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Re: As x increases from 165 to 166, which of the following must [#permalink]
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) _________________

Re: As x increases from 165 to 166, which of the following must [#permalink]
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 _________________

As x increases from 165 to 166, which of the following must [#permalink]
22 Oct 2014, 06:26

selfishmofo wrote:

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, ..... ...... For the second problem, I used the same method, third problem, decreases by theory, no need to solve.

I have done the first two in the same way you did, but third one took time. Can you please connect or explain the theory that helped you?

Re: As x increases from 165 to 166, which of the following must [#permalink]
22 Oct 2014, 06:49

1

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appleid wrote:

selfishmofo wrote:

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, ..... ...... For the second problem, I used the same method, third problem, decreases by theory, no need to solve.

I have done the first two in the same way you did, but third one took time. Can you please connect or explain the theory that helped you?

x^2 - x is an equation of upward parabola, intercepting the x axis at 0 and 1.

Attachment:

graph.png [ 7.08 KiB | Viewed 2742 times ]

So, far away from the roots, the values of the function (x^2 - x) are increasing as x increases. Therefore 1/(x^2 - x) decreases.

As x increases from 165 to 166, which of the following must [#permalink]
24 Oct 2014, 03:11

Bunuel wrote:

appleid wrote:

selfishmofo wrote:

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, ..... ...... For the second problem, I used the same method, third problem, decreases by theory, no need to solve.

I have done the first two in the same way you did, but third one took time. Can you please connect or explain the theory that helped you?

x^2 - x is an equation of upward parabola, intercepting the x axis at 0 and 1.

Attachment:

graph.png

So, far away from the roots, the values of the function (x^2 - x) are increasing as x increases. Therefore 1/(x^2 - x) decreases.

Similar questions to practice: .... Hope it helps.

Thank you! However, I did understand the value of x^2-x will always goes up, but I am not getting the basic theory (or relevant foundation/topic) behind it. Could you please suggest me any topic which will teach me this from ground level?

gmatclubot

As x increases from 165 to 166, which of the following must
[#permalink]
24 Oct 2014, 03:11

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