If 9 is a factor of 2x, then w=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)/2
E. (2x – 3)/3
Algebraic Problem
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Answer is D
Explanation:
(81 – 4x^2)/2 = (9^2 – (2x)^2)/2 = (9+2x)*(9-2x)/2
As 2x is an even number, both 9+2x and 9-2x are odd and hence when devided by 2 will result in a fraction.
Answer is D.
Explanation:
possible values for x satisfying the above conditions:
x 2x
9 18
18 36
27 54
36 72
45 90
54 108
63 126
.. ..
putting x = 9 in the above all conditions, all expressions are giving integer number
as result except D. So D is the right answer.
What about (A)? Since 9 is a factor of 2x, 2x can be 9 also. Substituting this value in (A) gives a non-integer value. Can anyone explain ?
TakeGMAT, please provide the correct answer with explaination.
d
d
D
The Answer is D
ans is D)
explanation given by abp is perfect
Sorry, but the answer is A. Both ABP’s and Nyn’s explanations make the assumption that x is an integer, which is not necessarily true.
Answer A:
Let x = 4.5, then 2x = 9
6x/54 + 2x/3 =
(3 * 9)/54 + 9/3 = 27/54 + 3: not an integer
I should modify my above statement…as written, the question as given could be A OR D. A for the reasons I explained above.
For D, an integer result is returned HALF the time. That is, for 2x=9, 27, etc.
It is possible that the original question intended to use x as an integer only (in which case the answer would be D, per ABP and Nyn’s answers above), but by not specifying the writers have created ambiguity. As written, a bad question.
D
Ans : A
2x = 9
x = 9/2 ; So A becomes 5/2 , which is not an integer.
I myself think the answer could be A or D.
This question is there for more than one year, without an official answer
Undoubtedly D
Answer should be D.
Hello Guys,
I believe there is catch, the question says 9 is factor of 2x. Means x should not be less than 9, fraction cannot be considered.
So, the answer here is D.
Hi,
By definition factor shall be whole no. (Courtesy :Kaplan). Then there is no question of x = 4.5. The least possible value of x is 9 and hence D is the answer.
A or D
Since 9 is a factor of 2x we can write 2x = 9k where k is an integer > 0.
Now substituting 2x = 9k in all above equations:
a) k/2 + 3k
d) (81 – (9k)^2)/2
a is an integer only if k is even and d is an integer only when k = 1 (=0) or when (1-k^2) is even i.e. k^2 is odd or k is odd.
Must be D
take x=9
all answers ruled out except D
D