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# M28-46

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Math Expert
Joined: 02 Sep 2009
Posts: 58381

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16 Sep 2014, 01:31
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Difficulty:

95% (hard)

Question Stats:

37% (00:54) correct 63% (00:57) wrong based on 251 sessions

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

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

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

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Joined: 02 Sep 2009
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16 Sep 2014, 01:31
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.

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26 Dec 2014, 05:20
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.
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Joined: 02 Sep 2009
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26 Dec 2014, 08:03
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.
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21 Oct 2015, 14:40
Hi Bunuel,

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

Thanks.
Math Expert
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21 Oct 2015, 21:08
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
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graphic-approach-to-problems-with-inequalities-68037.html
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14 Feb 2016, 05:06
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.
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14 Feb 2016, 05:11
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.

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09 Mar 2016, 00:40
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
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07 Apr 2016, 02:35
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
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07 Apr 2016, 08:30
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.
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24 Jul 2016, 19:20
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
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24 Jul 2016, 21:57
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
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25 Jul 2016, 03:25
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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.
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11 Dec 2018, 14:45
This came up my email from the QOTD.

I said (b), but stupidly didn't consider x=0
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23 Jan 2019, 06:12
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
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Re: M28-46   [#permalink] 23 Jan 2019, 06:12
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# M28-46

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