If |x – y| = 10, what is the value of x? (1) x 0 (2) y = 12

Question

If |x – y| = 10, what is the value of x?

(1) x > 0
(2) y = 12

AkshdeepS · Answer

Question: If absolute value of difference of x and y is 10, then find "x"?

Statement -1 is insufficient as it does not gives us the value of "y".

Statement - 2 is insufficient as x can be 2 or 22.

Even combining both we don't get a single value for "x"
So IMO (E)

yezz · Answer

Distance between x and y on the number line is 10, what is x

1 is obviously insuff

From 2

X could be 22 or 2

Both

Still insuff

E

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lauramo · Answer

Hi, 
I don´t understand why statement 2 is also insuficient.
 
Statement 2: y=12

x-12=10
x=10+12
x= 22

Suff.
Thanks!!

AkshdeepS · Answer

The concept is an "absolute value" is the distance between two points on a number line and therefore it is always greater than or equal to zero. It can never be negative as distance can never be negative.

For this question, LHS is an absolute value so it can't be negative and hence x can be 2 & 22 both.

|2-12| = |-10| = 10

|22-12| = |10| = 10

So there are two values of x satisfying this equation, and hence the answer is E.

For Y/N questions we need one and only one value to make the statement sufficient.

Hope this helps.

lauramo · Answer

Thank you very much for the response.

I see why x can have two values: 2 or 10.
However what I still don´t understand is why we cannot resolve this inequality as a regular equation to obtain only one value.

Thanks.

AkshdeepS · Answer

It can be solved as a regular inequality if there is no modulus sign.

If  x - y = 10  then as per statement 2 x can only have a single value as 22.

But for |x – y| = 10 , we need to take care of absolute value on both sides of "0"on number line.

|x – y| = (x - y) = 10  , putting y = 12 we get x - 12 = 10 and  x = 22

|x – y| = -(x - y) = 10 , putting y = 12 we get,

-x + 12 = 10

-x =10 - 12

-x = -2

x = 2

If I say absolute value of x is 5 then it means distance of x from 0 on the number line is 5 units and these 5 units will be on both sides of "0".

lauramo · Answer

Of course!!
Thank you so much for your patience!

Nunuboy1994 · Answer

Let's break this down

Stmnt 1

No info about y and x and y could take on infinite values

Stmnt 2

two ways to break down abs. value

Pos 
x-12 =10
x =22

Neg
-lx-12l =10
-x +12 =10
 -x= -2
 x =2

insuff

Stmnt 1 and 2

Even if we know that x is greater than 0 there are two values that fit that criteria insuff

E

merajul · Answer

If |x – y| = 10, what is the value of x?

(1) x > 0
(2) y = 12

|x-y| =10

(1) does not say the value of y. INSUFFICIENT.

(2) x-y=10 => x =22 or 2. There are 2 possible values. INSUFFICIENT

(1) + (2) does not satisfy, as both values are >0. INSUFFICIENT

Thus correct answer E

Archit3110 · Answer

|x – y| = 10
#1
x>0
x can have many values insufficeint
#2
y=12 , x= 2,22
insufficient
from 1&2
value of x cannot be determined
IMO E

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If |x – y| = 10, what is the value of x? (1) x > 0 (2) y = 12

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