It is currently 23 Nov 2017, 04:27

### 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 and y are positive, which of the following must be

Author Message
Senior Manager
Joined: 08 Jun 2004
Posts: 494

Kudos [?]: 95 [0], given: 0

Location: Europe
If x and y are positive, which of the following must be [#permalink]

### Show Tags

12 May 2006, 05:03
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If x and y are positive, which of the following must be greater than 1/√(x+y)?
I. √(x+y)/2x,
II. (√x+√y)/(x+y)
III. (√x-√y)/(x+y)

Kudos [?]: 95 [0], given: 0

Director
Joined: 13 Nov 2003
Posts: 788

Kudos [?]: 64 [0], given: 0

Location: BULGARIA

### Show Tags

12 May 2006, 05:59
Hallo M8,
For I when x=y both stem and A) are equal
For III when x=y nominator is 0 so the ratio is 0 and the number is less than stem for sure.
For II used brute force with values >< than 1 it is also less than stem so seems that NONE of the 3 is bigger than stem

Kudos [?]: 64 [0], given: 0

Director
Joined: 16 Aug 2005
Posts: 937

Kudos [?]: 30 [0], given: 0

Location: France

### Show Tags

12 May 2006, 11:01
Plugging in x=2 and y=2

1/√(x+y) = 1/2

I. √(x+y)/2x = 2/4 = 1/2 not greater so we can rule this out.

II. (√x+√y)/(x+y) = (1.414 + 1.414) / 4 = 2.828/4 > 1/2 so this one could be true, needs further testing

III. (√x-√y)/(x+y) = 0, we can rule this out.

Without further calculation, since None is not a choice here, I will guess II only

But if None is an option we probably need to dig further and it gets ugly. Im sure there are easier way to do this, anyone??

MB what is OA?

Kudos [?]: 30 [0], given: 0

Director
Joined: 06 May 2006
Posts: 790

Kudos [?]: 40 [0], given: 2

### Show Tags

12 May 2006, 11:19

If the stem from each of the options, II is the only one that would definitely evaluate to a positive real number. Try it!

New here, so unable to figure out how to type in those 'root' symbols, so unable to show you the calculations - apologies.

Kudos [?]: 40 [0], given: 2

Intern
Joined: 04 May 2006
Posts: 49

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

### Show Tags

12 May 2006, 14:14
Its II(2).

subtracting 1/√(x+y) from (√x+√y)/(x+y)
it gives: [√x+√y-√(x+y)]/(x+y)
Here, Square root of individual +ve numbers is always more than square root of sum of numbers.
So this value is always +ve.
Similar reasoning can be used to prove for other statements that we can't conclude for surity.
_________________

If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut.
Albert Einstein

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

Senior Manager
Joined: 08 Jun 2004
Posts: 494

Kudos [?]: 95 [0], given: 0

Location: Europe

### Show Tags

12 May 2006, 22:48

New here, so unable to figure out how to type in those 'root' symbols, so unable to show you the calculations - apologies.

Just copy/paste it buddy.

Kudos [?]: 95 [0], given: 0

Director
Joined: 06 May 2006
Posts: 790

Kudos [?]: 40 [0], given: 2

### Show Tags

13 May 2006, 00:29
In an ideal world, people would leave lazy guys like me in peace, but you make me do the calculations

Here they are:

Subtracting (1) from stem, we get
1/√(x+y) - √(x+y)/2x
= (2x - x - y)/[2x√(x+y)]
= (x - y)/[2x√(x+y)]

We don't know relative values of x and y, hence can't say if (1) is greater than stem, as we can't say whether the expression is +ve or -ve.

Subtracting (2) from stem, we can definitely say that (2) is greater than stem, as mendiratta has explained.

Subtracting (3) from stem, we get
1/√(x+y) - (√x-√y)/(x+y)
= [√(x+y) - √x + √y]/(x + y)
This is always +ve, which means the stem is always larger than (3).

Kudos [?]: 40 [0], given: 2

13 May 2006, 00:29
Display posts from previous: Sort by