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

Question

Is x > 1?

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

chetan2u · Accepted Answer

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..

We are asked whether X>1..
(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

kunalcvrce · Answer

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

KanishkM · Answer

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

Debashis Roy · Answer

VeritasKarishma   chetan2u 
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?

Debashis Roy · Answer

chetan2u

thank you...

Archit3110 · Answer

#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

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

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