It is currently 11 Dec 2017, 21:45

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

Which of the following expressions can be written as an integer?

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

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 31 Oct 2011
Posts: 337

Kudos [?]: 1272 [0], given: 18

Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 16 May 2012, 17:29
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

75% (00:32) correct 25% (00:32) wrong based on 226 sessions

HideShow timer Statistics

Which of the following expressions can be written as an integer?

1. \((\sqrt{82} + \sqrt{82})^2\)

2. \(82*\sqrt{82}\)

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}\)

A. none
B. 1 only
C. 3 only
D. 1 and 2
E. 1 and 3
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Aug 2017, 03:39, edited 2 times in total.
Edited the question

Kudos [?]: 1272 [0], given: 18

1 KUDOS received
Manager
Manager
User avatar
Affiliations: Project Management Professional (PMP)
Joined: 30 Jun 2011
Posts: 194

Kudos [?]: 84 [1], given: 12

Location: New Delhi, India
Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 17 May 2012, 01:05
1
This post received
KUDOS
eybrj2 wrote:
Which of the following expression can be written as an integer?

1) (\sqrt{82} + \sqrt{82})^2
2) 82*\sqrt{82}
3) \sqrt{82}*\sqrt{82}/82

a. none
b. 1 only
c. 3 only
d. 1 and 2
e. 1 and 3


I doubt OA.


Hi

Option E is correct:

1) (\sqrt{82} + \sqrt{82})^2 = (2*\sqrt{82)^2= 4*82= Integer
2) 82*[square_root]82}= not an integer
3) (\sqrt{82} * \sqrt{82})/82
= 82/82=1= Integer
_________________

Best
Vaibhav

If you found my contribution helpful, please click the +1 Kudos button on the left, Thanks

Kudos [?]: 84 [1], given: 12

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135294 [1], given: 12686

Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 17 May 2012, 01:25
1
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
eybrj2 wrote:
Which of the following expression can be written as an integer?

1. \((\sqrt{82} + \sqrt{82})^2\)

2. \(82*\sqrt{82}\)

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}\)

A. none
B. 1 only
C. 3 only
D. 1 and 2
E. 1 and 3

I doubt OA.


1. \((\sqrt{82} + \sqrt{82})^2=(2\sqrt{82})^2=4*82=integer\)

2. \(82*\sqrt{82}\) --> since \(\sqrt{82}\) is not an integer then \(82*\sqrt{82}\) is not integer either.

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}=\frac{82}{82}=1=integer\).

Answer: E.
_________________

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 [?]: 135294 [1], given: 12686

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14909

Kudos [?]: 287 [0], given: 0

Premium Member
Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 10 Nov 2016, 18:33
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

Kudos [?]: 287 [0], given: 0

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 788

Kudos [?]: 21 [0], given: 275

Premium Member CAT Tests
Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 08 Aug 2017, 03:31
Bunuel wrote:
eybrj2 wrote:
Which of the following expression can be written as an integer?

1. \((\sqrt{82} + \sqrt{82})^2\)

2. \(82*\sqrt{82}\)

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}\)

A. none
B. 1 only
C. 3 only
D. 1 and 2
E. 1 and 3

I doubt OA.


1. \((\sqrt{82} + \sqrt{82})^2=(2\sqrt{82})^2=4*82=integer\)

2. \(82*\sqrt{82}\) --> since \(\sqrt{82}\) is not an integer then \(82*\sqrt{82}\) is not integer either.

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}=\frac{82}{82}=1=integer\).

Answer: E.





Hello Bunuel

Your explanation is to the point but in the official explanation, its mentioned:

82* 82^3/2

82^3= 2^3 *41^3

How did we get this cube?

Kudos [?]: 21 [0], given: 275

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135294 [0], given: 12686

Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 08 Aug 2017, 03:42
Shiv2016 wrote:
Bunuel wrote:
eybrj2 wrote:
Which of the following expression can be written as an integer?

1. \((\sqrt{82} + \sqrt{82})^2\)

2. \(82*\sqrt{82}\)

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}\)

A. none
B. 1 only
C. 3 only
D. 1 and 2
E. 1 and 3

I doubt OA.


1. \((\sqrt{82} + \sqrt{82})^2=(2\sqrt{82})^2=4*82=integer\)

2. \(82*\sqrt{82}\) --> since \(\sqrt{82}\) is not an integer then \(82*\sqrt{82}\) is not integer either.

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}=\frac{82}{82}=1=integer\).

Answer: E.





Hello Bunuel

Your explanation is to the point but in the official explanation, its mentioned:

82* 82^3/2

82^3= 2^3 *41^3

How did we get this cube?


Could you please post a screenshot or post entire solution?
_________________

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 [?]: 135294 [0], given: 12686

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 788

Kudos [?]: 21 [0], given: 275

Premium Member CAT Tests
Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 08 Aug 2017, 03:50
Expression II does not represent an integer because (82)* 82^1/2= 82^3/2 and 82^3= 2^3* 41^3 is not a perfect square. Regarding this last assertion, note that the square of any integer has the property that each of its distinct prime factors is repeated an even number of times.



(Explanation taken from official guide 2017)
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Kudos [?]: 21 [0], given: 275

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135294 [0], given: 12686

Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 08 Aug 2017, 04:00
Shiv2016 wrote:
Expression II does not represent an integer because (82)* 82^1/2= 82^3/2 and 82^3= 2^3* 41^3 is not a perfect square. Regarding this last assertion, note that the square of any integer has the property that each of its distinct prime factors is repeated an even number of times.



(Explanation taken from official guide 2017)


\(82*82^{(\frac{1}{2})}=82^{(1+\frac{1}{2})}=82^{\frac{3}{2}}=\sqrt{82^3}\)
_________________

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 [?]: 135294 [0], given: 12686

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1922

Kudos [?]: 1011 [0], given: 3

Location: United States (CA)
Re: Which of the following expressions can be written as an integer? [#permalink]

Show Tags

New post 10 Aug 2017, 10:48
eybrj2 wrote:
Which of the following expressions can be written as an integer?

1. \((\sqrt{82} + \sqrt{82})^2\)

2. \(82*\sqrt{82}\)

3. \(\frac{\sqrt{82}*\sqrt{82}}{82}\)

A. none
B. 1 only
C. 3 only
D. 1 and 2
E. 1 and 3


Let’s simplify each expression:

1. (√82 + √82)^2

(√82 + √82)^2 = (2√82)^2 = 4 x 82 = 328

We see that this an integer.

2. 82√82

Since √82 is a non-terminating decimal, 82√82 is not an integer.

3. (√82√82)/82

(√82√82)/82 = 82/82 = 1

We see that this is an integer.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1011 [0], given: 3

Re: Which of the following expressions can be written as an integer?   [#permalink] 10 Aug 2017, 10:48
Display posts from previous: Sort by

Which of the following expressions can be written as an integer?

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


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®.