Is X < Y ?

[26vani26]

Is x less than y?
(1) x-y+1<0
(2) x-y-1<0

Ans is A. Please guide me to the solution.
What should be the general approach to such questions?

[frankiesteinster]

@26Vani26: To approach DS question, kindly take some time in figuring out what each of the option can hint to. Lets consider the question above as an example.

Choice 1: "x-y+1<0" which in turn means "x-y<-1" [shifting 1 to the right does not harm, make sure you change the sign though. Here, -1]. Now, I am sure you are aware of the concept in equality where if you put negative on both side, the inequality sign reverses. In this case:
x-y<-1 => -(x-y)>-(-1) => y-x>1 [refer this for further analysis now]
Now in the expression above. x and y can either be positive or negative.
Scenario 1: Is x negative and y negative: X is certainly in this case of greater absolute value than y for the result 1. In negative integer, the bigger the absolute value, the less it is.
Scenario 2: Is x negative and y positive or equal to zero: You know your answer here. It is sufficient.
Scenario 3: Is x positive and y negative or equal to zero: There is no such possibility for the difference to be greater than 1
Scenario 4: Is x positive or equal to zero and similarly y positive or equal to zero: To be greater than 1, y must exceed x by 1.

Choice 2:x-y-1<0
which is same as "x-y<1". Consider just positive values of x and y for the start. Both being positive, y could be smaller than x to give a difference of 0.5 or much bigger than x to give a difference less than 1. So this alone is not enough to answer.

My first trail to answer someone on GMAT and hope this helps!:)..this should be faster if you practise.

[tim]

there are much easier ways to do this one of course. i'd like to invite the original poster to indicate what he or she tried and where things went wrong, and i'll be glad to help further..

[amycompton]

The answer is X-Y+1<0

The reason is :
consider x and y are two positive integers and taken the value.And apply the vale in this equation also in the second equation X-Y-1<0 apply the value.
In the two case value 0>1 in the equation X-Y+1<0.

[tim]

That can never be the "answer" to a data sufficiency question. Are you saying you think the answer is A? If so, remember you have to demonstrate not only why (1) is sufficient but also why (2) is insufficient..

[kapilnitt]

Hi all,

St 1= X<Y-1
St 2= X<Y+1

Y-1, Y and Y+1 on the numberline

_____Y-1____Y____Y+1____

From St 1:
_X____Y-1____Y____Y+1____ => X<Y

From St 2:

X can be any of the three places
__x___Y-1__x__Y__x__Y+1____ => Can't say anything.

Hope the above make some sense.

Thanks
Kapil

[RonPurewal]

kapil, that's very good. thanks.

you can also isolate the expression (x - y) in each statement.
remember -- "x < y" is equivalent to "x - y < 0".
(you can figure this out by subtracting y from both sides of the left-hand inequality -- or you can just think about the result of subtracting a bigger number from a smaller one.)

if you subtract y from both sides of statement 1, you get
x - y < -1
if x - y is less than -1, then it's definitely less than 0, so that's enough to tell you "yes" to the question.


if you subtract y from both sides of statement 1, you get
x - y < 1
if x - y is less than 1, it still may or may not be less than 0, so this statement is insufficient.

[kapilnitt]

Thanks Ron.

[tim]

:)

[lyl9021]

if
x<y
so
x-y<0<-1
so
x-y+1<0

[kapilnitt]

Answer to your question is marked in blue color

if
x<y
so
x-y<0<-1 (The blue one is not right, as x-y<0 does not mean that it is always less than -1; instead x-y can be -0.5 which is less than 0 but not less than -1. ) Please note that X,Y are not mentioned as integer.
so
x-y+1<0

[lyl9021]

Is x less than y?
(1) x-y+1<0
(2) x-y-1<0


sorry for my careless

if
x-y+1<0
so
x-y<-1<0
so
x-y<0

[tim]

looks good to me. let me know if you have any further questions on this one..