Data Sufficiency

Is x - y > 0?
(1) 4 < 1/x < 10.
(2) -3 < 1/y < 6.


[spoiler]Source: Of course: writegmat.com[/spoiler]

sanju09 wrote:Is x - y > 0?
(1) 4 < 1/x < 10.
(2) -3 < 1/y < 6.


[spoiler]Source: Of course: writegmat.com[/spoiler]

1 is INSUFF.. not info about y
2 is INSUFF.. no info about x

Combining:
let x=1/5, y = 1/5.5
x>y
let x=1/9, y = 1/5
x<y
2 different answers

Hence INSUFF

pick E

How do you quickly determine which values to pick and test?

Sidney wrote:How do you quickly determine which values to pick and test?

Thats a good question.

I look at the statements and think critically, which combination can fail the condition.
I try choosing numbers normally in the following way:

Look at the boundaries of inequalities. Suppose 3<x<6, what is the reason that the writer of the question wants x to be confined between 3 and 6? there should be a problem if the numbers are chosen away from this range.

In normal problems without inequalities, I plugin in the following order:
Positive Integers
Zero
Negative Integers
Fractions (positive and negative)
Fractions between 0 and 1
Fractions between 0 and -1
Square roots

By the time you reach the end of this list, you will definitely have found the answer.

But the important thing is I plugin when I am almost sure that it is insufficient condition. I plugin to confirm that my analysis is right. A sufficient condition is difficult to prove with plugins. We will need to prove it mathematically.

Hope this helps!!

it has to be c or e since we need to know the values of x and y
x=1/5,1/9
y=-1/2,-1,0,1,1/2..1/5

x-y
1/5-(-1/2) >0
1/5-(1/5) = 0

hence E

sanju09 wrote:Is x - y > 0?
(1) 4 < 1/x < 10.
(2) -3 < 1/y < 6.


[spoiler]Source: Of course: writegmat.com[/spoiler]

Interesting question.

We know that for x - y > 0 to be true, the difference must be 1 or greater.

Individually, both statements are insufficient. 1 only provides information about x; 2 only provides information about y.

Since the question only asks if x - y > 0, we don't care about narrowing in on specific numbers. But we can actually solve algebraically and easily by comparing the range of numbers in statements 1 and 2.

1: 4 < 1/x < 10
2: -3 < 1/y < 6

The two number ranges overlap, which means x could be greater than y... but y could be greater than x. And if y is greater than x, then x - y gives us a negative number. But since we can't be certain... The info together is insufficient.

ANSWER: E

Agree with the other posters.

Is x>y ?

Simple logical version- Is atleast the max 'y' greater than the min 'x'? If yes then the ans to our question is no
OR
Is the atleast the max 'x' greater than the min 'y'? If yes then the ans to our question is yes.

Quick glance suggests that neither stmts is suff.


St1] 4 < 1/x < 10.

St2] -3 < 1/y < 6.

Together we know that max 'y' is approaching 1/6 while min 'x' is approaching 1/10.
Also we know that max 'x' is approaching 1/4 while min 'y' is approaching -1/3.

Hence both the above scenarios are possible.

Choose E.