If 9 is a factor of 2x, then which of the following may not be an integer?
A) 6x/54 + 2x/3
B) 4x-18/9
C) 2x-27/9
D) 81-4x^2/81
E) 2x-3/3
Here is my thought process:
If 9 is a factor of 2x then 9 is hiding in the prime factorization of 2x
2x: 2 x 3 x 3 x.... other unknown numbers that could even be 1
Hence X: 3 x 3 x ...... other numbers that could be even 1
Hence X is a 9 or a multiple of 9
When I plugged in 9 in the answer choices all answers yielded to integers.
I am confused!
please help
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finding the non integer
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Amrabdelnaby
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Test the SMALLEST POSSIBLE CASE.Amrabdelnaby wrote:If 9 is a factor of 2x, then which of the following may not be an integer?
A) 6x/54 + 2x/3
B) 4x-18/9
C) 2x-27/9
D) 81-4x^2/81
E) 2x-3/3
Here is my thought process:
If 9 is a factor of 2x then 9 is hiding in the prime factorization of 2x
2x: 2 x 3 x 3 x.... other unknown numbers that could even be 1
Hence X: 3 x 3 x ...... other numbers that could be even 1
Hence X is a 9 or a multiple of 9
When I plugged in 9 in the answer choices all answers yielded to integers.
I am confused!
please help
If 2x=9, then x=9/2.
Plugging X=9/2 into the answer choices, we get:
A) 6x/54 + 2x/3 = (6 * 9/2)/54 + (2 * 9/2)/3 = 1/2 + 3 = 3.5.
The correct answer is A.
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Amrabdelnaby
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Thanks Mitch,
i actually assumed that x is an integer and then thought that if 9 is a factor if 2x then 9 is hiding in the prime factorization of 2x.
hence prime factorization of 2x would be: 2 . 3 . 3 and some other numbers
and prime factorization of x would be : 3 . 3 . and some other numbers
Didn't think about assuming that x itself could be 4.5!
However, when should I use the prime factorization technique then? only when told that x is an integer?
i actually assumed that x is an integer and then thought that if 9 is a factor if 2x then 9 is hiding in the prime factorization of 2x.
hence prime factorization of 2x would be: 2 . 3 . 3 and some other numbers
and prime factorization of x would be : 3 . 3 . and some other numbers
Didn't think about assuming that x itself could be 4.5!
However, when should I use the prime factorization technique then? only when told that x is an integer?
GMATGuruNY wrote:Test the SMALLEST POSSIBLE CASE.Amrabdelnaby wrote:If 9 is a factor of 2x, then which of the following may not be an integer?
A) 6x/54 + 2x/3
B) 4x-18/9
C) 2x-27/9
D) 81-4x^2/81
E) 2x-3/3
Here is my thought process:
If 9 is a factor of 2x then 9 is hiding in the prime factorization of 2x
2x: 2 x 3 x 3 x.... other unknown numbers that could even be 1
Hence X: 3 x 3 x ...... other numbers that could be even 1
Hence X is a 9 or a multiple of 9
When I plugged in 9 in the answer choices all answers yielded to integers.
I am confused!
please help
If 2x=9, then x=9/2.
Plugging X=9/2 into the answer choices, we get:
A) 6x/54 + 2x/3 = (6 * 9/2)/54 + (2 * 9/2)/3 = 1/2 + 3 = 3.5.
The correct answer is A.
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Hi amrabdelnaby,
Tougher GMAT questions are sometimes designed to test the thoroughness of your thinking. This prompt NEVER stated that X was an integer; it even goes so far as to state that 9 is a factor of 2X (not that 9 is a factor of X). When a prompt is built around some quirky language or 'design elements', it's often worthwhile to ask yourself what you really KNOW and what you don't know. As Mitch pointed out in his explanation, thinking about X=4.5 is the easiest way to get to the correct answer (even though 4.5 isn't the easiest value that fits the given description).
GMAT assassins aren't born, they're made,
Rich
Tougher GMAT questions are sometimes designed to test the thoroughness of your thinking. This prompt NEVER stated that X was an integer; it even goes so far as to state that 9 is a factor of 2X (not that 9 is a factor of X). When a prompt is built around some quirky language or 'design elements', it's often worthwhile to ask yourself what you really KNOW and what you don't know. As Mitch pointed out in his explanation, thinking about X=4.5 is the easiest way to get to the correct answer (even though 4.5 isn't the easiest value that fits the given description).
GMAT assassins aren't born, they're made,
Rich
