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If ax+b=0 is x>0?

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Source: — Data Sufficiency |
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by neelgandham » Sat May 12, 2012 9:53 am
If ax+b=0 Is x>0?
From the question, x = -b/a. So the question can be rephrased to

Is -b/a>0?
1) a+b>0
Let the value of a be 7 and the value of b be -3. Then the value of a+b = 4>0 and the value of -b/a = 3/7 > 0.

Let the value of a be 7 and the value of b be 3. Then the value of a+b = 10>0 and the value of -b/a = -3/7 < 0.

Since there are two different answers to the question, statement 1 is insufficient to answer the question.
2) a-b > 0
Let the value of a be 7 and the value of b be -3. Then the value of a-b = 10>0 and the value of -b/a = 3/7 > 0.

Let the value of a be 7 and the value of b be 3. Then the value of a-b = 4>0 and the value of -b/a = -3/7 < 0.

Since there are two different answers to the question, statement 2 is insufficient to answer the question.
Statement 1 + 2
Let the value of a be 7 and the value of b be -3. Then the value of a-b = 10>0, the value of a+b=4>0 and the value of -b/a = 3/7 > 0.

Let the value of a be 7 and the value of b be 3. Then the value of a-b = 4>0, the value of a+b=10>0 and and the value of -b/a = -3/7 < 0.

Since there are two different answers for the question, statement 1+2 combined is insufficient to answer the question.

Hence the correct answer choice is E
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by krishna239455 » Sat May 12, 2012 11:12 am
Alternate way:

Statement 1: a+b>0, which means a-ax>0, which means a(1-x)>0, which means (1-x)>0 and (1-x)<0 both are possible, since we dont know about "a" INSUFFECIENT

Statement 2: a-b>0, whcih means a+ax>0, which means a(1+x)>0, which means (1+x)>0 and (1+x)<0 both are possible. since we dont know about "a"INSUFFECIENT

Combined: (a-ax+a+ax)>0, which means a>0, still we get -1<x<1. Hence not suffecient
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