If y -1, is (x + 1)/(y + 1) x (2) x 0

Question

If y ≠ -1, is  \frac{(x+1)}{(y+1)} < \frac{x}{y}  ?

(1) y > x
(2) x > 0

chinmay94 · Answer

Can someone explain why statement II is necessary? I'm getting (x+1)/(y+1) is greater than x/y for x>0 and x<=0

x/y = 4/5 < 5/6

x/y = -4/5 < -3/6

x/y = 0/4 < 1/5

x/y = -5/2 < -4/3

It only seems to change when y<x, which we are using statement I for.

x/y = 5/2 > 4/3

x/y = 5/-2 > 6/-1

HoustonRocks · Answer

Try and plug in a negative number for X AND Y.

-2+1/-3+1 = -1/2 Which is < -2/-3 (2/3)
-1/2 < -2/3. So the answer is YES

Now use X = 2 and y =3 
2+1 / 3+1 = 3/4 which > thanks 2/3 so the argument x+1/y+1 < x/y can not be determined unless we establish that X is +

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kulshresthaarjun · Answer

But y>x so -2/-3 isn't a valid example right?
In the case where we take -3/-2, (-3+1)/(-2+1) = -2/-1 = 2 > -3/-2 = 1.5

aggt · Answer

Consider the case where x=-1/2 and y=-1/3. In this case y>x and the answer to the inequality is YES

arvind910619 · Answer

Imo C (x+1)/(y+1) < x/y (x+1)/(y+1) - x/y < 0 (Y-X)/Y*(Y+1) < 0 Statement 1 y > x Case1 both are positive then (Y-X)/Y*(Y+1) > 0 Answer is no Case 2 both are negative (Y-X)/Y*(Y+1) < 0 Answer is Yes Statement 1 insufficient Statement 2 x > 0 X is positive but no information about Y So Insufficient Together X is positive and Y >X then (Y-X)/Y*(Y+1) > 0 then answer is No So C

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If y -1, is (x + 1)/(y + 1) < x/y ? (1) y > x (2) x > 0

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