If ax + b = 0, is x > 0 ?
a) a +b > 0
b) a - b > 0
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Anju@Gurome
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Consider the following two examples,actofman wrote:If ax + b = 0, is x > 0 ?
a) a + b > 0
b) a - b > 0
- a = 2, b = 1, and x = -1/2 < 0 ---> NO
a = 2, b = -1, and x = 1/2 > 0 ---> YES
So, both statements together are also not sufficient.
The correct answer is E.
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GMATGuruNY
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Given that ax + b = 0, if a=0, then b=0.actofman wrote:If ax + b = 0, is x > 0 ?
a) a + b > 0
b) a - b > 0
Looking at the statements, we can see that it is not possible that both a=0 and b=0.
Thus, we know that a≠0, allowing us to rephrase the question stem.
ax + b = 0
ax = -b
x = - (b/a).
Substituting -(b/a) = x into x > 0, we get:
-(b/a) > 0
b/a < 0.
Question stem rephrased: Do a and b have different signs?
Both statements are satisfied by a=10 and b=1.
In this case, a and b have the same sign.
Both statements are satisfied by a=10 and b=-1.
In this case, a and b have different signs.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is E.
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fcabanski
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"Consider the following two examples,
a = 2, b = 1, and x = -1/2 < 0 ---> NO
a = 2, b = -1, and x = 1/2 > 0 ---> YES
Both of the above examples satisfy both statements but the answer to the original question are different in each case. "
The only thing I'd like to add is a test strategy element. People often go wrong by not solving these problems in a systematic manner. It's not just "When a problem seems easy, still write down the steps and take your time" it's "Especially when a problem seems easy, write down the steps and take your time. Who wants to get a simple problem wrong because of a silly mistake?"
Step 1: Evaluate Statement a.
a = 2, b = 1, and x = -1/2 < 0 ---> NO
a = 2, b = -1, and x = 1/2 > 0 ---> YES
Statement a is not sufficient by itself.
Step 2: Eliminate incorrect choices based on A evaluation.
Eliminate A and D.
Step 3: Evaluate statement b.
Statement b is not sufficient by itself.
Step 4: Eliminate incorrect choices based on b evaluation.
Eliminate B.
Step 5: Evaluate both statements working together.
The new statements the kind expert provided satisfy both statements a and b, but result in different answers.
Step 6: Eliminate incorrect choices based on a and b evaluation.
Eliminate C.
The answer is E.
If you couldn't figure out whether a and b together were sufficient, at least you would have eliminated 3 of the 5 answer choices before guessing.
If my answer helped, please click thanks.
a = 2, b = 1, and x = -1/2 < 0 ---> NO
a = 2, b = -1, and x = 1/2 > 0 ---> YES
Both of the above examples satisfy both statements but the answer to the original question are different in each case. "
The only thing I'd like to add is a test strategy element. People often go wrong by not solving these problems in a systematic manner. It's not just "When a problem seems easy, still write down the steps and take your time" it's "Especially when a problem seems easy, write down the steps and take your time. Who wants to get a simple problem wrong because of a silly mistake?"
Step 1: Evaluate Statement a.
a = 2, b = 1, and x = -1/2 < 0 ---> NO
a = 2, b = -1, and x = 1/2 > 0 ---> YES
Statement a is not sufficient by itself.
Step 2: Eliminate incorrect choices based on A evaluation.
Eliminate A and D.
Step 3: Evaluate statement b.
Statement b is not sufficient by itself.
Step 4: Eliminate incorrect choices based on b evaluation.
Eliminate B.
Step 5: Evaluate both statements working together.
The new statements the kind expert provided satisfy both statements a and b, but result in different answers.
Step 6: Eliminate incorrect choices based on a and b evaluation.
Eliminate C.
The answer is E.
If you couldn't figure out whether a and b together were sufficient, at least you would have eliminated 3 of the 5 answer choices before guessing.
If my answer helped, please click thanks.
