uzzy12 wrote:
If ax + b = 0, is x > 0
(1) a + b > 0
(2) a - b > 0
Target question: Is x > 0 Given: ax + b = 0 Statement 1: a + b > 0 At this point, we have 1 equation, 1 inequality, and THREE variables.
Even if we had 2 EQUATIONS and 3 variables, we probably wouldn't be able to make any conclusions about whether x is positive or negative.
Given this, let's TEST some values
There are several values of a, b and x that satisfy statement 1 (and the given equation
ax + b = 0). Here are two:
Case a: a = 2, b = -1 and x = 0.5. In this case, the answer to the target question is
YES, x is positiveCase b: a = 2, b = 1 and x = -0.5. In this case, the answer to the target question is
NO, x is NOT positiveSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a - b > 0This is the same scenario as statement 1, so let's TEST some values
There are several values of a, b and x that satisfy statement 1 (and the given equation
ax + b = 0). Here are two:
Case a: a = 2, b = -1 and x = 0.5. In this case, the answer to the target question is
YES, x is positiveCase b: a = 2, b = 1 and x = -0.5. In this case, the answer to the target question is
NO, x is NOT positiveSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the
same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: a = 2, b = -1 and x = 0.5. In this case, the answer to the target question is
YES, x is positiveCase b: a = 2, b = 1 and x = -0.5. In this case, the answer to the target question is
NO, x is NOT positiveSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
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