Given that x/y

Question

Given that x/y < 1, and both x and y are positive integers, which one of the following must be greater than 1?

A. x/y^2
B. x^2/y
C. x^2/y^2
D. y/x
E. √(x/y)

chetan2u · Answer

\frac{x}{y}<1

Since x and y are positive integers, we can multiply both sides by y without changing inequality sign.

\frac{x}{y}*y<1*y...............x<y

Since x and y are positive integers, we can divide both sides by x without changing inequality sign.

\frac{x}{x}<\frac{y}{x}

\frac{y}{x}>1

D

Let us check other options

A)  \frac{x}{y^2} 
Here we are increasing the denominator of a fraction that is less than 1, so the new fraction will also be <1.

\frac{x}{y^2}<\frac{x}{y}<1

B)  \frac{x^2}{y} 
Whenever x^2<y, the fraction will be less than 1.....x=2 and y=9

\frac{x^2}{y}=\frac{4}{9}<1

C)  \frac{x^2}{y^2} 
Here we are squaring the fraction that is less than 1, so the new fraction will also be <1 as the value between 0 and 1 reduces as we increase the power.

\frac{x^2}{y^2}<\frac{x}{y}<1

E) The square root will increase the value but will still be less than 1 always.

\sqrt{4/9}=\frac{2}{3}<1

EgmatQuantExpert · Answer

Given • \frac{x}{y} < 1. • x and y are positive integers To find • The inequality > 1 among the given options. Approach and Working out : Let’s look at each option one by one. A. \frac{x}{y^2} • \frac{x}{y^2} = \frac{x}{y} × \frac{1}{y} • \frac{x}{y} < 1 and y >0. • But, we don’t know whether the multiplication of \frac{x}{y} and \frac{1}{y} will be greater than 1 or not. • Not correct B. \frac{x^2}{y} • \frac{x^2}{y} = \frac{x}{y} × x • \frac{x}{y} < 1 and x >0. • But, we don’t know whether the multiplication of \frac{x}{y} and x will be greater than 1 or not. • Not correct C. \frac{x^2}{y^2} • \frac{x^2}{y^2} = \frac{x}{y} × \frac{x}{y} • \frac{x}{y} < 1. • Multiplication of two numbers that are less than 1 will be less than 1 only. • Not correct D. \frac{y}{x} • \frac{y}{x} = \frac{1}{\frac{x}{y}} • \frac{x}{y} < 1 and inverse of a positive number that is less than 1 is a number greater than 1. • This is correct. E. \sqrt{\frac{x}{y}} • \sqrt{\frac{x}{y}} = √< 1 = Number less than 1 • Not correct Hence, option D is the correct answer. Correct Answer: Option D

Given that x/y < 1, and both x and y are positive integers, which one

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