It is currently 19 Oct 2017, 11:34

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

M26-30

  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: 41892

Kudos [?]: 128888 [0], given: 12183

M26-30 [#permalink]

Show Tags

New post 16 Sep 2014, 01:26
Expert's post
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

27% (01:14) correct 73% (01:24) wrong based on 37 sessions

HideShow timer Statistics

If \(x\), \(y\), and \(z\) are positive integers and \(xyz=2,700\). Is \(\sqrt{x}\) an integer?


(1) \(y\) is an even perfect square and \(z\) is an odd perfect cube.

(2) \(\sqrt{z}\) is not an integer.
[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 [?]: 128888 [0], given: 12183

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128888 [0], given: 12183

Re M26-30 [#permalink]

Show Tags

New post 16 Sep 2014, 01:26
Expert's post
1
This post was
BOOKMARKED
Official Solution:


Note: a perfect square, is an integer that can be written as the square of some other integer. For example \(16=4^2\), is a perfect square. Similarly, a perfect cube is an integer that can be written as the cube of some other integer. For example, \(27=3^3\) is a perfect cube.

Make prime factorization of 2,700: \(xyz=2,700=2^2*3^3*5^2\).

(1) \(y\) is an even perfect square and \(z\) is an odd perfect cube. If \(y\) is either \(2^2\) or \(2^2*5^2\) and \(z=3^3= \text{odd perfect square}\) then \(x\) must be a perfect square which makes \(\sqrt{x}\) an integer: \(x=5^2\) or \(x=1\). But if \(z=1^3= \text{odd perfect cube}\) then \(x\) could be \(3^3\) which makes \(\sqrt{x}\) not an integer. Not sufficient.

(2) \(\sqrt{z}\) is not an integer. Clearly insufficient.

(1)+(2) As from (1) \(\sqrt{z} \ne integer\) then \(z \ne 1\), therefore it must be \(3^3\) (from 1), so \(x\) must be a perfect square which makes \(\sqrt{x}\) an integer: \(x=5^2\) or \(x=1\). 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 [?]: 128888 [0], given: 12183

Intern
Intern
avatar
Joined: 11 Aug 2014
Posts: 5

Kudos [?]: 2 [0], given: 31

Re: M26-30 [#permalink]

Show Tags

New post 16 Nov 2014, 00:21
1
This post was
BOOKMARKED
Bunuel wrote:
Official Solution:


Note: a perfect square, is an integer that can be written as the square of some other integer. For example \(16=4^2\), is a perfect square. Similarly, a perfect cube is an integer that can be written as the cube of some other integer. For example, \(27=3^3\) is a perfect cube.

Make prime factorization of 2,700: \(xyz=2,700=2^2*3^3*5^2\).

(1) \(y\) is an even perfect square and \(z\) is an odd perfect cube. If \(y\) is either \(2^2\) or \(2^2*5^2\) and \(z=3^3= \text{odd perfect square}\) then \(x\) must be a perfect square which makes \(\sqrt{x}\) an integer: \(x=5^2\) or \(x=1\). But if \(z=1^3= \text{odd perfect cube}\) then \(x\) could be \(3^3\) which makes \(\sqrt{x}\) not an integer. Not sufficient.

(2) \(\sqrt{z}\) is not an integer. Clearly insufficient.

(1)+(2) As from (1) \(\sqrt{z} \ne integer\) then \(z \ne 1\), therefore it must be \(3^3\) (from 1), so \(x\) must be a perfect square which makes \(\sqrt{x}\) an integer: \(x=5^2\) or \(x=1\). Sufficient.


Answer: C



can you please explain 2) \sqrt{z} is not an integer. Clearly insufficient. and sqrt{z} ne integer then z ne 1

Kudos [?]: 2 [0], given: 31

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128888 [0], given: 12183

Re: M26-30 [#permalink]

Show Tags

New post 16 Nov 2014, 06:06
parameswaranprasad wrote:
Bunuel wrote:
Official Solution:


Note: a perfect square, is an integer that can be written as the square of some other integer. For example \(16=4^2\), is a perfect square. Similarly, a perfect cube is an integer that can be written as the cube of some other integer. For example, \(27=3^3\) is a perfect cube.

Make prime factorization of 2,700: \(xyz=2,700=2^2*3^3*5^2\).

(1) \(y\) is an even perfect square and \(z\) is an odd perfect cube. If \(y\) is either \(2^2\) or \(2^2*5^2\) and \(z=3^3= \text{odd perfect square}\) then \(x\) must be a perfect square which makes \(\sqrt{x}\) an integer: \(x=5^2\) or \(x=1\). But if \(z=1^3= \text{odd perfect cube}\) then \(x\) could be \(3^3\) which makes \(\sqrt{x}\) not an integer. Not sufficient.

(2) \(\sqrt{z}\) is not an integer. Clearly insufficient.

(1)+(2) As from (1) \(\sqrt{z} \ne integer\) then \(z \ne 1\), therefore it must be \(3^3\) (from 1), so \(x\) must be a perfect square which makes \(\sqrt{x}\) an integer: \(x=5^2\) or \(x=1\). Sufficient.


Answer: C



can you please explain 2) \sqrt{z} is not an integer. Clearly insufficient. and sqrt{z} ne integer then z ne 1


\(z \ne 1\) because if it were 1, then \(\sqrt{z}\) would be an integer and that would violate the second statement.
_________________

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 [?]: 128888 [0], given: 12183

Intern
Intern
avatar
Joined: 30 Jun 2012
Posts: 13

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

M26-30 [#permalink]

Show Tags

New post 07 Dec 2014, 16:21
Why is the answer not D) Why is 2) not sufficient, if the square root of Z is not an integer that means that Z must be 3^ 3 and x must be either 5^2 or 2^2 and the square root of either of those number is an integer.

Make prime factorization of 2,700: xyz=2,700=22∗33∗52xyz=2,700=2^2*3^3*5^2.

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

CEO
CEO
User avatar
G
Joined: 17 Jul 2014
Posts: 2604

Kudos [?]: 394 [0], given: 184

Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
M26-30 [#permalink]

Show Tags

New post 07 Dec 2014, 16:57
rsamant wrote:
Why is the answer not D) Why is 2) not sufficient, if the square root of Z is not an integer that means that Z must be 3^ 3 and x must be either 5^2 or 2^2 and the square root of either of those number is an integer.

Make prime factorization of 2,700: xyz=2,700=22∗33∗52xyz=2,700=2^2*3^3*5^2.



would like as well answer to this question.

Kudos [?]: 394 [0], given: 184

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 128888 [0], given: 12183

Re: M26-30 [#permalink]

Show Tags

New post 08 Dec 2014, 05:10
mvictor wrote:
rsamant wrote:
Why is the answer not D) Why is 2) not sufficient, if the square root of Z is not an integer that means that Z must be 3^ 3 and x must be either 5^2 or 2^2 and the square root of either of those number is an integer.

Make prime factorization of 2,700: xyz=2,700=22∗33∗52xyz=2,700=2^2*3^3*5^2.



would like as well answer to this question.


There are other cases possible. For example, z=3, y=2*3*5^2 and x=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

Kudos [?]: 128888 [0], given: 12183

Intern
Intern
avatar
Joined: 23 Apr 2016
Posts: 22

Kudos [?]: 9 [0], given: 39

Location: Finland
Concentration: General Management, International Business
GPA: 3.65
Premium Member
Re: M26-30 [#permalink]

Show Tags

New post 07 Nov 2016, 10:24
Really nice question Bunuel !

Kudos [?]: 9 [0], given: 39

Intern
Intern
avatar
Joined: 04 Jan 2017
Posts: 5

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

CAT Tests
Re: M26-30 [#permalink]

Show Tags

New post 10 Apr 2017, 09:19
Awesome question!

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

Intern
Intern
avatar
B
Joined: 24 Jun 2017
Posts: 15

Kudos [?]: 0 [0], given: 22

CAT Tests
Re: M26-30 [#permalink]

Show Tags

New post 30 Sep 2017, 09:21
Wow what a question! Very difficult without blatantly trying to trick you.

This one took me a while, but I'm very proud to say I got it right!

Kudos [?]: 0 [0], given: 22

Re: M26-30   [#permalink] 30 Sep 2017, 09:21
Display posts from previous: Sort by

M26-30

  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®.