Last visit was: 24 Nov 2024, 10:12 It is currently 24 Nov 2024, 10:12
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep Club Daily Prep

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 GRE 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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC

x(4 – x)

 1   2   
Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36371 [26]
Given Kudos: 25928
Send PM
x(4 – x) [#permalink] New post   15 Jun 2017, 08:18
6
Expert Reply
20
Bookmarks
00:00

Question Stats:

62% (00:54) correct 37% (00:37) wrong based on 592 sessions

Hide Show timer Statistics





Quantity A
Quantity B
\(x(4 - x)\)
\(6\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
ShowHide Answer
Official Answer
B
Most Helpful Community Reply
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [14]
Given Kudos: 136
Send PM

Top Member of the Month
Re: x(4 – x) [#permalink] New post   19 Jun 2017, 10:10
13
1
Bookmarks
Carcass wrote:




Quantity A
Quantity B
x(4 – x)
6


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


VERY tough question!! (165+)

I'm going to turn x(4 – x) into a perfect square
Before I do that, here are some other perfect squares:
x² + 6x + 9 = (x + 3)²
x² - 10x + 25 = (x - 5)²
x² - 4x + 4 = (x - 2)²
etc...

Given: x(4 – x) = 4x - x²
= -x² + 4x
= -1(x² - 4x)

What do we need to add to x² - 4x to make it a perfect square?
We need to add 4 to it to get x² - 4x + 4, which is equal to (x - 2)²
Of course, we can't just randomly add 4 to the given expression, since that totally changes the expression.
Instead, we're going to add 0 to the given expression. This is fine since adding 0 does not change anything.
HOWEVER, we're going to add 0 in a very SPECIAL WAY. We're going to add + 4 - 4 to the expression.
This is fine, since adding + 4 - 4 to the expression is the same as adding 0 to the expression.

We get: x(4 – x) = 4x - x²
= -x² + 4x
= -1(x² - 4x)
= -1(x² - 4x + 4 - 4)
= -1(x² - 4x + 4) + 4 [to remove -4 from the brackets, I had to multiply it by -1, since we are multiplying everything in the brackets by -1]
= -1(x - 2)² + 4

So, we can now write the following:
Quantity A: -1(x - 2)² + 4
Quantity B: 6

At this point, we must recognize that 4 is the GREATEST possible value of -1(x - 2)² + 4
We know this, because (x - 2)² is always greater than or equal to 0
So, -1(x - 2)² is always less than or equal to 0
So, the greatest value of -1(x - 2)² is 0. This occurs when x = 2
If 0 is the greatest possible value of -1(x - 2)², then 4 is the greatest possible value of -1(x - 2)² + 4

So, we get:
Quantity A: some number less than or equal to 4
Quantity B: 6

Answer:
Show: ::
B


Phew!!!!
General Discussion
avatar
wongpcla
Manager
Manager
Joined: 03 Dec 2017
Posts: 64
Own Kudos [?]: 23 [3]
Given Kudos: 0
Send PM
Re: x(4 – x) [#permalink] New post   19 Dec 2017, 22:48
3
I just simply plug number in,
when X is negative, X=-10
-10(4-(-10))=negative
when x is positive, x=10
10(4-10)= negative

B is always greater
avatar
pranab223
Retired Moderator
Joined: 20 Apr 2016
Posts: 1307
Own Kudos [?]: 2273 [3]
Given Kudos: 251
WE:Engineering (Energy and Utilities)
Send PM

Top Member of the Month
Re: x(4 – x) [#permalink] New post   19 Dec 2017, 23:23
3
wongpcla wrote:
I just simply plug number in,
when X is negative, X=-10
-10(4-(-10))=negative
when x is positive, x=10
10(4-10)= negative

B is always greater


This time you got Lucky,
However in this type of Ques you have to consider every possible aspects. Since no information is given for x, so it can be negative, positive , fraction or integer
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36371 [0]
Given Kudos: 25928
Send PM
Re: x(4 – x) [#permalink] New post   20 Dec 2017, 14:04
Expert Reply
What panab01 pointed out is ONE of the most common mistakes made by the students.

Keep it in mind. Always.

Regards
avatar
wongpcla
Manager
Manager
Joined: 03 Dec 2017
Posts: 64
Own Kudos [?]: 23 [0]
Given Kudos: 0
Send PM
Re: x(4 – x) [#permalink] New post   20 Dec 2017, 17:58
If I plug four different number
(negative, positive , fraction or integer)
Can I avoid all the calculation?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36371 [0]
Given Kudos: 25928
Send PM
Re: x(4 – x) [#permalink] New post   21 Dec 2017, 16:37
Expert Reply
wongpcla wrote:
If I plug four different number
(negative, positive , fraction or integer)
Can I avoid all the calculation?



I think no. At least to a minimum extent.

Regards
avatar
GREMasterBlaster
Intern
Intern
Joined: 11 Jan 2018
Posts: 44
Own Kudos [?]: 104 [2]
Given Kudos: 0
Send PM
Re: x(4 – x) [#permalink] New post   01 Mar 2018, 05:18
2
In such questions, always play with the extremes. i.e
Plug in 0, -ve (betwen 0 and -1), -ve( less than -1), +ve(between 0 and 1) and +ve (greater than 1)

There's how you will damn sure about your answer.

So in this question above, we need to solve in like an inequality expression as below:

Quantity A: x(4-x) or 4x - x^2
Quantity B: 6

We can add x^2 on both Quantities, the inequality will not effect, i.e

Quantity A: 4x
Quantity B: 6 + x^2

Similarly, we can add 6 on both Quantities, the inequality will not effect, i.e

Quantity A: 4x - 6
Quantity B: x^2

Now, if you put x = 0, 0.1, 10, -0.1 and -10

Actually, don't put -ve values, because in all negative values, Quantity B will be greater being positive.

Also, don't put 0, because Quantity A will be negative, while Quantity B remain 0.

Finally, only you need to put any +ve value, Quantity B will always greater.

So, Choice B is correct.

It was a good question.
avatar
Fatemeh
Manager
Manager
Joined: 22 Feb 2018
Posts: 163
Own Kudos [?]: 214 [2]
Given Kudos: 0
Send PM
Re: x(4 – x) [#permalink] New post   28 Mar 2018, 11:06
1
1
Bookmarks
Answer: B
There is no limit for x.
If x is negative:
x(4-x) = 4x - x^2 is always negative because x^2 is always positive and thus -x^2 is negative, also 4x is negative.

If x is positive:
x(4-x) = 4x - x^2
For x = 4 the equation is 0. For 1 <= x <=3 it is positive and for values more than 4 for x, it is negative. Because x^2 is bigger for 4x.
x =1 4x-x^2 = 2
x =2 4x-x^2 = 4
x =3 4x-x^2 = 3
So either the equation is negative or is less than 6 ( 2,3,4). B is bigger than A.
avatar
novice07
Intern
Intern
Joined: 20 Mar 2018
Posts: 39
Own Kudos [?]: 127 [5]
Given Kudos: 0
GRE 1: Q163 V149

GRE 2: Q168 V162
GPA: 3.5
Send PM
Reviews Badge
Re: x(4 – x) [#permalink] New post   19 Apr 2018, 05:18
4
1
Bookmarks
We can find the maximum value of the expression x(4-x) by using the identity: Arithmetic Mean > Geometric Mean:
So,
AM > GM
(x + (4-x))/2 > \sqrt{x(4-x)}
2 > \sqrt{x(4-x)}
Squaring both sides
4 > x(4-x)
So, Quantity A would be less than 4. Hence Quantity B is larger


Another way of doing it is using a little bit of Calculus
The expression x(4-x) would be maximum/ minimum when we put first derivative of x(4-x) = 0
First Derivative: 4 - 2x = 0 --> x =2

So to see if the expression would have a maximum or minimum value at x =2, we see the second derivative of x(4-x). If the second derivative is negative, the expression x(4-x) would have the maximum value at 2 and if the second derivative is positive, the expression would have the minimum value at 2.
Second Derivative: -2

Hence the expression x(4-x) has the maximum value at 2 and that is 2(4-2) = 4
avatar
Nala16
Intern
Intern
Joined: 27 Jan 2020
Posts: 31
Own Kudos [?]: 36 [0]
Given Kudos: 0
Send PM
Re: x(4 – x) [#permalink] New post   03 Feb 2020, 01:28
1
We can compare the two quantities with a placeholder:

4x -x^2 ? 6 | -6
-x^2 +4x -6 ? 0 | take quadratic formula

--> see that -b + 4ac = -8 --> therefore no solution for x, either all outcomes are positive or negative

--> x= 1 f(1)= - 3
--> x= -1 f(-1)= -11

--> therefore the quadratic formula -x^2 +4x -6 is always negative, hence 6 is greater --> B is the correct answer
avatar
S
FCOCGALVAN
Manager
Manager
Joined: 01 Dec 2018
Posts: 87
Own Kudos [?]: 35 [0]
Given Kudos: 38
Send PM
Re: x(4 – x) [#permalink] New post   20 Feb 2020, 17:23
@GreenlightTestPrep
@Carcass

Why isn´t correct just to plug 0 in the first term? x(4-0) .... 0(4-0) = 0 and B would be greater?

What is wrong with doing that?

Regards!
User avatar
P
GreenlightTestPrep
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12196 [0]
Given Kudos: 136
Send PM

Top Member of the Month
Re: x(4 – x) [#permalink] New post   20 Feb 2020, 17:45
1
FCOCGALVAN wrote:
@GreenlightTestPrep
@Carcass

Why isn´t correct just to plug 0 in the first term? x(4-0) .... 0(4-0) = 0 and B would be greater?

What is wrong with doing that?

Regards!


Once you test one x-value, you're not done.

Yes, when x = 0, Quantity B is greater than Quantity A, but that doesn't necessarily mean the correct answer is B.
It could still be the case that the correct answer is D.

That's the problem with testing values. You can never be 100% certain have the correct answer until you get TWO CONFLICTING outcomes (e.g., in one case, quantity B is greater, and in another case, quantity A is greater).

Consider this rudimentary example:
Quantity A: x
Quantity B: 5

If we test x = 1, we find that Quantity B is greater than Quantity A, but this doesn't mean that we can now conclude that the correct answer is B.

The same applies to your solution.

Cheers,
Brent
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36371 [0]
Given Kudos: 25928
Send PM
Re: x(4 – x) [#permalink] New post   20 Feb 2020, 17:48
Expert Reply
Because zero could bring you in unchartered territory.

We do know that zero is only even but neither positive nor negative.

When you test number, it is a rule of thumb to test the following

-1/2,-1,0,1/1/2

of course, in this case, zero has no sense because of a question that you could solve in one second using zero ......mmmmmhhh something is wrong. Too easy.

I hope what I said to make sense.

Regards
avatar
chacinluis
Manager
Manager
Joined: 22 Jan 2020
Posts: 120
Own Kudos [?]: 240 [2]
Given Kudos: 10
Send PM
Re: x(4 – x) [#permalink] New post   15 Aug 2020, 18:41
2
..Quantity A...Quantity B
......x(4-x)...............6
......4x-x^2..............6
........0................x^2-4x+6
........0................x^2-4x+4+2.........(we complete the square to get vertex form of parabola)
........0................(x-2)^2+2..........(this is an upward facing parabola with vertex at (2,2))


The lowest y value of the parabola is 2. Therefore it will always be greater than 0.

Final Answer: B
avatar
Shubham51
Intern
Intern
Joined: 07 Sep 2020
Posts: 15
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
Re: x(4 – x) [#permalink] New post   12 Sep 2020, 08:24
My question is that
how to prepare for gre quants i am done with ets official and 5lb ,what is the good source for gre quants preparation and that to hard and tricky questions?
User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 30017
Own Kudos [?]: 36371 [1]
Given Kudos: 25928
Send PM
Re: x(4 – x) [#permalink] New post   12 Sep 2020, 09:22
Expert Reply
1
Bookmarks
Shubham51 wrote:
My question is that
how to prepare for gre quants i am done with ets official and 5lb ,what is the good source for gre quants preparation and that to hard and tricky questions?


We do have literally thousands of questions

here https://gre.myprepclub.com/forum/gre-quant ... -3523.html

here https://gre.myprepclub.com/forum/gre-quant ... 18001.html

and here https://gre.myprepclub.com/forum/free-gre- ... 18796.html

Hope this helps

Also use our tags to search for hard questions https://gre.myprepclub.com/forum/search.php

at the bottom
avatar
Scorplong
Intern
Intern
Joined: 14 Nov 2021
Posts: 5
Own Kudos [?]: 4 [2]
Given Kudos: 1
Send PM
x(4 – x) [#permalink] New post   Updated on: 16 Nov 2021, 16:05
1
1
Bookmarks
I would like to contribute a much simpler way to get the solution to this problem.

f(x) = x(4-x) = 4x - x^2

We can find an inflection point when the derivative is 0:
f'(x) = 4 - 2x = 0
x = 2

Then, taking the second derivative tells us if this is a min/max:
f''(x) = -2x
f''(2) = -4 < 0

So this is a maximum. Then we plug in f(2) = 2 * (4 - 2) = 4 < 6.

This is much more straightforward (at least for me) than previously given solutions.

Edit: I noticed that novice07 gave this solution before I did

Originally posted by Scorplong on 14 Nov 2021, 14:49.
Last edited by Scorplong on 16 Nov 2021, 16:05, edited 1 time in total.
User avatar
B
Niraj137
Manager
Manager
Joined: 03 Nov 2021
Posts: 92
Own Kudos [?]: 101 [1]
Given Kudos: 17
Send PM
x(4 – x) [#permalink] New post   Updated on: 16 Nov 2021, 21:20
1
The solution I posted was wrong. So I am not able to delete it somehow. So ignore please do ignore this post. Apologies from my side.

Originally posted by Niraj137 on 16 Nov 2021, 08:03.
Last edited by Niraj137 on 16 Nov 2021, 21:20, edited 1 time in total.
avatar
Scorplong
Intern
Intern
Joined: 14 Nov 2021
Posts: 5
Own Kudos [?]: 4 [0]
Given Kudos: 1
Send PM
Re: x(4 – x) [#permalink] New post   16 Nov 2021, 09:41
Niraj137

your answer only proves that f(x) < 4 for x in (0, 1) U (3, 4), it does not say anything about the value of x in [1, 3]. And unfortunately since the maximum of f(x) occurs at x=2, your answer does not prove a bound on the value of f.

Furthermore, even if the maximum of f occurred in the interval you discuss, you would still need to prove the maximum occurs in that interval. You can't just assume it does, otherwise you may assume incorrectly.
Prep Club for GRE Bot
gmatclubot
Re: x(4 – x) [#permalink]
16 Nov 2021, 09:41
 1   2   
Moderators:
adewale223
GRE Instructor
84 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1111 posts
VibhuAnurag
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact