A$ is always greater than 1 , and Quantity $B$ is always less than 1, Quantity $A$ must be greater than Quantity B.
$$
\(\frac{\text { Larger }}{\text { Smaller }}>1 \quad \text { and } \quad \frac{\text { Smaller }}{\text { Larger }}<1\)
$$
The relationship is: Quantity \($\mathrm{A}>\)$ Quantity B .
Therefore, the correct answer is (A).
$$
\(y>x>0\)
$$
Since both $x$ and $y$ are positive, we know that $y$ is the larger number and $x$ is the smaller number.
Analysis of Quantities
Quantity A
$$
\(\frac{y}{x}\)
$$
This is the ratio of the larger positive number $(y)$ to the smaller positive number $(x)$. Since $\(y>x\)$, the result of this division must be greater than $\(\mathbf{1}\)$.
Example: If $\(y=4\)$ and $\(x=2\)$, then $\(\frac{y}{x}=\frac{4}{2}=2\)$.
Quantity B
$$
\(\frac{x}{y}\)
$$
This is the ratio of the smaller positive number ( $x$ ) to the larger positive number ( $y$ ). Since $x<y$, the result of this division must be a positive fraction that is less than 1 .
Example: If $\(y=4\)$ and $\(x=2\)$, then $\(\frac{x}{y}=\frac{2}{4}=\frac{1}{2}=0.5\)$.
Conclusion
Since Quantity $A$ is always greater than 1 , and Quantity $B$ is always less than 1, Quantity $A$ must be greater than Quantity B.
$$
\(\frac{\text { Larger }}{\text { Smaller }}>1 \quad \text { and } \quad \frac{\text { Smaller }}{\text { Larger }}<1\)
$$
The relationship is: Quantity \($\mathrm{A}>\)$ Quantity B .
Therefore, the correct answer is (A).
gmatclubot
Re: y>x>0 [#permalink]
31 Oct 2025, 11:42
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