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Is a + b > 0 ?

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Is a + b > 0 ?  [#permalink]

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New post 11 Nov 2015, 01:57
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Is a + b > 0 ?

(1) The point (a, b) is in Quadrant II.

(2) |a| - |b| > 0

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Is a + b > 0 ?  [#permalink]

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New post 11 Nov 2015, 02:03
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1
Is a + b > 0 ?

(1) The point (a, b) is in Quadrant II.

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.

Answer: C.

Hope it's clear.
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Re: Is a + b > 0 ?  [#permalink]

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New post 11 Nov 2015, 17:26
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Bunuel wrote:
Is a + b > 0 ?

(1) The point (a, b) is in Quadrant II.

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.
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Re: Is a + b > 0 ?  [#permalink]

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New post 11 Nov 2015, 21:06
yeps, x must be negative, y positive
but since we need to know the absolute value, A isn't sufficient by itself.
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Re: Is a + b > 0 ?  [#permalink]

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New post 11 Nov 2015, 21:26
shyind wrote:
Is a + b > 0 ?

(1) The point (a, b) is in Quadrant II.

(2) |a| - |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
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Re: Is a + b > 0 ?  [#permalink]

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New post 11 Nov 2015, 22:07
Mo2men wrote:
Bunuel wrote:
Is a + b > 0 ?

(1) The point (a, b) is in Quadrant II.

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Is a + b > 0 ?  [#permalink]

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New post 12 Nov 2015, 04:26
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.

Hope this helps.
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Re: Is a + b > 0 ?  [#permalink]

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New post 15 Aug 2017, 07:36
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