GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2018, 10:13

# Saturday Quant Quiz:

Starts promptly at 10 AM PST - Join in to Have Fun & Win Prizes

### 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

# If x and y are positive, is x^(1/2) + y^(1/2) ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Oct 2016
Posts: 55
Location: India
GMAT 1: 650 Q47 V33
GPA: 4
If x and y are positive, is x^(1/2) + y^(1/2) ?  [#permalink]

### Show Tags

06 Nov 2017, 06:00
5
00:00

Difficulty:

85% (hard)

Question Stats:

43% (01:44) correct 57% (02:17) wrong based on 97 sessions

### HideShow timer Statistics

If x and y are positive, is $$\sqrt{x}+ \sqrt{y} > 1$$ ?

(1) $$\sqrt{x+y}>1$$

(2) $$x > y > \frac{1}{4}$$
Math Expert
Joined: 02 Sep 2009
Posts: 50007
Re: If x and y are positive, is x^(1/2) + y^(1/2) ?  [#permalink]

### Show Tags

06 Nov 2017, 06:37
2
2
If x and y are positive, is $$\sqrt{x}+ \sqrt{y} > 1$$ ?

Is $$\sqrt{x}+ \sqrt{y} > 1$$ ?
Square: is $$x+ 2\sqrt{xy}+y > 1$$ ?

(1) $$\sqrt{x+y}>1$$. Square: x + y > 1. Since x and y are positive, then $$2\sqrt{xy}>0$$, and thus $$x+ 2\sqrt{xy}+y=(x+y)+2\sqrt{xy}=(number \ more \ than \ 1)+(positive \ value)>1$$. Sufficient.

(2) $$x > y > \frac{1}{4}$$. Since both x and y are greater than 1/4, then both $$\sqrt{x}$$ and $$\sqrt{y}$$ are greater than 1/2. Hence, $$\sqrt{x}+ \sqrt{y} > 1$$. Sufficient.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6967
Re: If x and y are positive, is x^(1/2) + y^(1/2) ?  [#permalink]

### Show Tags

06 Nov 2017, 06:38
leshwarnag wrote:
If x and y are positive, is $$\sqrt{x}+ \sqrt{y} > 1$$ ?

(1) $$\sqrt{x+y}>1$$

(2) $$x > y > \frac{1}{4}$$

hi...

$$\sqrt{x}+ \sqrt{y} > 1$$
square both sides....
$$(\sqrt{x}+ \sqrt{y})^2 > 1^2.............x+y+2\sqrt{xy}>1$$

lets see statements

(1) $$\sqrt{x+y}>1$$
square both sides..
$$x+y>1$$...
if $$x+y >1$$, when you add another positive value $$2\sqrt{xy}$$, it will surely be >1
so $$x+y+2\sqrt{xy}>1$$
suff

(2) $$x > y > \frac{1}{4}$$
lets take both as 1/4
so $$\sqrt{x}+ \sqrt{y} = \sqrt{1/4}+\sqrt{1/4}=1/2+1/2=1$$
so the equation will be >1
suff

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 28 Dec 2010
Posts: 49
If x and y are positive, is x^(1/2) + y^(1/2) ?  [#permalink]

### Show Tags

06 Nov 2017, 06:42
Square root of a positive fraction is greater than itself

1. $$\sqrt{x+y} > 1$$
For the above statement to be true: x+y > 1
You can check with any combination of x and 1-x
0.5, 0.5 : $$\sqrt{0.5} + \sqrt{0.5} => 1.4$$
0.1, 0.9 : $$\sqrt{0.1} + \sqrt{0.9} => 0.31 + 0.94 => 1.25$$
0.01, 0.99 : $$\sqrt{0.01} + \sqrt{0.99} => 0.1 + 0.995 => 1.095$$
It would always be greater than 1
Yes

2. $$x > y > \frac{1}{4}$$

$$\sqrt{1/4} = 0.5$$
So $$\sqrt{x} > \sqrt{y} > 0.5$$
$$\sqrt{x} + \sqrt{y} > 1$$
YES

D.
_________________

_________________________________________

If x and y are positive, is x^(1/2) + y^(1/2) ? &nbs [#permalink] 06 Nov 2017, 06:42
Display posts from previous: Sort by