Don’t lose your progress!

We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.

Up to 90+ points GMAT score improvement guarantee

The best guarantee you’ll find

Our Premium and Ultimate plans guarantee up to 90+ points score increase or your money back.

Master each section of the test

Comprehensive GMAT prep

We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.

Schedule-free studying

Learn on the go

Study whenever and wherever you want with our iOS and Android mobile apps.

The most effective way to study

Personalized GMAT prep, just for you!

Adaptive learning technology focuses on your academic weaknesses.

Plugging In: DOZEN F for "Must Be" Questions

Given that $$\frac{x}{y} \lt 1$$, and both $$x$$ and $$y$$ are positive integers, which one of the following expressions must be greater than 1?
Correct. [[Snippet]] __Plug In__ $$x = 1$$ and $$y = 5$$: > $$\frac{y}{x} = \frac{5}{1}=5$$. Since $$5 \gt 1$$, this answer choice cannot be eliminated for this Plug-In. All the other answer choices give a result that is smaller than 1 for the same Plug-In and thus are eliminated since it is not required that they are greater than 1. Therefore, $$\frac{y}{x}$$ is the correct answer. __Alternative explanation__: Since both $$x$$ and $$y$$ are positive, it is possible to multiply the original inequality by $$y$$ without flipping the sign. Thus, the inequality $$\frac{x}{y} \lt 1$$ becomes $$x \lt y$$, which can then be further divided by $$x$$ to get $$1 \lt \frac{y}{x}$$.
Incorrect. [[Snippet]] __Plug In__ $$x = 1$$ and $$y = 5$$: > $$\frac{x}{y^2} = \frac{1}{5^2} = \frac{1}{25}$$. Since $$\frac{1}{25}$$ is **not** greater than 1, this expression does not need to be greater than 1. Eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$x = 1$$ and $$y = 5$$: > $$\frac{x^2}{y} = \frac{1^2}{5} = \frac{1}{5}$$. Since $$\frac{1}{5}$$ is **not** greater than 1, this expression does not need to be greater than 1. Eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$x = 1$$ and $$y = 5$$: > $$\frac{x^2}{y^2} = \frac{1^2}{5^2} = \frac{1}{25}$$. Since $$\frac{1}{25}$$ is **not** greater than 1, this expression does not need to be greater than 1. Eliminate this answer choice.
Incorrect. [[Snippet]] __Plug In__ $$x = 1$$ and $$y = 5$$: > $$\sqrt{\frac{x}{y}} = \sqrt{\frac{1}{5}}=\frac{1}{\sqrt{5}}$$. Since $$\frac{1}{\sqrt{5}}$$ is **not** greater than 1, this expression does not need to be greater than 1. Eliminate this answer choice.
$$\frac{x}{y^2}$$
$$\frac{x^2}{y}$$
$$\frac{x^2}{y^2}$$
$$\frac{y}{x}$$
$$\sqrt{\frac{x}{y}}$$