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# Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21

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Math Expert
Joined: 02 Sep 2009
Posts: 61385
Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 00:19
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:00) correct 58% (02:03) wrong based on 183 sessions

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Competition Mode Question

Is $$x > 0$$?

(1) $$|2x - 12| < 10$$
(2) $$x^2 - 10x \geq {-21}$$

Are You Up For the Challenge: 700 Level Questions

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Joined: 30 Nov 2017
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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07 Nov 2019, 01:10
4
Raxit85 wrote:
Can anyone please explain regarding x <=3 rather than x >=3??

Posted from my mobile device

I also got this wrong for the same reason. Looking back makes sense:

(x—3)(x—7) >=0

LHS will be positive only when (x-3) and (x-7) have same signs. So when we take x>=3 but less than 7 i.e let’s say x = 4 then LHS is (4-3)*(4-7)= -3 which isn’t correct. Hence the only set of nos which satisfy the above equation is either x>=7 or x<=3.
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 01:54
2
(1) |2x - 12| < 10
—> -10 < 2x - 12 < 10
—> - 10 + 12 < 2x - 12 + 12 < 10 + 12
—> 2 < 2x < 22
—> 1 < x < 11
—> x > 0 always —> Sufficient

(2) x^2 - 10x ≥ -21
—> x^2 - 10x + 21 ≥ 0
—> (x - 7)(x - 3) ≥ 0
—> x ≤ 3 or x ≥ 7

Since x ≤ 3, it can take values less than zero also —> Insufficient

IMO Option A

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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 02:36
1
(1) |2x-12|<10

From this we can get 11>x>1

Sufficient

(2) x^2-10x >= -21

We get (x-7)(x-3)>=0

x>=7 or x<=3
Not sufficient

OA:A

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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 03:38
1
Quote:
Is $$x>0$$?

(1) $$|2x−12|<10$$
(2) $$x^2−10x≥−21$$

(1) $$|2x−12|<10$$ sufic.

$$|2x−12|<10…(2x-12)^2<10^2…4x^2+44-48x<0…x^2-12x+11<0…(x-11)(x-1)<0$$
$$(x-11)(x-1)<0…[less.than.sign=inside.range]…1<x<11$$

(2) $$x^2−10x≥−21$$ insufic.

$$x^2−10x≥−21…x^2-10x+21≥0…(x-7)(x-3)≥0$$
$$(x-7)(x-3)≥0…[greater.than.sign=outside.range]…x≥3…or…x≤7$$
$$x=[-9,-1,0,1,2,3,7,8,100…]$$

Answer (A)
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 08:41
1
We are to determine if x>0?

1. |2x-12|<10
when x>0, 2x-12<10
hence x<11

when x<0
-(2x-12)<10
2x-12>-10
x>1
Hence x>1
This results in a range of 1<x<11
Statement 1 alone is therefore sufficient since x>1 in the range above.

2. x^2 -10x ≥-21
x^2 -10x + 21≥0
(x-7)(x-3)≥0
This results in the range x≥7 and x≤3
This is insufficient because when x≥7 then x is always greater than 0. But when x≤3, then x is not always greater than 0, because x can be -1, which is less than 0.

The answer is therefore A.
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 10:11
1
Is x >0?

(Statement1): -10 < 2x—12< 10
—> 2< 2x< 22
1 < x < 11
Sufficient

(Statement2): $$x^{2} —10x+ 21>=0$$
(x—3)(x—7) >=0

x <=3 and x>=7
—> If x=2, then YES
—> If x= —1, then NO
Insufficient

The answer is A

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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 14:52
1
Question : is X>0

(1) Given : |2x−12|<10
i.e |x-6|<5
This implies 1<x<11

Statement 1 is sufficient

(2) x^2−10x≥−21
i.e x^2−10x+21≥0
This imples x<3 or x>7
According to this X could take positive and negative values.

Therefore answer is A.
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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07 Nov 2019, 00:48
1
Can anyone please explain regarding x <=3 rather than x >=3??

Posted from my mobile device
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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14 Nov 2019, 07:28
1
Bunuel wrote:

Competition Mode Question

Is $$x > 0$$?

(1) $$|2x - 12| < 10$$
(2) $$x^2 - 10x \geq {-21}$$

Are You Up For the Challenge: 700 Level Questions

Bunuel

Please categorize the question in DS section.
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 00:54
Is x>0x>0?

(1) |2x−12|<10|2x−12|<10
a.
Solving for x:
2x-12<10
2x<22
x<11

Or
2x-12>-10
2x>2
x>1

From above we get 1<x<11. Ans Yes. Sufficient
(2) x2−10x≥−21
(x-3)(x-7)≥0
x≥3 or x≥7. Yes. Sufficient.

Ans D
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 01:08
Is x>0?

(1) |2x−12|<10

Ix-6I<5

-1<x<11

x=-0.5 No
X=6 yes

(2) x^2−10x≥−21

x^2-10x+21≥0

x≤3; x≥7

X=0 no
X=7 yes

combining both the options:

-1<x≤3; 7≤x<11

E is the correct option!

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Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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Updated on: 07 Nov 2019, 00:55
Is x>0?

(1) |2x−12|<10
(2) x2−10x≥−21

#1
2x-12<10
2x<22
x<11
and
-2x+12<10
-2x<-2
x>1
sufficient

1<x<11
yes insufficient
#2
x2−10x≥−21
(x-7)(x-3)>=0
x>=7 and x<=3
insufficient
IMO A

Originally posted by Archit3110 on 06 Nov 2019, 01:37.
Last edited by Archit3110 on 07 Nov 2019, 00:55, edited 1 time in total.
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Posts: 527
Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 09:16
Is x>0?
Is x +ve ?

(1) |2x−12|<10, 2x-12 <10 or -2x+12<10, 2x<22 or 2x>2, x<11 or x>1, x = +ve. Sufficient.
2) x^2−10x≥−21, x^2-10x+21≥0, x-7≥0 or x-3≥0, x≥7 or x≥3, x = +ve, sufficient.

Imo. D
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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06 Nov 2019, 10:04
Is x > 0?

(1) |2x − 12| < 10
|2||x − 6| < 10
|x − 6| < 5
x - 6 < 5 or - x + 6 < 5
1 < x < 11

SUFFICIENT.

(2) $$x^2−10x ≥ − 21$$
$$x^2−10x + 21 ≥ − 21 + 21$$
(x - 3)(x - 7) ≥ 0
x ≥ 3 or x ≥ 7
x ≥ 7

SUFFICIENT.

IMO Answer D.
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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07 Nov 2019, 01:19
Thank you vg18!

I missed the concept while solving the problem that product of two numbers will be >= to 0 only when two numbers have the same sign.

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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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07 Nov 2019, 01:29
vg18 wrote:
Raxit85 wrote:
Can anyone please explain regarding x <=3 rather than x >=3??

Posted from my mobile device

I also got this wrong for the same reason. Looking back makes sense:

(x—3)(x—7) >=0

LHS will be positive only when (x-3) and (x-7) have same signs. So when we take x>=3 but less than 7 i.e let’s say x = 4 then LHS is (4-3)*(4-7)= -3 which isn’t correct. Hence the only set of nos which satisfy the above equation is either x>=7 or x<=3.

I should have rechecked it..!!
Fell for the 'Timer' which always takes the worst out of me.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
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Posts: 61385
Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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14 Nov 2019, 07:42
Rohit2015 wrote:
Bunuel wrote:

Competition Mode Question

Is $$x > 0$$?

(1) $$|2x - 12| < 10$$
(2) $$x^2 - 10x \geq {-21}$$

Are You Up For the Challenge: 700 Level Questions

Bunuel

Please categorize the question in DS section.

_________________________
Moved to DS forum. Thank you.
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Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21  [#permalink]

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03 Jan 2020, 10:09
vg18 wrote:
Raxit85 wrote:
Can anyone please explain regarding x <=3 rather than x >=3??

Posted from my mobile device

I also got this wrong for the same reason. Looking back makes sense:

(x—3)(x—7) >=0

LHS will be positive only when (x-3) and (x-7) have same signs. So when we take x>=3 but less than 7 i.e let’s say x = 4 then LHS is (4-3)*(4-7)= -3 which isn’t correct. Hence the only set of nos which satisfy the above equation is either x>=7 or x<=3.

Thanks this once slipped out of my mind...clock gets the worst out of me
Re: Is x > 0? (1) |2x - 12| < 10 (2) x^2 - 10x >= -21   [#permalink] 03 Jan 2020, 10:09
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