ineqaulity

[nikhilagrawal]

Is x > y?

(1) root of x > y

(2) x^3 > y

c, but I think it shld be e

[parallel_chase]

Is x > y?

(1) root of x > y

(2) x^3 > y

c, but I think it shld be e

Statement I & II are clearly insufficient alone.

Combining I & II

if x is a positive integer
x^3 > x > sqrtx, therefore if sqrt x is greater than y, x will also be greater than y.

if x is a negative integer.
We cannot have this case because, sqrt x will always be positive.

if x is less than 1 and greater than 0

sqrtx > x > x^3, if x^3 is greater than y, then x will certainly be greater than y.

Sufficient.

Hence C.

Hope this helps. Let me know if you still have any doubts.

[lunarpower]

Is x > y?

(1) root of x > y

(2) x^3 > y

c, but I think it shld be e

Statement I & II are clearly insufficient alone.

Combining I & II

if x is a positive integer
x^3 > x > sqrtx, therefore if sqrt x is greater than y, x will also be greater than y.

if x is a negative integer.
We cannot have this case because, sqrt x will always be positive.

if x is less than 1 and greater than 0

sqrtx > x > x^3, if x^3 is greater than y, then x will certainly be greater than y.

Sufficient.

Hence C.

Hope this helps. Let me know if you still have any doubts.

very well done. note the crucially important TAKEAWAY from this problem:

TAKEAWAY: if you see comparison of different powers/roots of a variable, then you should consider both POS/NEG (if appropriate) and LESS THAN/GREATER THAN 1.

you'll be able to resolve most questions of this type by splitting into these cases, even if you don't fully understand the theory behind the problem.

[Arunlal]

Is there are post where in we have a accumulated list of TAKEAWAY's.
If that exists, plese share the link.

thanks
Arun

[cramya]

Arun,
I dont think there is a comprehensive link withtakeways.

My suggestion is to start making your own flash cards when you read through the posts and see concepts explained. However there is flash card with quant formulas made by Eric(search for it or if I find it will send u)

Hoping Parallel Chase and Ron dont mind

Eg: The takeawy from what parallel chase said would be

if x is a positive integer
x^3 > x > sqrtx, therefore if sqrt x is greater than y, x will also be greater than y.

Eg:x =2

if x is less than 1 and greater than 0

sqrtx > x > x^3, if x^3

eg:x=1/4


The takeaway from Ron's statement is in bold

I was missing a lot of ds question when I started (I miss some now too) since I did not consider what Ron said(taking negative values or values between 0 and 1 etc...)

For example when a problem does not mention x/y as integers fractions come in to play big time. Also echoing Ron's statement considering negative and positive values i.e if the problem says integers and does not specifically say positive integers

Good luck.

[cramya]

I was missing a lot of ds question when I started (I miss some now too) since I did not consider what Ron said(taking negative values or values between 0 and 1 etc.. in to consideration to determine SUFFICIENCY.)

For example when a problem does not mention x/y as integers fractions come in to play big time(I.E u need to check for these 2 before u confirm a choice from A-E). Also echoing Ron's statement considering negative and positive values i.e if the problem says integers and does not specifically say positive integers

Good luck.