It is currently 11 Dec 2018, 20:09
My Tests

Close

GMAT 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 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.

x(4 – x)

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5149
Followers: 77

Kudos [?]: 1030 [0], given: 4638

CAT Tests
x(4 – x) [#permalink] New post 15 Jun 2017, 08:18
Expert's post
00:00

Question Stats:

50% (00:39) correct 50% (00:26) wrong based on 94 sessions




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.
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

4 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 1232
Followers: 45

Kudos [?]: 1113 [4] , given: 7

Re: x(4 – x) [#permalink] New post 19 Jun 2017, 10:10
4
This post received
KUDOS
Expert's post
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:
[Reveal] Spoiler:
B


Phew!!!!
_________________

Brent Hanneson – Creator of greenlighttestprep.com
Image
Sign up for our free GRE Question of the Day emails

1 KUDOS received
Manager
Manager
Joined: 03 Dec 2017
Posts: 65
Followers: 0

Kudos [?]: 15 [1] , given: 20

Re: x(4 – x) [#permalink] New post 19 Dec 2017, 22:48
1
This post received
KUDOS
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
1 KUDOS received
Director
Director
Joined: 20 Apr 2016
Posts: 756
Followers: 6

Kudos [?]: 511 [1] , given: 94

CAT Tests
Re: x(4 – x) [#permalink] New post 19 Dec 2017, 23:23
1
This post received
KUDOS
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
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5149
Followers: 77

Kudos [?]: 1030 [0], given: 4638

CAT Tests
Re: x(4 – x) [#permalink] New post 20 Dec 2017, 14:04
Expert's post
What panab01 pointed out is ONE of the most common mistakes made by the students.

Keep it in mind. Always.

Regards
_________________

Get the 2 FREE GREPrepclub Tests

Manager
Manager
Joined: 03 Dec 2017
Posts: 65
Followers: 0

Kudos [?]: 15 [0], given: 20

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?
Moderator
Moderator
User avatar
Joined: 18 Apr 2015
Posts: 5149
Followers: 77

Kudos [?]: 1030 [0], given: 4638

CAT Tests
Re: x(4 – x) [#permalink] New post 21 Dec 2017, 16:37
Expert's post
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
_________________

Get the 2 FREE GREPrepclub Tests

1 KUDOS received
Intern
Intern
Joined: 11 Jan 2018
Posts: 44
Followers: 0

Kudos [?]: 26 [1] , given: 7

Re: x(4 – x) [#permalink] New post 01 Mar 2018, 05:18
1
This post received
KUDOS
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.
_________________

Persistence >>>>>>> Success

Don't say thanks, just give KUDOS.
1 kudos = 1000 Thanks

1 KUDOS received
Manager
Manager
Joined: 22 Feb 2018
Posts: 120
Followers: 2

Kudos [?]: 71 [1] , given: 14

CAT Tests
Re: x(4 – x) [#permalink] New post 28 Mar 2018, 11:06
1
This post received
KUDOS
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.

_________________

Follow your heart

Intern
Intern
Joined: 20 Mar 2018
Posts: 34
GRE 1: Q164 V150
Followers: 1

Kudos [?]: 24 [0], given: 2

Re: x(4 – x) [#permalink] New post 19 Apr 2018, 05:18
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
Re: x(4 – x)   [#permalink] 19 Apr 2018, 05:18
Display posts from previous: Sort by

x(4 – x)

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.