Is x 0? (1) |2x - 12| = -21

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Is  x > 0 ?

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

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CareerGeek · Accepted Answer

(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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vg18 · Answer

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.

Archit3110 · Answer

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=0 x>=7 and x<=3 insufficient IMO A

madgmat2019 · Answer

(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 Posted from my mobile device

exc4libur · Answer

(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… …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… …x≥3…or…x≤7 
 x=

Answer (A)

eakabuah · Answer

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.

lacktutor · Answer

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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suchithra · Answer

Question : is X>0 (1) Given : |2x−12|<10 i.e |x-6|<5 This implies 17 According to this X could take positive and negative values. Therefore answer is A.

Raxit85 · Answer

Can anyone please explain regarding x <=3 rather than x >=3??

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Vibhatu · Answer

Bunuel  please post the official solution

Bunuel · Answer

Is x > 0 ? (1) |2x - 12| < 10 . Get rid of the modulus sign: -10<2x - 12 < 10 ; Add 12 to all three parts: 2<2x < 22 ; Divide by 2: 1 0 is not true. Two different answers. Not sufficient. Another approach: x^2 - 10x \geq {-21} ; x^2 - 10x +21\geq {0} ; (x - 7) (x - 3)\geq {0} ; Check Factoring Quadratics: https://www.purplemath.com/modules/factquad.htm Transitions points are x = 3 and x = 7. " \geq " sign indicates that the solution is to the left of the smaller root and to the right of the larger root. Thus x \leq 3 and x \geq 7 . Check Solving Quadratic Inequalities - Graphic Approach: https://gmatclub.com/forum/solving-quad ... 70528.html So, x may or may not be greater than 0. Not sufficient. Answer: A. Hope it's clear.

bumpbot · Answer

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

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