Is x < w ?

is x < w ?

1) x - w < x

2) x + w < w


Can someone please explain the OA along with the process of solving such sums?
Thanks in advance

Ok i got it now

1) x - w < x
subtract x from both sides :

-w < 0
w > 0 but no clue about x ------> insufficient

2) x + w < w
subtract w from both sides :
x < 0 =====> no clue about w ---> insufficient

C) 1 + 2
w > 0 and x < 0 hence x < w ------> sufficient

Can some one please confirm whether my reasoning is correct.
I believe dividing or multiplying by an expression (such as w and or x) in this case is wrong, Since it is not mentioned whether x & or w is +ve/-ve and or int or a fraction
But subtraction should be ok.

IMO,

You are absolutely correct since both side of the inequities in Statement(1 and (2) have same expression.Their subtructions are ok

Hi Bunuel
As per GMAT Club Math Book - "When you divide both sides by a variable (or do operations like "canceling x on both sides") you implicitly assume that the variable cannot be equal to 0, as division by 0 is undefined."
Does this apply only for division. Is it allowed to add, subtract or multiply without knowing the sign (+ve or -ve) for that variable in an inequality.
Please explain or share any link which addresses this confusion.
In both the case above you have subtracted one of the variable from both sides.
Thanks

We are concerned about the sign of a number when multiplying/dividing an inequality by that number. However we can safely add/subtract a number from both sides of an inequality.

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Hope this helps.

Is x < w ?

(1) x - w < x

-w < 0 ...........W>0.......No info about X

Insufficient

(2) x + w < w

x< 0......No info abut W

Insufficient

Combining 1 & 2

x< 0 <w

Answer: C

Alternatively, we can sum up 2 inequalities :

2x-w+w<x +w.............2x<x+w.............2x-x<w...............x<w

Can x<w be re-written as x-w<0?
If not, then why?

You can add or subtract a value from both parts of an inequality freely. So, you can subtract w from x < w and get x - w < 0.

dividing both sides by the corresponding letter is easy, however I did not feel sure about that method because in some questions is not possible to solve them in that way so I just thought about possible values for the letters.

(1)x-w<x

so in order to subtract something from x with a result less than x, either x is negative and w is positive (x<w) or x is positive and w is positive (x<>=w), since we have many different values for x and w, (1) is insufficient.

(2)x+w<w

when will w+x be smaller than w? either w is negative and x is negative (w><=x) or w is positive and x is negative (w>x). Becase we have multiple values for x and W, (2) is insufficient.

(1)+(2) add the inequalities
x-w+x+w<x+w
2x<x+w
x<w

IMO C