It is currently 23 Sep 2017, 15:03

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

M06-34

  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: 41698

Kudos [?]: 124653 [0], given: 12079

M06-34 [#permalink]

Show Tags

New post 16 Sep 2014, 00:33
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (01:33) correct 47% (01:42) wrong based on 129 sessions

HideShow timer Statistics

If \(a\), \(b\), and \(c\) are positive and \(a^2 + c^2 = 202\), what is the value of \(b - a - c\)?


(1) \(b^2 + c^2 = 225\)

(2) \(a^2 + b^2 = 265\)
[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 [?]: 124653 [0], given: 12079

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124653 [0], given: 12079

Re M06-34 [#permalink]

Show Tags

New post 16 Sep 2014, 00:33
Expert's post
1
This post was
BOOKMARKED
Official Solution:


(1) \(b^2+c^2=225\). Not sufficient on its own.

(2) \(a^2+b^2=265\). Not sufficient on its own.

(1)+(2) Subtract \(a^2+c^2=202\) from \(b^2+c^2=225\): \(b^2-a^2=23\).

Now, sum this with \(a^2+b^2=265\): \(2b^2=288\).

So, \(b^2=144\), giving \(b=12\) (since it is given that \(b\) is a positive number). Since \(b=12\), then from \(b^2-a^2=23\) we get that \(a=11\) and from \(a^2+c^2=202\) we get that \(c=9\). Sufficient.


Answer: C
_________________

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 [?]: 124653 [0], given: 12079

Current Student
avatar
Joined: 06 Aug 2014
Posts: 15

Kudos [?]: 16 [0], given: 44

Concentration: Entrepreneurship, Marketing
Schools: ISB '17 (A)
GMAT 1: 720 Q50 V37
GPA: 3.3
Re: M06-34 [#permalink]

Show Tags

New post 23 Sep 2014, 02:01
Hi Bunuel,

In this question, if I take only the first statement and subtract the two equations given we get:-

b^2-a^2=23.
Thus possible values positive values will be- b=12, a=11.
Upon substitution in any of the two equations we get c=9.
Thus can we not answer the question using only statement 1.

Please kindly point out the flaw in this reasoning. Is it because the question does not give us that only integer values are possible?

Kudos [?]: 16 [0], given: 44

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124653 [0], given: 12079

Re: M06-34 [#permalink]

Show Tags

New post 23 Sep 2014, 02:07
madhavmarda wrote:
Hi Bunuel,

In this question, if I take only the first statement and subtract the two equations given we get:-

b^2-a^2=23.
Thus possible values positive values will be- b=12, a=11.
Upon substitution in any of the two equations we get c=9.
Thus can we not answer the question using only statement 1.

Please kindly point out the flaw in this reasoning. Is it because the question does not give us that only integer values are possible?


The problem with your solution is that you assume, with no ground for it, that variables represent integers only. From b^2 - a^2 = 23 you cannot say that b = 12 and a = 11. For example b could be \(\sqrt{24}\) and a could be 1.
_________________

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 [?]: 124653 [0], given: 12079

Intern
Intern
avatar
Joined: 30 Jun 2012
Posts: 13

Kudos [?]: 3 [0], given: 0

M06-34 [#permalink]

Show Tags

New post 29 Nov 2014, 22:25
Tricky question but a good one. -- I also had assumed that B = 12 , A = 11 C = 9.

Kudos [?]: 3 [0], given: 0

Intern
Intern
avatar
Joined: 18 Feb 2015
Posts: 3

Kudos [?]: [0], given: 15

Re: M06-34 [#permalink]

Show Tags

New post 11 Apr 2015, 05:19
From st1, we get b^2-a^2=23=>(b+a)(b-a)=23, now as 23 is prime so (b+a)(b-a)=23*1, only solution b=12 & a=11, from this we can get unique value of c as c is positive.
So statement 1 is sufficient.

Bunuel please let me know where i am wrong.

Kudos [?]: [0], given: 15

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124653 [0], given: 12079

Re: M06-34 [#permalink]

Show Tags

New post 11 Apr 2015, 08:16
goGMAT2015 wrote:
From st1, we get b^2-a^2=23=>(b+a)(b-a)=23, now as 23 is prime so (b+a)(b-a)=23*1, only solution b=12 & a=11, from this we can get unique value of c as c is positive.
So statement 1 is sufficient.

Bunuel please let me know where i am wrong.


Please read the whole thread: m06-183731.html#p1419052
_________________

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 [?]: 124653 [0], given: 12079

Manager
Manager
avatar
Joined: 05 Feb 2015
Posts: 67

Kudos [?]: 43 [0], given: 8

Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: M06-34 [#permalink]

Show Tags

New post 11 Apr 2015, 09:10
good question..I also did the same mistake of assuming the numbers as integers.

Kudos [?]: 43 [0], given: 8

Intern
Intern
avatar
Joined: 09 Sep 2015
Posts: 3

Kudos [?]: [0], given: 1

Re: M06-34 [#permalink]

Show Tags

New post 27 Nov 2015, 16:17
To solve 3 different variables, you need 3 different equations. hence it was simple to identify 'C' as the option. Is the approach correct
? I did this question in less than 30 seconds

Kudos [?]: [0], given: 1

Intern
Intern
avatar
B
Joined: 29 Feb 2016
Posts: 1

Kudos [?]: [0], given: 1

Premium Member
M06-34 [#permalink]

Show Tags

New post 04 Aug 2016, 09:45
(a-b)(a+b)=23 which is a prime. Two numbers can multiple into a prime only when one of the number is itself and the other being 1. how does the solution go around this concept?

Kudos [?]: [0], given: 1

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124653 [0], given: 12079

Re: M06-34 [#permalink]

Show Tags

New post 04 Aug 2016, 10:26

Kudos [?]: 124653 [0], given: 12079

Intern
Intern
avatar
B
Joined: 07 Feb 2016
Posts: 21

Kudos [?]: 1 [0], given: 8

GMAT 1: 650 Q47 V34
GMAT 2: 710 Q48 V39
CAT Tests
Re: M06-34 [#permalink]

Show Tags

New post 18 Apr 2017, 22:24
HK17 wrote:
To solve 3 different variables, you need 3 different equations. hence it was simple to identify 'C' as the option. Is the approach correct
? I did this question in less than 30 seconds


I did it the same way without calculating the individual values. Is there a possiblity that this assumption will not hold?

Kudos [?]: 1 [0], given: 8

Intern
Intern
avatar
B
Joined: 29 Mar 2016
Posts: 1

Kudos [?]: [0], given: 13

Re M06-34 [#permalink]

Show Tags

New post 03 Aug 2017, 23:08
I think this is a high-quality question and I agree with explanation.

Kudos [?]: [0], given: 13

Re M06-34   [#permalink] 03 Aug 2017, 23:08
Display posts from previous: Sort by

M06-34

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

Moderators: Bunuel, Vyshak



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®.