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

It is currently 07 Dec 2019, 09:24
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
CLICK HERE TO HIDE/SHOW EVENTS

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Print view
First unread post
 
  Sort by Date Sort by Kudos  
Search for:
 
PREVIOUS TOPIC
NEXT TOPIC
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59588
CAT Tests
Top Member of the Month
Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 16 Oct 2015, 07:27
11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

79% (00:43) correct 21% (00:44) wrong based on 1062 sessions

HideShow timer Statistics

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

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

II. \(82\sqrt{82}\)

III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III


Kudos for a correct solution.
Spoiler: OA

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2435
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 16 Oct 2015, 07:38
2
1. ( (82)^(1/2) + (82)^(1/2) )^2
= ( 2 *(82)^(1/2))^2
= 4 * 82
= 328
Integer

2. 82 (82)^(1/2)
can't be written as an integer as 82 is not a perfect square .

3. ((82)^(1/2) * (82)^(1/2) )/82
= 1
Integer

Answer E
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Signature Read More
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2492
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 16 Oct 2015, 08:47
2
1st:

[SQRT(82) + SQRT(82)]^2

we have formula (a+b)^2 = a^2 +b^2 +2ab
we can rewrite the first statement as 82+82 + 2*[SQRT(82)*SQRT(82)]
[SQRT(82)*SQRT(82)] this is equal to 82. we get an integer.

We can eliminate
(A) None
(C) III only

Statement II:
82*sqrt(82)
we know that 82 is not a perfect square, thus, it is not an integer. Statement II will not yield an integer.
We can eliminate:

(D) I and II


Statement III:
[sqrt(82) * sqrt (82)]/82
sqrt(82) multiplied by itself will result in 82. 82 divide by 82, and get 1. This is an integer.

Eliminate answer choice B, and the only answer choice left, the correct one is E.
Manager
Manager
avatar
P
Joined: 01 Mar 2015
Posts: 68
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 16 Oct 2015, 09:35
4
Bunuel wrote:
Which of the following expressions can be written as an integer?

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

II. \(82\sqrt{82}\)

III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III


I. \((\sqrt{82} + \sqrt{82})^2\)
= \((2\sqrt{82})^2\)
= 4 * 82 = 328 integer

2. \(82\sqrt{82}\)
cannot be expressed as integer

3. \(\frac{\sqrt{82}\sqrt{82}}{82}\)
= 82/82
= 1, which is integer

Answer option E
Intern
Intern
avatar
Joined: 02 Oct 2015
Posts: 11
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 16 Oct 2015, 12:07
1
l can be written as (2√82)^2 ..a integer
lll will equal to 1 so Option E is correct answer.
Manager
Manager
User avatar
Joined: 10 Aug 2015
Posts: 54
Concentration: General Management, Entrepreneurship
Schools: Wharton '18 (D), LBS '18 (M), Insead July'17 (A)
GMAT 1: 730 Q48 V42
GMAT ToolKit User Reviews Badge
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 17 Oct 2015, 11:56
1
I. We use the identity (a+b)^2 = a^2+2ab+b^2 which gives us:
82 + (2*\(\sqrt{82}\)*\(\sqrt{82}\)) + 82
Since \(\sqrt{82}\)*\(\sqrt{82}\) equals 82 this will yield an integer.

II. No since \(\sqrt{82}\) is not a perfect square and you cannot separate it either into to two perfect squares.


III. Since \(\sqrt{82}\)*\(\sqrt{82}\) equals 82 this will yield an integer : 82/82=1


Answer E : I and III only
Director
Director
User avatar
P
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 715
Location: United States (CA)
Age: 40
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 10 May 2016, 17:57
4
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-10 at 5.49.00 PM.png
Screen Shot 2016-05-10 at 5.49.00 PM.png [ 153.51 KiB | Viewed 11982 times ]


_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching worldwide since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V.

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y7knw7bt Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu (I do not respond to PMs on GMAT Club) or find me on reddit: http://www.reddit.com/r/GMATpreparation
Signature Read More
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2548
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 11 Nov 2016, 14:00
lets see the options =>
Option 1=> (2√82)^2=> 4*82 => integer
Option 2 => 82√82 => non integer
Option 3 => √82*√82 / 82 => 82/82=> 1 , which is off course an integer.
Hence E
_________________
Give me a hell yeah ...!!!!!

MBA Recruiting:- EMPLOYMENT AND SALARY STATISTICS AT TOP B-SCHOOLS IN THE US! (2018)
MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!
The MOST AFFORDABLE MBA programs!
STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)
AVERAGE GRE Scores At The Top Business Schools!
Signature Read More
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4125
Location: Canada
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 11 Nov 2016, 14:59
Top Contributor
Bunuel wrote:
Which of the following expressions can be written as an integer?

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

II. \(82\sqrt{82}\)

III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III


We'll use the fact that (√82)(√82) = 82

I. (√82 + √82)² = (2√82)² = (2√82)(2√82) = (2)(2)(√82)(√82) = (4)(82) = some integer
II. Doesn't look like it could be an integer. I'm not sure, so I'll move onto to statement III
III. (√82)(√82)/82 = 82/82 = 1

NOTE: As we check each statement, we should also check the answer choices.
Since I and III both work, the correct answer must be E, since there's no option for all 3 to be true.

Answer:
Spoiler: ::
E


RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
Signature Read More
Manager
Manager
User avatar
S
Status: On a 600-long battle
Joined: 22 Apr 2016
Posts: 136
Location: Hungary
Concentration: Accounting, Leadership
Schools: Erasmus '19
GMAT 1: 410 Q18 V27
GMAT 2: 490 Q35 V23
GMAT ToolKit User
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 23 Mar 2017, 23:16
i. \({ \left( \sqrt { 82 } +\sqrt { 82 } \right) }^{ 2 }=\left( 2\sqrt { 82 } \right) ^{ 2 }\Rightarrow\) At this moment you already know you have an integer without further calculations.

ii. \(82\sqrt { 82 } \Rightarrow\) We also know that perfect squares don't end in 2, 3, 7 or 8. So, rule this one out as this product won't yield an integer.

iii. \(\cfrac { \sqrt { 82 } \sqrt { 82 } }{ 82 } =\quad \cfrac { \sqrt { 82\ast 82 } }{ 82 } =\cfrac { \sqrt { { 2 }^{ 2 }\ast { 41 }^{ 2 } } }{ 2\ast { 41 } } =\cfrac { 2\ast 41 }{ 2\ast 41 } =\quad 1\quad \Rightarrow \quad integer\)

OA
Spoiler: ::
E

_________________
"When the going gets tough, the tough gets going!"

|Welcoming tips/suggestions/advices (you name it) to help me achieve a 600|
Signature Read More
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8622
Location: United States (CA)
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 27 Mar 2017, 17:26
1
Bunuel wrote:
Which of the following expressions can be written as an integer?

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

II. \(82\sqrt{82}\)

III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III



Let’s simplify each Roman numeral:

I. (√82 + √82)^2

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

We see that this an integer.

II. 82√82

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

III. (√82√82)/82

(√82√82)/82 = 82/82 = 1

We see that this is an integer.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Signature Read More
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1876
Location: India
Schools: HBS '22, Wharton '22, CBS '22
Premium Member Reviews Badge CAT Tests
Re: Which of the following expressions can be written as an integer?  [#permalink]

Show Tags

New post 14 Sep 2019, 00:04
Bunuel wrote:
Which of the following expressions can be written as an integer?

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

II. \(82\sqrt{82}\)

III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III


Kudos for a correct solution.


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

I. \((\sqrt{82} + \sqrt{82})^2\)
82 + 82 + 2*82 = 4*82 = 328
INTEGER

II. \(82\sqrt{82}\)
82 * \sqrt{82}
9<\sqrt{82}<10 and is NOT an integer
NOT AN INTEGER

III. \(\frac{\sqrt{82}\sqrt{82}}{82}\)
82/82 = 1
INTEGER

IMO E
GMAT Club Bot
Re: Which of the following expressions can be written as an integer?   [#permalink] 14 Sep 2019, 00:04
Print view
First unread post
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  
Search for:
PREVIOUS TOPIC
NEXT TOPIC





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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions