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As x increases from 165 to 166, which of the following must

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As x increases from 165 to 166, which of the following must [#permalink] New post 26 Dec 2012, 06:13
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As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III
[Reveal] Spoiler: OA
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Re: As x increases from 165 to 166, which of the following must [#permalink] New post 26 Dec 2012, 06:16
Expert's post
Walkabout wrote:
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III


I. 2x - 5 --> x increases from 165 to 166 --> 2x increases --> 2x - 5 increases. Correct.

II. 1 - 1/x --> x increases from 165 to 166 --> 1/x decreases --> 1 -1/x increases. Correct.

III. 1/(x^2 - x) --> x increases from 165 to 166 --> x^2-x increases --> 1/(x^2 - x) decreases.

Answer: C.
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Re: As x increases from 165 to 166, which of the following must [#permalink] New post 12 Aug 2013, 19:31
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For the first part, I simply plugged in a positive whole number for x, then I retested with a higher number than the number I chose originally for x,

X=5

2x-5=
2*5-5
10-5=5

X=6

2*6-5
12-5=7

X increases, and so does 2x-5

For the second problem, I used the same method, third problem, decreases by theory, no need to solve.
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Re: As x increases from 165 to 166, which of the following must [#permalink] New post 13 Aug 2013, 07:12
Walkabout wrote:
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III

...
I and II can be counted easily, both increases.
And III is 1/x(x-1)
Now, 1/(165×164) > 1/(166×165) , so it decreases as 165 turns to 166 .
so I and II = C (Answer)
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Re: As x increases from 165 to 166, which of the following must [#permalink] New post 13 Aug 2013, 09:40
Walkabout wrote:
As x increases from 165 to 166, which of the following must increase?

I. 2x - 5
II. 1 - 1/x
III. 1/(x^2 - x)

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) II and III


The max difference b/w 165 and 166 is '1' and the min value can be 0.000000000000000000001 but for our convenience we shall choose 0.1
Equation 1 ==> for min value of 0.1, the value is 2(0.1) - 5 = -4.8

for max value of 1, 2(1)-5=-3
so the values are increasing from -4.8 to -3

similary submit the values 0.1 and 1 and we notice that the value increases from -9 to 0 ==> equation 2 is also increasing

for double confirmation substitute the values of 0.1 and 1 in equation 3.
for min value of x=0.1, the value is 1/(0.01-0.1)=-1/0.09
for max value of 1, the value is 'infinite' ... hence we dont count this.

So equations 1 & 2 are increasing. This is the answer
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Re: As x increases from 165 to 166, which of the following must   [#permalink] 13 Aug 2013, 09:40
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