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M28-46

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M28-46  [#permalink]

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New post 16 Sep 2014, 00:31
1
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

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

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Re M28-46  [#permalink]

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New post 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.


Answer: C
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Re: M28-46  [#permalink]

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New post 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.


Answer: C


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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Re: M28-46  [#permalink]

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New post 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.


Answer: C


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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Re: M28-46  [#permalink]

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New post 21 Oct 2015, 13:40
Hi Bunuel,

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

Thanks.
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Re: M28-46  [#permalink]

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New post 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.

For more check below links:

Inequalities Made Easy!

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
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Re: M28-46  [#permalink]

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New post 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.
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Re: M28-46  [#permalink]

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New post 14 Feb 2016, 04:11
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Re: M28-46  [#permalink]

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New post 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
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Re: M28-46  [#permalink]

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New post 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.


Answer: C
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Re: M28-46  [#permalink]

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New post 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.


Answer: C


Yes, only positive integers can be primes, if that's what you mean.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M28-46  [#permalink]

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New post 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
any imp theory link you like to share please...
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Re: M28-46  [#permalink]

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New post 24 Jul 2016, 20:57
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M28-46  [#permalink]

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New post 25 Jul 2016, 02:25
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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
any imp theory link you like to share please...



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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Re: M28-46  [#permalink]

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

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

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New post 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


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Re: M28-46   [#permalink] 23 Jan 2019, 05:12
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