Hi Mo2men,
I think there's a typo in this question (either in the original source material or in how you transcribed it). The prompt states that X is GREATER THAN ZERO, but the question then asks if X is greater than 0.... The answer would be 'yes' without having to consider the two Facts.
GMAT assassins aren't born, they're made,
Rich
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If a, b, & x are greater than zero, is x > 0
Source: Beat The GMAT — Data Sufficiency |
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Thanks Rich for your observation. It is my problem actually. Problem fixed.[email protected] wrote:Hi Mo2men,
I think there's a typo in this question (either in the original source material or in how you transcribed it). The prompt states that X is GREATER THAN ZERO, but the question then asks if X is greater than 0.... The answer would be 'yes' without having to consider the two Facts.
GMAT assassins aren't born, they're made,
Rich
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Mo2men wrote:If a, b, & x are greater than zero, is x > 4?
1) (ax^2 - 9a)/(12xb) = (ax - 3a)/ (bx + 3b)
2)a + b =5 and a - b= 4
Statement 1: (ax² - 9a)/(12xb) = (ax - 3a) / (bx + 3b)
a(x² - 9)/(12xb) = a(x-3) / b(x+3)
(x² - 9)/(12x) = (x-3) / (x+3)
(x+3)(x-3) / (12x) = (x-3) / (x+3)
[(x+3)(x-3) / 12x] - [(x-3) / (x+3)] = 0
(x-3)[ (x+3)/(12x) - 1/(x+3) ] = 0.
Case 1: x-3 = 0
Here, x=3.
Case 2: (x+3)/(12x) - 1/(x+3) = 0
Thus:
(x+3)/(12x) = 1/(x+3)
(x+3)² = 12x
x² + 6x + 9 = 12x
x² - 6x + 9 = 0
(x-3)² = 0
x=3.
Since x=3 in each case, the answer to the question stem is NO.
SUFFICIENT.
Statement 2: a+b = 5 and a-b = 4
No information about x.
INSUFFICIENT.
The correct answer is A.
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Dear Mitch,GMATGuruNY wrote:Mo2men wrote:If a, b, & x are greater than zero, is x > 4?
1) (ax^2 - 9a)/(12xb) = (ax - 3a)/ (bx + 3b)
2)a + b =5 and a - b= 4
Statement 1: (ax² - 9a)/(12xb) = (ax - 3a) / (bx + 3b)
a(x² - 9)/(12xb) = a(x-3) / b(x+3)
(x² - 9)/(12x) = (x-3) / (x+3)
(x+3)(x-3) / (12x) = (x-3) / (x+3)
[(x+3)(x-3) / 12x] - [(x-3) / (x+3)] = 0
(x-3)[ (x+3)/(12x) - 1/(x+3) ] = 0.
Case 1: x-3 = 0
Here, x=3.
Case 2: (x+3)/(12x) - 1/(x+3) = 0
Thus:
(x+3)/(12x) = 1/(x+3)
(x+3)² = 12x
x² + 6x + 9 = 12x
x² - 6x + 9 = 0
(x-3)² = 0
x=3.
Since x=3 in each case, the answer to the question stem is NO.
SUFFICIENT.
In third line in green, why did not you cancel out (x-3) from both sides? x is greater zero so we zero won't be answer.
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Only NONZERO factors may be canceled out from both sides.Mo2men wrote: Dear Mitch,
In third line in green, why did not you cancel out (x-3) from both sides? x is greater zero so we zero won't be answer.
If x=3, then x-3 = 0.
Since it's possible that x-3 = 0, we cannot cancel out x-3.
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Suppose in a prompt y > 0 and after factoring out we have following:GMATGuruNY wrote:Only NONZERO factors may be canceled out from both sides.Mo2men wrote: Dear Mitch,
In third line in green, why did not you cancel out (x-3) from both sides? x is greater zero so we zero won't be answer.
If x=3, then x-3 = 0.
Since it's possible that x-3 = 0, we cannot cancel out x-3.
(1+y)(..........) = (1+y) (.............)
Can we cancel out (1 +y) as we are sure is always positive? or are their any other restrictions?
Thanks in advance
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In an equation, any nonzero factor can be canceled out from both sides.Mo2men wrote:Suppose in a prompt y > 0 and after factoring out we have following:
(1+y)(..........) = (1+y) (.............)
Can we cancel out (1 +y) as we are sure is always positive? or are their any other restrictions?
Thanks in advance
If y>0, then 1+y>0.
Since 1+y is nonzero, it can be canceled out from both sides of the equation above.
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