Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 01 Jul 2016, 18:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# if x>y>0, which of the following must be true? I.

Author Message
Manager
Joined: 25 Jul 2006
Posts: 97
Followers: 1

Kudos [?]: 1 [0], given: 0

if x>y>0, which of the following must be true? I. [#permalink]

### Show Tags

29 May 2007, 17:00
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

if x>y>0, which of the following must be true?

I. root(x) - root(y) < root(x-y)
II. x^2 - y^2 > (x-y)^2

1. None
2. I only
3. II only
4. I and II
5. Cannot be determined

If you can, please provide an ALGEBRAIC SOLUTION/DERIVATION/PROOF for the two inequations. I got some answers after testing with several numbers - but it took a while and number plug-in method makes me unsure. Thanks.
Manager
Joined: 04 May 2007
Posts: 111
Followers: 1

Kudos [?]: 1 [0], given: 0

### Show Tags

29 May 2007, 20:18
i don't know of an algebraic/proof way to answer this q- there are some smart people on this board who might have a 'number theory' type of answer/explanation for you... but sometimes i think you just gotta plug in.

i think you can answer this quickly by picking an x and y value that satisfies the inequality (x is bigger than y, y is bigger than zero) and keeping the x and y the same acorss inequalities keeps it consistent

i pikced 100 and 36

10-6<8>16 yup

you can estimate with fractions even:

x=1/4 y=1/9

I: 1/2-1/3 < square root 5/36
1/6 < use 4/36 instead (a smaller # but easy to find root of)

1/6<2/6 yup!
Manager
Joined: 28 Aug 2006
Posts: 160
Followers: 2

Kudos [?]: 14 [0], given: 0

### Show Tags

29 May 2007, 20:38
Its 4. Both Statements I and II are true.

Since X and Y are positive. We will have to check when X and Y are integers and when they are between 0 and 1 (0<x>1 and 0<Y>1).

When you simplify stat II we get
2XY>y^2, Plug in values below

I used X=4 and Y=9 for integers and X=1/4 and Y=1/9 and found that both statements are valid.
Display posts from previous: Sort by