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

It is currently 18 Nov 2018, 21:15

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

M02-13

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
M02-13  [#permalink]

Show Tags

New post 15 Sep 2014, 23:17
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (02:08) correct 30% (02:31) wrong based on 165 sessions

HideShow timer Statistics

\(x\) and \(y\) are positive integers. If \(y = \sqrt{64}\) and \(x^2 - 10x = (-4y^3 + 64y)*\frac{1}{96}\), what is the minimum possible value of \(x\)?

A. 2
B. 4
C. 8
D. 12
E. 16

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re M02-13  [#permalink]

Show Tags

New post 15 Sep 2014, 23:17
Official Solution:

\(x\) and \(y\) are positive integers. If \(y = \sqrt{64}\) and \(x^2 - 10x = (-4y^3 + 64y)*\frac{1}{96}\), what is the minimum possible value of \(x\)?

A. 2
B. 4
C. 8
D. 12
E. 16


We know that \(y = 8\).

Plugging this into the second equation gives:
\(x^2-10x = \frac{-4*8^3 + 8^3}{8*4*3} = \frac{-3*8^3}{8*4*3} = -16\)
\(x^2-10x = -16\)
\(x^2-10x +16 = 0\)
\((x-8)(x-2)=0\)

The possible values of \(x\) are 8 and 2. Therefore the minimum value of \(x\) is 2.


Answer: A
_________________

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

Intern
Intern
avatar
Joined: 04 Sep 2014
Posts: 5
Re: M02-13  [#permalink]

Show Tags

New post 31 Mar 2015, 07:08
Bunel,

I am a bit lost to the answer. what did u do with the 64Y? i see you have x-10x= -4*8^3 + 8^3.
Intern
Intern
avatar
Joined: 29 Jan 2015
Posts: 5
Concentration: Technology, Finance
M02-13  [#permalink]

Show Tags

New post 31 Mar 2015, 08:46
floody84 wrote:
Bunel,

I am a bit lost to the answer. what did u do with the 64Y? i see you have x-10x= -4*8^3 + 8^3.


Steps:
  • \sqrt{64} is 8. That is y=8
  • Insert 8 in quadratic formula and calculate the left hand side
    • Factor 96: 96 = 8*4*3 (denominator of the fraction)
    • Cancel out all possible factors to get -16 for the left hand side
  • Use -16 in quadratic expression to get the roots 8 and 2
  • Solution is 2 because the question asked for the min. value
Current Student
avatar
Joined: 14 Oct 2013
Posts: 45
GMAT ToolKit User
M02-13  [#permalink]

Show Tags

New post Updated on: 22 Apr 2015, 19:38
Couldn't Y also equal -8? I know that when you plug in y=-8 you end up getting x^2 - 10x -16 = 0 which you can't factor out, but I didnt realize that until after I plugged in -8 (I plugged in -8 since we were trying to find the smallest value of X, I figured a negative Y would give us smaller values for X)

Originally posted by healthjunkie on 04 Apr 2015, 10:52.
Last edited by healthjunkie on 22 Apr 2015, 19:38, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: M02-13  [#permalink]

Show Tags

New post 05 Apr 2015, 04:31
2
healthjunkie wrote:
Couldn't Y also equal -8? I know that when you plug in y=-8 you end up getting x^2 - 10x -16 = 0 which you can't factor out, but I didnt realize that until after I plugged in -8 (I plugged in -8 since we were trying to find the smallest value of X, I figured a negative Y would give us smaller values for X)


No.

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).

Theory on Number Properties: math-number-theory-88376.html
Tips on Numper Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59


Hope it helps.
_________________

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

Manager
Manager
User avatar
Joined: 17 Mar 2014
Posts: 228
Location: India
Concentration: Operations, Strategy
GMAT 1: 670 Q48 V35
GPA: 3.19
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: M02-13  [#permalink]

Show Tags

New post 09 Aug 2015, 06:08
Bunuel wrote:
healthjunkie wrote:
Couldn't Y also equal -8? I know that when you plug in y=-8 you end up getting x^2 - 10x -16 = 0 which you can't factor out, but I didnt realize that until after I plugged in -8 (I plugged in -8 since we were trying to find the smallest value of X, I figured a negative Y would give us smaller values for X)


No.

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).

Theory on Number Properties: math-number-theory-88376.html
Tips on Numper Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59


Hope it helps.


Hi Bunuel ,

Please correct me if i amwrong

Does this mean when gmat gives sqare root sign itself in question stem , then it means we should consider only positive root
and on the other hand gmat gave me a quadratic eqaution in question stem and when i solve it i should consider both +ve and - ve root ?

right ?
_________________

Press +1 Kudos if you find this Post helpful :)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: M02-13  [#permalink]

Show Tags

New post 17 Aug 2015, 02:27
adityadon wrote:
Bunuel wrote:
healthjunkie wrote:
Couldn't Y also equal -8? I know that when you plug in y=-8 you end up getting x^2 - 10x -16 = 0 which you can't factor out, but I didnt realize that until after I plugged in -8 (I plugged in -8 since we were trying to find the smallest value of X, I figured a negative Y would give us smaller values for X)


No.

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).

Theory on Number Properties: math-number-theory-88376.html
Tips on Numper Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59


Hope it helps.


Hi Bunuel ,

Please correct me if i amwrong

Does this mean when gmat gives sqare root sign itself in question stem , then it means we should consider only positive root
and on the other hand gmat gave me a quadratic eqaution in question stem and when i solve it i should consider both +ve and - ve root ?

right ?


\(\sqrt{}\) sign always means non-negative root.

In contrast x^2 = 4 gives two solutions: 2 and -2.
_________________

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

Intern
Intern
avatar
Joined: 01 Sep 2016
Posts: 12
GMAT ToolKit User
Re M02-13  [#permalink]

Show Tags

New post 10 Sep 2016, 20:29
I think this is a high-quality question and I agree with explanation.
Intern
Intern
avatar
B
Joined: 25 Jan 2016
Posts: 9
Location: United States (NJ)
GPA: 2.34
WE: Analyst (Commercial Banking)
Re: M02-13  [#permalink]

Show Tags

New post 23 Mar 2017, 16:06
Bunuel wrote:
Official Solution:

\(x\) and \(y\) are positive integers. If \(y = \sqrt{64}\) and \(x^2 - 10x = (-4y^3 + 64y)*\frac{1}{96}\), what is the minimum possible value of \(x\)?

A. 2
B. 4
C. 8
D. 12
E. 16


We know that \(y = 8\).

Plugging this into the second equation gives:
\(x^2-10x = \frac{-4*8^3 + 8^3}{8*4*3} = \frac{-3*8^3}{8*4*3} = -16\)
\(x^2-10x = -16\)
\(x^2-10x +16 = 0\)
\((x-8)(x-2)=0\)

The possible values of \(x\) are 8 and 2. Therefore the minimum value of \(x\) is 2.


Answer: A


How did you get The numerator to -3*8^3? ->>> \(x^2-10x = \frac{-4*8^3 + 8^3}{8*4*3} = \frac{-3*8^3}{8*4*3} = -16\)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: M02-13  [#permalink]

Show Tags

New post 24 Mar 2017, 03:55
Prostar wrote:
Bunuel wrote:
Official Solution:

\(x\) and \(y\) are positive integers. If \(y = \sqrt{64}\) and \(x^2 - 10x = (-4y^3 + 64y)*\frac{1}{96}\), what is the minimum possible value of \(x\)?

A. 2
B. 4
C. 8
D. 12
E. 16


We know that \(y = 8\).

Plugging this into the second equation gives:
\(x^2-10x = \frac{-4*8^3 + 8^3}{8*4*3} = \frac{-3*8^3}{8*4*3} = -16\)
\(x^2-10x = -16\)
\(x^2-10x +16 = 0\)
\((x-8)(x-2)=0\)

The possible values of \(x\) are 8 and 2. Therefore the minimum value of \(x\) is 2.


Answer: A


How did you get The numerator to -3*8^3? ->>> \(x^2-10x = \frac{-4*8^3 + 8^3}{8*4*3} = \frac{-3*8^3}{8*4*3} = -16\)


It's basic manipulation: \(-4*8^3 + 8^3 = 8^3(-4+1) = 3*8^3\). The same way -4x + x = -3x.
_________________

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

GMAT Club Bot
Re: M02-13 &nbs [#permalink] 24 Mar 2017, 03:55
Display posts from previous: Sort by

M02-13

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

Moderators: chetan2u, Bunuel



Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.