It is currently 15 Dec 2017, 21:36

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

S96-14

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135771 [0], given: 12708

S96-14 [#permalink]

Show Tags

New post 16 Sep 2014, 00:51
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:54) correct 31% (02:54) wrong based on 29 sessions

HideShow timer Statistics

The harmonic mean of two numbers \(x\) and \(y\), symbolized as \(h(x, y)\), is defined as 2 divided by the sum of the reciprocals of \(x\) and \(y\), whereas the geometric mean \(g(x, y)\) is defined as the square root of the product of \(x\) and \(y\) (when this square root exists), and the arithmetic mean \(m(x, y)\) is defined as \(\frac{x + y}{2}\). For which of the following pairs of values for \(x\) and \(y\) is \(g(x, y)\) equal to the arithmetic mean of \(h(x, y)\) and \(m(x, y)\)?

A. \(x = -2\), \(y = -1\)
B. \(x = -1\), \(y = 2\)
C. \(x = 2\), \(y = 8\)
D. \(x = 8\), \(y = 8\)
E. \(x = 8\), \(y = 64\)
[Reveal] Spoiler: OA

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135771 [0], given: 12708

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135771 [0], given: 12708

Re S96-14 [#permalink]

Show Tags

New post 16 Sep 2014, 00:51
Official Solution:

The harmonic mean of two numbers \(x\) and \(y\), symbolized as \(h(x, y)\), is defined as 2 divided by the sum of the reciprocals of \(x\) and \(y\), whereas the geometric mean \(g(x, y)\) is defined as the square root of the product of \(x\) and \(y\) (when this square root exists), and the arithmetic mean \(m(x, y)\) is defined as \(\frac{x + y}{2}\). For which of the following pairs of values for \(x\) and \(y\) is \(g(x, y)\) equal to the arithmetic mean of \(h(x, y)\) and \(m(x, y)\)?

A. \(x = -2\), \(y = -1\)
B. \(x = -1\), \(y = 2\)
C. \(x = 2\), \(y = 8\)
D. \(x = 8\), \(y = 8\)
E. \(x = 8\), \(y = 64\)


We should be organized as we try to make sense of all the given definitions. First, translate the definitions into algebraic symbols:
\(h(x, y) = \frac{2}{\frac{1}{x} + \frac{1}{y}}\)
\(g(x, y) = \sqrt{xy}\)

\(m(x, y)\) is the normal arithmetic mean, \(\frac{x + y}{2}\)

Now, we are asked for a special pair of values for which the following is true: once we calculate these three means, we'll find that \(g\) is the normal average (arithmetic mean) of \(h\) and \(m\). This seems like a lot of work, so we should look for a shortcut. One way is to look among the answer choices for "easy" pairs, for which \(h\), \(g\), and \(m\) are easy to calculate. We should also recognize that the question's statement can only be true for one pair; it must be different from the others, so if we spot two easy pairs, we should first compute \(h\), \(g\), and \(m\) for the "more different-looking" of the two candidate pairs. Scanning the answer choices, looking for an easy pair to calculate, our eye should be drawn to (D), since the two values are equal. If both \(x\) and \(y\) equal 8, then \(m\) is super easy to calculate: \(m\) also equals 8. Let's now figure out \(g\) and \(h\). Since \(g\) is defined as the square root of \(xy\), in this case \(g\) equals the square root of 64, so \(g = 8\) as well. Finally, \(h\) equals \(\frac{2}{\frac{1}{8} + \frac{1}{8}} = \frac{2}{\frac{2}{8}} = 8\). The arithmetic mean of \(h\) (= 8) and \(m\) (= 8) is also 8, which equals \(g\). We can stop right now: there can only be one right answer.


Answer: D
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135771 [0], given: 12708

Intern
Intern
avatar
B
Joined: 31 Dec 2012
Posts: 12

Kudos [?]: 2 [0], given: 135

S96-14 [#permalink]

Show Tags

New post 05 Jul 2017, 07:49
We can summarise that if X=Y , then Harmonic mean, arithmetic mean and geometric mean will be X or Y.

Kudos [?]: 2 [0], given: 135

Intern
Intern
User avatar
B
Joined: 26 Jun 2016
Posts: 24

Kudos [?]: 5 [0], given: 275

Location: Viet Nam
Concentration: Finance, Entrepreneurship
Schools: Insead Sept'18
GMAT 1: 580 Q48 V23
GPA: 3.25
S96-14 [#permalink]

Show Tags

New post 22 Nov 2017, 19:56
Another way is finding the relation between x & y:

g(x,y) = m(x,y)
-> square both sides we have: \(xy = (x+y)^2/4\)
-> \(4xy = x^2+y^2 + 2xy\)
-> \(x^2+y^2-2xy = 0\)
->\((x-y)^2 = 0\)
-> \(x=y\)

-> answer D

Kudos [?]: 5 [0], given: 275

S96-14   [#permalink] 22 Nov 2017, 19:56
Display posts from previous: Sort by

S96-14

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.