If 0

Question

If  0<\frac{x}{y}<1 , then which of the following must be true ?

I.  \frac{x^2}{y^2}<\frac{x}{y}

II.  \frac{x^2}{y }> \frac{x}{y}

III.  \frac{(x+5)}{(y+5)}<1

A. I only
B. II only
C. III only
D. I and III only
E. I, II, and III

chetan2u · Accepted Answer

0<\frac{x}{y}<1 Analyzing the inequality: 1) Both x and y have same sign. 2) If both positive xy. for example -2>-3 I. \frac{x^2}{y^2}<\frac{x}{y} Any fraction in range 0 to 1 will decrease as the power is increased. TRUE II. \frac{x^2}{y }> \frac{x}{y} If x and y are negative, say -2 and -3 \frac{(-2)^2}{-3}>\frac{-2}{-3}......-\frac{4}{3}>\frac{2}{3} ...NO III. \frac{(x+5)}{(y+5)}<1 x=2, and y=3...... \frac{x+5}{y+5}=\frac{7}{8}<1 ..Yes x=-2, and y=-3...... \frac{x+5}{y+5}=\frac{3}{2}<1 ..No Need not be TRUE Only I A

beeunoia · Answer

According to the condition 0 Let's pick numbers 4/9 = 2/3, but 1/4 < 1/2 - not sufficient 2. x^2/y > x/y => Let's pick numbers 4/3 > 2/3, but 1/2 = 1/2 - not sufficient 3. (x+5)/(y+5)<1 => Let's pick numbers (2+5)/(3+5)<1 and (1+5)/(2+5)<1 - sufficient Option C is correct!

dan0015 · Answer

I know a property which states that if you increase the numerator and the denominator of a fraction < 1 by the same number, the fraction approaches 1. Is that only applicable when the numbers are positive?

chetan2u · Answer

Yes, you are correct. 
The following link has further details on the same topic. 
 https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

astiles67 · Answer

1. calc error here; 4/9 = 2/4.5, not 2/3

1 works

3. use -.5 x and -1 y: -.5+5 = 4.5, -1+5 = 4; 4.5/4 not less than 1.

3 doesnt work

beeunoia · Answer

As for 3, yes, thanks, did not consider the negative number. But as for 1 - I considered it as  \frac{\sqrt{4}}{\sqrt{9}}

kovid231 · Answer

The answer should be D (I and III). Numbers are lying in the range of 0 to 1 will always have a lower numerator and higher denominator.

I: This is a property. The more you square this number, the smaller it will become.

II: Is not true for single case 1/2. (Should be enough to negate this in a 'must be true' answer)

III: We are adding a constant to the numerator and denominator. Hence the distance travelled by the numbers will be the same on the number line. So Denominator will still be larger than the numerator. Hence it will always be less than 1.

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If 0 < x/y < 1, then which of the following must be true ?

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