If x + y 1 and y - x

Question

If x + y > 1 and y - x < 3, which of the following must be true?

I. x < -1
II. x > -1
III. y > 2

(A) I only
(B) II only
(C) III only
(D) I and III
(E) None

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Whoisdmx15 · Answer

Given: x + y > 1 (i) and y - x < 3(ii) y - x < 3 => x-y>-3(iii) (i)+(iii) 2x>-2 => x>-1 Now in (i) (>-1)+y>1=> y>=1 (Edited after suggestions in following comments) Hence IMO B

Krunaal · Answer

When you substitute x > -1 in (i), x can take the value of 0, in that case y > 1

Hence, only x > -1 must be true.

Answer B.

ravi1522 · Answer

Hello,
x + y > 1 and y - x < 3
from 1st equation 
x>1-y
from 2nd equation 
x>y-3
taking 1&2
we get 2x>-2
x>-1
Option 2 is must be true 
Option B is correct 
as Option 2 is only in option B

Whoisdmx15 · Answer

Yes  Krunaal  seems like an oversight on my part.

sujoykrdatta · Answer

x + y > 1 
y - x < 3 ------> multiply throughout with (-1): -y + x > -3
Add the first inequality to this:

x + y > 1
x - y > -3
Adding (we can add ONLY because both are now of the same nature, i.e. "greater than"): 2x > -2 => x > -1

We cannot determine a specific range for y since we cannot eliminate x from the above inequalities

Ans B

hr1212 · Answer

Can even be derived from graph by plotting both the inequalities.

As can be seen, overlapping area starts at x=-1 and is valid for all values greater than -1.

IMO: B

kevincan1 · Answer

y > 1 - x y < 3+ x it follows that 1 - x < 3 + x and thus -2 < 2x. We can then conclude that x > -1. Thus I is false and II is true. The correct answer must be B.

vasu1104 · Answer

x+y > 1
x> 1-y

y-x<3
x-y>-3
x>-3+y

add both equation

2x> 1-y-3+y
2x> -2
x>-1

only option B

Ngocvb10 · Answer

The question does not state  x,y need to be integer .
For example: x = -0.5, y = 1.6 then x+y =1.1, y-x= 2.1 >> Answer should be E

Bunuel · Answer

The question does not need x and y to be integers.

Your example actually supports answer B, not E:

x = -0.5, so x > -1.

That is exactly statement II.

If x + y > 1 and y - x < 3, which of the following must be true?

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