January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Aug 2013
Posts: 74
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q41 V29 GMAT 2: 540 Q44 V20
GPA: 3.5
WE: Programming (Computer Software)

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
11 Sep 2013, 01:32
study wrote: If x and y are positive, which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)?
1. \(\frac{\sqrt{x+y}}{2x}\)
2. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\)
3. \(\frac{\sqrt{x}\sqrt{y}}{x+y}\)
(A) None (B) 1 only (C) 2 only (D) 1 and 3 only (E) 2 and 3 only 1 way to look at this problem is : I) Cross Multiplying LHS : x+y RHS 2x (So y can be anything greater than or less than x), hence ruled out II) LHS : [square_root]x + [square_root]y = [square_root]x+y Now if x were a^2, y were b^2 then LHS : a + b and RHS [square_root]a^2 + b^2 which is nothing but a right triangle with RHS as diagonal and a and b as sides of it. And that the sum of the 2 sides of the triangle is always greater than the third side. Hence this will be true. III) Similarly as with 2, this will become LHS : a  b and RHS : [square_root]a^2 + b^2. Any side will always be greater than the difference between the 2 sides. Hence this will be false. Thus Answer will be C



Senior Manager
Joined: 21 Jan 2010
Posts: 253

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
11 Sep 2013, 23:11
study wrote: If x and y are positive, which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)?
1. \(\frac{\sqrt{x+y}}{2x}\)
2. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\)
3. \(\frac{\sqrt{x}\sqrt{y}}{x+y}\)
(A) None (B) 1 only (C) 2 only (D) 1 and 3 only (E) 2 and 3 only I am not sure why everyone is deriving complex formulas for this problem. I answered this question in 30 seconds. Put x=y=1. Only 2 survives. You can test by a couple of more values. It will always hold good. Hence C.



SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
05 Feb 2014, 08:49
I did the following, nothing too complicated
First statement clearly not enough since after cross multiplying we get is y>x? We don't know
For the second statement we have is (sqrt (x) + sqrt (y)(sqrt (x+y)> x+y
x + y = sqrt (x+y) ^2 so what we really need to know is if (sqrt (x) + sqrt (y) > sqrt (x+y) and yes, since sqrt (n) where n is any number is always more than 1 so >1 + >1 is always more than >1. Therefore this statement is true
For the last statement we get something a bit different but still We have sqrt (x+y)(sqrt (x)  sqrt (y)) > x+y
Again x+y = sqrt (x+y)^2
Therefore question is ' Is sqrt (x)  sqrt (y) > sqrt (x+y)
This will never be the case as >1  >1 will never be >1
Therefore our only correct answer choice is the second statement
Hope its clear Cheers J



Manager
Joined: 03 Jan 2015
Posts: 61
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
30 Jan 2015, 20:27
Hi all,
If I assume x = 3 and y = 6, then:
Original expression = 1/3
1 evaluates to 1/2 2 evaluates to (1/9)*something 3 evaluates to (1/9)*something
Thus, I get only 1 as an answer.
Any comments?
TO



Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
31 Jan 2015, 04:25



Intern
Joined: 07 Jul 2010
Posts: 7

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
15 Jun 2015, 03:17
study wrote: If x and y are positive, which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)?
1. \(\frac{\sqrt{x+y}}{2x}\)
2. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\)
3. \(\frac{\sqrt{x}\sqrt{y}}{x+y}\)
(A) None (B) 1 only (C) 2 only (D) 1 and 3 only (E) 2 and 3 only Interesting ..... It's not a good question What if i take x = y = 2 ....Then c option would work out to be 0 /4 . Nothing in the prompt prevents me from considering x and y to be equal and doing that Option C is not possible as well I think the question should have made it very clear that x is not equal to y



Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
15 Jun 2015, 03:19
amlan009 wrote: study wrote: If x and y are positive, which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)?
1. \(\frac{\sqrt{x+y}}{2x}\)
2. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\)
3. \(\frac{\sqrt{x}\sqrt{y}}{x+y}\)
(A) None (B) 1 only (C) 2 only (D) 1 and 3 only (E) 2 and 3 only Interesting ..... It's not a good question What if i take x = y = 2 ....Then c option would work out to be 0 /4 . Nothing in the prompt prevents me from considering x and y to be equal and doing that Option C is not possible as well I think the question should have made it very clear that x is not equal to y The question asks "which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)", not "which of the following could be greater than \(\frac{1}{\sqrt{x+y}}\)".
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 07 Jul 2010
Posts: 7

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
17 Jun 2015, 23:28
Bunuel wrote: amlan009 wrote: study wrote: If x and y are positive, which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)?
1. \(\frac{\sqrt{x+y}}{2x}\)
2. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\)
3. \(\frac{\sqrt{x}\sqrt{y}}{x+y}\)
(A) None (B) 1 only (C) 2 only (D) 1 and 3 only (E) 2 and 3 only Interesting ..... It's not a good question What if i take x = y = 2 ....Then c option would work out to be 0 /4 . Nothing in the prompt prevents me from considering x and y to be equal and doing that Option C is not possible as well I think the question should have made it very clear that x is not equal to y The question asks "which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)", not "which of the following could be greater than \(\frac{1}{\sqrt{x+y}}\)". Firstly , i am a huge fan and love the way you help people ...it's amazing Thanks bunuel , and now for the topic I think i have not explained my stance properly ..i am not very happy with the question because must implies true in all cases whereas in the specific case when x and Y are equal positive integers , i don't see the third option to be valid for the question stem anymore Let me explain , Since x and Y are positive integers , i take x = y= 2 ( which i am surely allowed to ) Now , question translates to what is greater than 1 / \sqrt{4} = 1 /2 = 0.5 When the expression c with this numbers translates to 0/(2+2) =0/4 i.e 0 Surely , 0.5 is not greater than 0 . Now, therefore when x and y are same , it is clearly not true . Am i assuming wrong thing's somewhere ?



Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
18 Jun 2015, 00:39
amlan009 wrote: Firstly , i am a huge fan and love the way you help people ...it's amazing Thanks bunuel , and now for the topic I think i have not explained my stance properly ..i am not very happy with the question because must implies true in all cases whereas in the specific case when x and Y are equal positive integers , i don't see the third option to be valid for the question stem anymore
Let me explain , Since x and Y are positive integers , i take x = y= 2 ( which i am surely allowed to ) Now , question translates to what is greater than 1 / \sqrt{4} = 1 /2 = 0.5
When the expression c with this numbers translates to 0/(2+2) =0/4 i.e 0 Surely , 0.5 is not greater than 0 .
Now, therefore when x and y are same , it is clearly not true .
Am i assuming wrong thing's somewhere ? The correct answer to the question is C, which says that only II option must be greater than \(\frac{1}{\sqrt{x}+\sqrt{y}}\). Why are talking about the third option?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Status: It's time...
Joined: 29 Jun 2015
Posts: 7
Location: India
Concentration: Operations, General Management
GPA: 3.59

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
20 Jun 2016, 04:25
Hi Bunuel, Can you please give me the link to a set of these type of problems to practice? Thanks in Advance.
_________________
Perseverance, the answer to all our woes. Amen.



Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
20 Jun 2016, 04:30



Manager
Joined: 14 Jun 2016
Posts: 67
Location: India
WE: Engineering (Manufacturing)

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
29 Aug 2017, 19:24
Hi Bunuel, For option 2, do we need to consider the negative values of of sqrt(x) and sqrt(y) as well? If x is positive sqrt(x) can be positive or negativebut if we take the negative values then option 2 is not working. For ex, I took x=16 & y = 9 & calculated putting the negative values but it didn't work. Please guide me. Thanks.
_________________
If you appreciate my post then please click +1Kudos



Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
29 Aug 2017, 21:02
buan15 wrote: Hi Bunuel,
For option 2, do we need to consider the negative values of of sqrt(x) and sqrt(y) as well? If x is positive sqrt(x) can be positive or negativebut if we take the negative values then option 2 is not working. For ex, I took x=16 & y = 9 & calculated putting the negative values but it didn't work.
Please guide me. Thanks. When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{16}=4\), NOT +4 or 4. Even roots have only a positive value on the GMAT.In contrast, the equation \(x^2=16\) has TWO solutions, +4 and 4. Odd roots have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{64} =4\).
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Aug 2017
Posts: 85
GMAT 1: 570 Q50 V18 GMAT 2: 610 Q49 V24 GMAT 3: 640 Q48 V29

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
29 Aug 2017, 21:43
study wrote: If x and y are positive, which of the following must be greater than \(\frac{1}{\sqrt{x+y}}\)?
1. \(\frac{\sqrt{x+y}}{2x}\)
2. \(\frac{\sqrt{x}+\sqrt{y}}{x+y}\)
3. \(\frac{\sqrt{x}\sqrt{y}}{x+y}\)
(A) None (B) 1 only (C) 2 only (D) 1 and 3 only (E) 2 and 3 only Pick easy substitutions x=2 and y=2 and you will get the answer straight to C
_________________
 Kudos are the only way to tell whether my post is useful.
GMAT PREP 1: Q50 V34  700
Veritas Test 1: Q43 V34  630 Veritas Test 2: Q46 V30  620 Veritas Test 3: Q45 V29  610 Veritas Test 4: Q49 V30  650
GMAT PREP 2: Q50 V34  700
Veritas Test 5: Q47 V33  650 Veritas Test 5: Q46 V33  650



Math Expert
Joined: 02 Sep 2009
Posts: 52294

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
29 Aug 2017, 22:23



Intern
Joined: 20 Sep 2016
Posts: 24

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
22 Oct 2017, 07:38
I used a simple approach of number picking. pick a small number say 2. it will take about 1 minute to eliminate the wrong answers.



Intern
Joined: 09 Sep 2017
Posts: 5

If x and y are positive, which of the following must be
[#permalink]
Show Tags
25 Oct 2017, 10:33
Most Simple Solution:
Keep x = y amd solve the equation



NonHuman User
Joined: 09 Sep 2013
Posts: 9444

Re: If x and y are positive, which of the following must be
[#permalink]
Show Tags
27 Oct 2018, 00:34
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x and y are positive, which of the following must be &nbs
[#permalink]
27 Oct 2018, 00:34



Go to page
Previous
1 2
[ 38 posts ]



