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finding the non integer

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by Amrabdelnaby » Sat Dec 26, 2015 8:17 am
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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by GMATGuruNY » Sat Dec 26, 2015 8:33 am
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
Test the SMALLEST POSSIBLE CASE.
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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by Amrabdelnaby » Sat Dec 26, 2015 9:17 am
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?
GMATGuruNY wrote:
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
Test the SMALLEST POSSIBLE CASE.
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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by [email protected] » Sat Dec 26, 2015 10:13 am
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).

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