If x

Question

If x < y < –1 , which of the following must be true? (A) \frac{x}{y} > xy (B) \frac{y}{x} > x + y (C) \frac{y}{x} > xy (D) \frac{y}{x} < x + y (E) \frac{y}{x} > \frac{x}{y} Source: Nova GMAT Difficulty Level: 600

ydmuley · Answer

x < y < –1 This means that both x and y are NEGATIVE numbers (A) \frac{x}{y} > xy Take x = -3 and y = -2 - when we add these values in the above equation we get x/y = 1.5 xy = 6 So x/y < xy ====> Hence, FALSE (B) \frac{y}{x} > x + y Take x = -3 and y = -2 - when we add these values in the above equation we get y/x = -2/-3 = 0.66 x+y = -3+(-2) = -3-2 = -5 So, y/x > x+y ===> TRUE (C) \frac{y}{x} > xy Take x = -3 and y = -2 - when we add these values in the above equation we get y/x = -2/-3 = 0.66 xy = 6 So y/x < xy ===> Hence, FALSE (D) \frac{y}{x} < x + y Take x = -3 and y = -2 - when we add these values in the above equation we get y/x = -2/-3 = 0.66 x+y = -3+(-2) = -3-2 = -5 So, y/x > x+y ===> Hence, FALSE (E) \frac{y}{x} > \frac{x}{y} Take x = -3 and y = -2 - when we add these values in the above equation we get y/x = -2/-3 = 0.66 x/y = -3/-2 = 1.5 So, y/x < x/y ===> Hence, FALSE Hence, the Answer is B

niks18 · Answer

it is clear that x & y are negative numbers. So summation of x & y will be negative (for eg. -3+-2=-5)
So,   x+y<0   and

y/x will be positive (as negative signs will cancel out. for eg. -3/-2 = 3/2 = 1.5)
So,   y/x >0

Obviously Positive number is greater than negative number

So,  \frac{y}{x} > x + y

Hence Option  B

Arjunarocks · Answer

Best way to solve such questions is take a value for x and y and put these values in all the options.

Let y be -5 and x be -10. 
Now, on solving, clearly B must be true.

GMATinsight · Answer

We should staraightaway check with option by assuming several values of x and y and judging the property of outcome x < y < -1 Let, x = -3 and y = -2 A. \frac{x}{y} > xy x/y = 1.5 and xy = 6 hence Incorrect option B. \frac{y}{x} > x+y y/x = 2/3 (Always Positive) and x+y = -5 (Always Negative) hence Correct option C. \frac{y}{x} > xy D. \frac{y}{x} < x+y E. \frac{y}{x} > \frac{x}{y} Answer: option B

PKN · Answer

Here x0 , RHS: x+y <0 So, \frac{y}{x} > x+y Ans. (B)

Archit3110 · Answer

If xxyxy>xy B. yx>x+yyx>x+y C. yx>xyyx>xy D. yxxyyx>xy + B. consider values for x= -4, y=-2 check for all options only B suffices

If x < y < –1, which of the following must be true?

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