GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Feb 2019, 14:44

### 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

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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Valentine's day SALE is on! 25% off.

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!
• ### Get FREE Daily Quiz for 2 months

February 18, 2019

February 18, 2019

10:00 PM PST

11:00 PM PST

Buy "All-In-One Standard (\$149)", get free Daily quiz (2 mon). Coupon code : SPECIAL

# M28-46

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

16 Sep 2014, 00:31
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

36% (00:51) correct 64% (00:55) wrong based on 234 sessions

### HideShow timer Statistics

Is $$x^2 \gt 2x$$?

(1) $$x$$ is a prime number.

(2) $$x^2$$ is a multiple of 9.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

16 Sep 2014, 00:31
2
Official Solution:

Is $$x(x-2) \gt 0$$?

Is $$x \lt 0$$ or $$x \gt 2$$. Basically if $$x$$ is not 0, 1, or 2 we have an YES answer to the question.

(1) $$x$$ is a prime number. If $$x=2$$ then the answer is NO but if $$x$$ is some other prime, then the answer is YES. Not sufficient.

(2) $$x^2$$ is a multiple of 9. If $$x=0$$ then the answer is NO but if $$x=3$$, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$x$$ is a prime and from (2) $$x^2$$ is a multiple of 9, then $$x$$ can only be 3. Therefore the answer to the question is YES. Sufficient.

_________________
Intern
Joined: 06 Oct 2010
Posts: 6
Location: Bangalore

### Show Tags

26 Dec 2014, 04:20
Bunuel wrote:
Official Solution:

Is $$x(x-2) \gt 0$$?

Is $$x \lt 0$$ or $$x \gt 2$$. Basically if $$x$$ is not 0, 1, or 2 we have an YES answer to the question.

(1) $$x$$ is a prime number. If $$x=2$$ then the answer is NO but if $$x$$ is some other prime, then the answer is YES. Not sufficient.

(2) $$x^2$$ is a multiple of 9. If $$x=0$$ then the answer is NO but if $$x=3$$, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$x$$ is a prime and from (2) $$x^2$$ is a multiple of 9, then $$x$$ can only be 3. Therefore the answer to the question is YES. Sufficient.

Hi Bunuel,

If X^2 is a multiple of 9,how can we say x can have a value of zero? Please clarify.
Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

26 Dec 2014, 07:03
royinkol wrote:
Bunuel wrote:
Official Solution:

Is $$x(x-2) \gt 0$$?

Is $$x \lt 0$$ or $$x \gt 2$$. Basically if $$x$$ is not 0, 1, or 2 we have an YES answer to the question.

(1) $$x$$ is a prime number. If $$x=2$$ then the answer is NO but if $$x$$ is some other prime, then the answer is YES. Not sufficient.

(2) $$x^2$$ is a multiple of 9. If $$x=0$$ then the answer is NO but if $$x=3$$, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$x$$ is a prime and from (2) $$x^2$$ is a multiple of 9, then $$x$$ can only be 3. Therefore the answer to the question is YES. Sufficient.

Hi Bunuel,

If X^2 is a multiple of 9,how can we say x can have a value of zero? Please clarify.

0 is divisible by EVERY integer except 0 itself, because 0/integer = 0 = integer.
_________________
Intern
Joined: 13 Oct 2012
Posts: 14
Schools: Foster '18
GMAT 1: 560 Q42 V24

### Show Tags

21 Oct 2015, 13:40
Hi Bunuel,

Can we consider Is x2>2x? as 'IS X>2'?

Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

21 Oct 2015, 20:08
patilvrishali101 wrote:
Hi Bunuel,

Can we consider Is x2>2x? as 'IS X>2'?

Thanks.

No. We cannot reduce an equation by a variable if we don't know its sign: if x is positive, then yes, from x^2 > 2x we get x > 2 BUT if x is negative, then when reducing by negative value we must flip the sign and we'd get x < 2.

Solving Quadratic Inequalities - Graphic Approach
Inequality tips

DS Inequalities Problems
PS Inequalities Problems

700+ Inequalities problems

inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html
_________________
Intern
Joined: 04 Sep 2015
Posts: 6

### Show Tags

14 Feb 2016, 04:06
Hi Bunuel,

could you elaborate why x<0? How did you come to that? I do understand that x-2>0 equals x>2.

Thx.
Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

14 Feb 2016, 04:11
Erina89 wrote:
Hi Bunuel,

could you elaborate why x<0? How did you come to that? I do understand that x-2>0 equals x>2.

Thx.

_________________
Current Student
Joined: 12 Aug 2015
Posts: 2621
Schools: Boston U '20 (M)
GRE 1: Q169 V154

### Show Tags

08 Mar 2016, 23:40
Excellent Question ..
here i was tempted to choose A and B but here is why i chose C
here in statement 1 => x can be 2
in statement 2 x can be 0 too as 0 is the multiple of every number .
Hence C
_________________
Manager
Joined: 15 May 2010
Posts: 159
Location: India
Concentration: Strategy, General Management
WE: Engineering (Manufacturing)

### Show Tags

07 Apr 2016, 01:35
Bunnel

Here, in option 1):- x is prime number, which is always positive one, so we ignored X<0 .

Only we checked the condition x>2

Am I right?

Bunuel wrote:
Official Solution:

Is $$x(x-2) \gt 0$$?

Is $$x \lt 0$$ or $$x \gt 2$$. Basically if $$x$$ is not 0, 1, or 2 we have an YES answer to the question.

(1) $$x$$ is a prime number. If $$x=2$$ then the answer is NO but if $$x$$ is some other prime, then the answer is YES. Not sufficient.

(2) $$x^2$$ is a multiple of 9. If $$x=0$$ then the answer is NO but if $$x=3$$, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$x$$ is a prime and from (2) $$x^2$$ is a multiple of 9, then $$x$$ can only be 3. Therefore the answer to the question is YES. Sufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

07 Apr 2016, 07:30
sun01 wrote:
Bunnel

Here, in option 1):- x is prime number, which is always positive one, so we ignored X<0 .

Only we checked the condition x>2

Am I right?

Bunuel wrote:
Official Solution:

Is $$x(x-2) \gt 0$$?

Is $$x \lt 0$$ or $$x \gt 2$$. Basically if $$x$$ is not 0, 1, or 2 we have an YES answer to the question.

(1) $$x$$ is a prime number. If $$x=2$$ then the answer is NO but if $$x$$ is some other prime, then the answer is YES. Not sufficient.

(2) $$x^2$$ is a multiple of 9. If $$x=0$$ then the answer is NO but if $$x=3$$, then the answer is YES. Not sufficient.

(1)+(2) Since from (1) $$x$$ is a prime and from (2) $$x^2$$ is a multiple of 9, then $$x$$ can only be 3. Therefore the answer to the question is YES. Sufficient.

Yes, only positive integers can be primes, if that's what you mean.
_________________
Retired Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 236
Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)

### Show Tags

24 Jul 2016, 18:20
Hi!
A small doubt..
x(x-2)>0
x>2 and x,0...
but is it not x>2 and x> 0?
why inequity sign changed in second while comparing to zero?
thanks
Math Expert
Joined: 02 Sep 2009
Posts: 52938

### Show Tags

24 Jul 2016, 20:57
Celestial09 wrote:
Hi!
A small doubt..
x(x-2)>0
x>2 and x,0...
but is it not x>2 and x> 0?
why inequity sign changed in second while comparing to zero?
thanks

Check here: m28-184544.html#p1590301
_________________
SVP
Joined: 26 Mar 2013
Posts: 2065

### Show Tags

25 Jul 2016, 02:25
2
Celestial09 wrote:
Hi!
A small doubt..
x(x-2)>0
x>2 and x,0...
but is it not x>2 and x> 0?
why inequity sign changed in second while comparing to zero?
thanks

I'm happy to answer your doubt, regardless of the question. I will answer it as we solve inequality.

What does it mean X(X-2)>0 ? Let's put it in simple way.

We have TWO number A & B are multiplied and result Bigger than 0. When does Happen?

From NUMBER PROPERTIES:

Case 1: A = positive & B= positive ............ A * B >0

Case 2: A =negative & B= negative ............ A * B >0

Let look to our inequality :

X(X-2)>0

Put: A=X & B= X-2

Using cases mentioned above let's analyze our inequality:

Case 1:

X (X-2)>0.......... Remember A & B positive means A >0 & B>0

X>0 & X-2>0 then X>2 ....... Can you come up with example that satisfy that X>0 & X>2 in same time???Answer:YES we can. Any number BIGGER than 2 does so

CASE 1 yields that X>2

Case 2

X (X-2)>0.......... Remember A & B negative means A <0 & B<0

X<0 & X-2<0 then X<2........Can you come up with example that satisfy that X<0 & X<2 in same time???Answer:YES we can. Any number SMALLER than 0 does so.

CASE 2 yields that X<0

From above Cases we can conclude FINALLY that: TO SATISFY the Inequality:

Either X<0 or X>2................NOTICE that when we combine TWO CASES, we use 'Either......OR......'

You can check number if you are in doubt.

I will expand my explanation about how to solve if you face this question:

X (X-2)<0

From NUMBER PROPERTIES:

Case 1: A = positive & B= negative ............ A * B <0

Case 2: A =negative & B= positive ............ A * B <0

Put: A=X & B= X-2

Using cases mentioned above let's analyze our inequality:

Case 1:

X (X-2)<0.......... Remember A = positive means A >0 & B=negative means B<0

X>0 & X-2<0 then X<2 ....... Can you come up with example that satisfy that X>0 & X<2 in same time???Answer:YES we can. Any number BIGGER than 0
& SMALLER than 2. We can put mathematically as 0<X<2. For example X=3/2

CASE 1 yields that 0<X<2

Case 2

X (X-2)>0.......... Remember A = negative means A < 0 & B=positive means B>0

X<0 & X-2>0 then X>2........Can you come up with example that satisfy that X<0 & X>2 in same time???Answer:NO, we can NOT. It means that we need a number that is negative and positive in same time. Can you find it?

CASE 2 yields no solution

From above Cases we can conclude FINALLY that: TO SATISFY the Inequality:

0<X<2

Check numbers if you want.
Manager
Joined: 14 Feb 2017
Posts: 121
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GPA: 2.61
WE: Management Consulting (Consulting)

### Show Tags

11 Dec 2018, 13:45
This came up my email from the QOTD.

I said (b), but stupidly didn't consider x=0
Manager
Joined: 13 Feb 2018
Posts: 154
GMAT 1: 640 Q48 V28

### Show Tags

23 Jan 2019, 05:12
After 1 minute i was about to smash B, but then I spent another 45 secs to arrive at a correct answer.

The difficulty level indicator plays a good role while solving such questions

Wish at real GMAT exam we had such priceless tiny indicator

Regards
L
Re: M28-46   [#permalink] 23 Jan 2019, 05:12
Display posts from previous: Sort by

# M28-46

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.