Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

13 Aug 2013, 08:12

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]

Show Tags

13 Aug 2013, 10:40

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]

Show Tags

22 Oct 2014, 07:26

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]

Show Tags

22 Oct 2014, 07:49

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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 4739 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]

Show Tags

24 Oct 2014, 04:11

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?

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

Show Tags

25 Nov 2015, 17:10

Bunuel wrote:

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.

Hi Bunuel, I was thinking that plugging in 2 instead of 165 and 3 instead of 166 and then solve could be an efficient approach for this particular question. Do you agree? _________________

Consider giving me Kudos if I helped, but don´t take them away if I didn´t!

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

Show Tags

28 Nov 2015, 21:05

2

This post received KUDOS

Expert's post

Hi All,

Roman Numeral questions are relatively rare on Test Day (you'll likely see just 1 in the Quant section), but they are almost always designed around Number Properties and logic 'shortcuts'...

Here, we're told that X increase from 165 to 166. We're asked which of the following MUST increase. While this prompt might appear 'calculation heavy', you can actually solve it WITHOUT doing calculations (and paying attention to the answer choices).

I. 2X - 5

The "-5" has the same 'math effect', regardless of what X is: the '-5' reduces the value by 5. So as X goes from 165 to 166, 2X gets BIGGER. Since the '-5' has the same effect, 2X-5 definitely gets bigger as X increases from 165 to 166. Roman Numeral 1 INCREASES Eliminate Answers B and E.

II. 1 - 1/X

As the denominator of a fraction gets BIGGER, the fraction gets SMALLER. Thus, 1/165 > 1/166. The "1" in this calculation is constant, so subtracting a SMALLER fraction from it will lead to a BIGGER result. As X increases from 165 to 166, 1/X gets SMALLER, so 1-(1/X) definitely gets bigger. Roman Numeral 2 INCREASES Eliminate Answers A and D.

There's only one answer remaining (and we don't even have to deal with Roman Numeral 3)...

So, my final tally is in. I applied to three b schools in total this season: INSEAD – admitted MIT Sloan – admitted Wharton – waitlisted and dinged No...

A few weeks ago, the following tweet popped up in my timeline. thanks @Uber_Mumbai for showing me what #daylightrobbery means!I know I have a choice not to use it...

“This elective will be most relevant to learn innovative methodologies in digital marketing in a place which is the origin for major marketing companies.” This was the crux...