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# Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x

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Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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04 Feb 2019, 08:01
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75% (hard)

Question Stats:

40% (01:40) correct 60% (01:39) wrong based on 68 sessions

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Is x > 1?

(1) 2x + 5 > 2 - x
(2) |x - 12| = 12 - 3x

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Chasing the dragon
Math Expert
Joined: 02 Aug 2009
Posts: 7975
Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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01 Mar 2019, 02:15
fitzpratik wrote:
Is x > 1?

(1) 2x + 5 > 2 - x
(2) |x - 12| = 12 - 3x

Yes, Debashish. If you start with assumption that X<0 and you get an answer such that X>0, then it is not a valid solution..

(1) $$2x+5>2-x$$

$$2x+x>2-5....3x>-3...x>-1..$$
Thus x could be 0 or 2 or 4 and so on.
Thus insufficient

(2) $$|x-12|=12-3x$$

Now the RHS has to be non negative, so $$12-3x\geq{0}...12\geq{3x}....x\leq{4}$$

As both sides are non-negative, we can square both sides
$$x^2-24x+144=144-72x+9x^2......8x^2-48x=0...8x(x-6)=0$$
So X can be 0 or 6, but we know that x is less than or equal to 4..
Hence x=0.. So, answer is "NO, x is not more than 1".

B
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Re: Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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04 Feb 2019, 08:15
fitzpratik wrote:
Is x > 1?

1. 2x+5 > 2-x
2. |x-12| = 12-3x

From 1 3x>-3, x>-1 ,Not sufficient
From 2 if x>12
then ,x-12=12-3x =>x=6 not possible since x>12
if x<12
then 12-x=12-3x, x=0 sufficient
B
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Re: Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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04 Feb 2019, 08:16
fitzpratik wrote:
Is x > 1?

1. 2x+5 > 2-x
2. |x-12| = 12-3x

from 1
When we solve the inequulity
we will get x > -1
which will answer the question as No, when x =0
which will answer the question as Yes, when x =2

from 2
x-12 = 12-3x or -x+12 = 12-3x
x = 6 or x = 0

Now we did get 2 values here, but will they both satisfy the modulus, lets see
At x = 6
|6-12| = 12-18
6 ! = 6, Not a valid value

At x = 0
12 = 12, True

So only one value comes out,which will answer the question as No

B
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Re: Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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01 Mar 2019, 01:25
2. |x-12| = 12-3x

For these conditions if we take x<0 but its solution comes to be x>0...then this statement will be regarded as insufficient..right?
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Re: Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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01 Mar 2019, 02:40
chetan2u

thank you...
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Re: Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x  [#permalink]

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03 Mar 2019, 04:40
fitzpratik wrote:
Is x > 1?

(1) 2x + 5 > 2 - x
(2) |x - 12| = 12 - 3x

#1
2x + 5 > 2 - x
we get
x>-1
not sufficient as x=0,1,2..
#2
|x - 12| = 12 - 3x
we get x=6 & 0
at x = 6 |x - 12| = 12 - 3x is not valid
x=0 |x - 12| = 12 - 3x is valid
so sufficient
IMO B
Re: Is x > 1? (1) 2x + 5 > 2 - x (2) |x - 12| = 12 - 3x   [#permalink] 03 Mar 2019, 04:40
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