If x and y are integers, and x - y + 2 0, is x negative?

Question

If x and y are integers, and x - y + 2 > 0, is x negative?

(1) x + y > 0
(2) 2x - 1 < y

chetan2u · Answer

x - y + 2 > 0.........x>y-2 (1) x + y > 0.......x>-y Also x>y-2 Add similar sides of both the equations => x+x>y-2-y........2x>-2.......x>-1 As x is an integer, the least value of x is 0, so x is not negative. Sufficient (2) 2x - 1 < y............2xy-2 Add both the equations => x+y+1>2x+y-2........x<3 So x can be 0, 1 or 2, then answer is no. But x can also be less than 0, then answer is yes. Insufficient A

GMATGuruNY · Answer

Inequalities can be added together.
Before adding, we must ensure that the < > symbol faces the SAME DIRECTION in each inequality.

Statement 1:
Adding together x-y+2 > 0 and x+y > 0, we get:
2x+2 > 0
2x > -2
x > -1
Since x must be an INTEGER, the least possible option for x is 0.
Since x cannot be negative, the answer to the question stem is NO.
SUFFICIENT.

Statement 2:
Adding together x-y+2 > 0 and y > 2x-1, we get:
x+2 > 2x-1
3 > x
If x=2, the answer to the question stem is NO.
If x=-1, the answer to the question stem is YES.
INSUFFICIENT.
 
A

BrentGMATPrepNow · Answer

Given : x - y + 2 > 0 Target question : Is x negative? Statement 1 : x + y > 0 There’s a useful inequality property that says If two inequalities have their inequality symbols facing the same way, we can ADD the inequalities. We have: x - y + 2 > 0 x + y > 0 When we add the two inequalities we get: 2x + 2 > 0 Subtract 2 from both sides of the inequality: 2x > -2 Divide both sides by 2 to get: x > -1 Since x is an integer, we know that x could equal 0 or 1 or 2 or 3 or 4 or . . . . For all possible values of x the answer to the target question is, NO, x is not negative Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2 : 2x - 1 < y We first need to rearrange this inequality so that the inequality symbol is facing the same direction as it is in the given information We can first rewrite it as: y > 2x - 1 Now subtract 2x from both sides to get: y - 2x > -1 We can rearrange the terms to get the following: -2x + y > -1 We now have: x - y + 2 > 0 -2x + y > -1 When we add the inequalities we get: -x + 2 > -1 Subtract 2 from both sides of the inequality: -x > -3 Multiply both sides of the inequality by -1 to get: x < 3 ( since we multiplied both sides of the inequality by a NEGATIVE value, we must reverse the direction of the inequality symbol ) If x < 3, then x COULD equal 2, in which case the answer to the target question is, NO, x is not negative Conversely, x COULD equal -1, in which case the answer to the target question is, YES, x is negative Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A RELATED VIDEO https://www.youtube.com/watch?v=S_fjYmCtvy0

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If x and y are integers, and x - y + 2 > 0, is x negative?

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If x and y are integers, and x - y + 2 > 0, is x negative?

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