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In this quadrant we have negative x's and positive y's. Hence a < 0 and b > 0. This is not sufficient to say whether a + b > 0. Consider a = -1 and b = 2; and a = -2 and b = 1.
(2) |a| - |b| > 0 --> |a| > |b|. This implies that a is further from 0, on the number line, then b is. Also, not sufficient.
(1)+(2) Since from (1) a < 0 and b > 0, then for (2) we get -a - b > 0 --> a + b < 0. Sufficient.
In this quadrant we have positive x's and negative y's. Hence a > 0 and b < 0. This is not sufficient to say whether a + b > 0. Consider a = 1 and b = -2; and a = 2 and b = -1.
(2) |a| - |b| > 0 --> |a| > |b|. This implies that a is further from 0, on the number line, then b is. Also, not sufficient.
(1)+(2) Since from (1) a > 0 and b < 0, then for (2) we get a - (-b) > 0 --> a + b > 0. Sufficient.
Answer: C.
Hope it's clear.
Hi Bunuel, Please review highlighted part
In Statement 1, it says (a,b) in Quadrant II, x should be negative and y should be positive. so a<0 and b>0.
1) statement 1 tells us that a is -ive , and b is positive.. But a+b>0 can have an answer NO if lal>lbl or if lal=lbl(in this case answer will be a+b=0) a+b>0 can have an answer YES if lal<lbl .... so insuff..
2) statement 2 tells us that the absolute value of a is > than that of b.. so if the points are in quadrant l : ans will be YES quadrant ll : ans will be NO quadrant lll : ans will be NO quadrant lV : ans will be YES so insuff
combined the answer is only NO.. suff C
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In this quadrant we have positive x's and negative y's. Hence a > 0 and b < 0. This is not sufficient to say whether a + b > 0. Consider a = 1 and b = -2; and a = 2 and b = -1.
(2) |a| - |b| > 0 --> |a| > |b|. This implies that a is further from 0, on the number line, then b is. Also, not sufficient.
(1)+(2) Since from (1) a > 0 and b < 0, then for (2) we get a - (-b) > 0 --> a + b > 0. Sufficient.
Answer: C.
Hope it's clear.
Hi Bunuel, Please review highlighted part
In Statement 1, it says (a,b) in Quadrant II, x should be negative and y should be positive. so a<0 and b>0.
Yes, it's II quadrant ot IV. Edited. Thank you.
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This can be solved by plugging in numbers to prove insufficiency of the statements.
1: (a, b) in Quadrant 2 i.e. a<0 and b>0 for a = -7, b = 3, a+b = -4 <0 for a = -2, b = 3, a+b = 1 > 0 Insufficient as we do not get a definite answer for Is (a+b) <0.
2. |a| - |b| >0 for a = -7, b = 3, |a|-|b| > 0 and a+b = -4 <0 for a = 7, b = -3, |a|-|b| > 0 however, a+b = 4 > 0 Insufficient as we do not get a definite answer for Is (a+b) <0.
Together, based on statement 1 we know that a is -ve and b is +ve. Based on statement 2, we know that absolute value of a is greater than absolute value of b. Therefore, any numbers that we choose that satisfies above condition will result in a+b <0 e.g. (-7, 3), (-10, 2), etc.
Answer: C. Both statements together are sufficient.
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78% (01:29) correct 
