Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Aug 2014, 11:42

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

GMAT Diagnostic Test Question 3

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Expert Post
7 KUDOS received
Founder
Founder
User avatar
Affiliations: UA-1K, SPG-G, HH-D
Joined: 04 Dec 2002
Posts: 12079
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2231

Kudos [?]: 8336 [7] , given: 3643

GMAT ToolKit User Premium Member CAT Tests
GMAT Diagnostic Test Question 3 [#permalink] New post 06 Jun 2009, 18:33
7
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

37% (01:53) correct 63% (00:54) wrong based on 592 sessions
GMAT Diagnostic Test Question 3
Field: Arithmetic, Roots
Difficulty: 700


If x is a positive number and \sqrt{x} * x - x = a, which of the following must be true?

I. a is Even
II. a is Positive
III. a is an Integer

A. I only
B. II only
C. III only
D. I and II
E. None of the above
[Reveal] Spoiler: OA

_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Have a blog? Feature it on GMAT Club!

Get the best GMAT Prep Resources with GMAT Club Premium Membership


Last edited by Bunuel on 06 Oct 2013, 23:04, edited 3 times in total.
Edited the stem and difficulty.
Kaplan Promo CodeKnewton GMAT Discount CodesGMAT Pill GMAT Discount Codes
Expert Post
4 KUDOS received
Founder
Founder
User avatar
Affiliations: UA-1K, SPG-G, HH-D
Joined: 04 Dec 2002
Posts: 12079
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2231

Kudos [?]: 8336 [4] , given: 3643

GMAT ToolKit User Premium Member CAT Tests
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 06 Jun 2009, 18:35
4
This post received
KUDOS
Expert's post
Explanation:
Official Answer: E

Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

If x=\frac{1}{4} then a=\sqrt{x} * x - x=\frac{1}{2}*\frac{1}{4}-\frac{1}{4}=-\frac{1}{8}. Now, -\frac{1}{8} is not an integer at all (hence not even) and also not positive, so none of the options MUST be true.

Answer: E.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Have a blog? Feature it on GMAT Club!

Get the best GMAT Prep Resources with GMAT Club Premium Membership


Last edited by bb on 28 Sep 2013, 10:34, edited 1 time in total.
Updated
1 KUDOS received
CIO
CIO
avatar
Joined: 02 Oct 2007
Posts: 1218
Followers: 87

Kudos [?]: 656 [1] , given: 334

GMAT ToolKit User GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 12 Aug 2009, 01:07
1
This post received
KUDOS
Good one, +1.
trangpham wrote:
I think the correct answer is "E" because if x=1, a=0 and 0 is not a positive.
If x=2, \sqrt{2} - 1 is not a integer or even.

ihero06, you seem to forget about x=0. If x=0, a is not positive. The question asks "which of the following must be true", meaning for all possible x. You're right that GMAT doesn't cover negative numbers under the radical sign. We have to remember that 0 is neither positive nor negative.

I've updated the OE a bit. Hopefully it's better now.
_________________

Welcome to GMAT Club! :)
Facebook TwitterGoogle+LinkedIn
Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Intern
Intern
avatar
Joined: 19 Dec 2009
Posts: 37
Followers: 0

Kudos [?]: 10 [1] , given: 8

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 19 Dec 2009, 14:45
1
This post received
KUDOS
I found the key to this question is "must be true" clause.

Meaning if we can prove that a could be a non-Integer (i.e. x = 2) or 0 then we rule out all answers but E.

Good question!
Intern
Intern
avatar
Joined: 04 Aug 2009
Posts: 1
Followers: 0

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

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 04 Aug 2009, 13:01
I think the answer could be B (II -- a is positive) if we consider sqrt of 2 and 3 as irrational (or sqrt of any other prime number).

or D (I and II -- a is positive and even). Anyway, I feel that the specification of x is not fully given.

The Q is
\sqrt{x}*x - x = a

and x is an integer.

If x is -ve, then we have an equation contains sqrt of negative integer- which is not covered in GMAT. So let's rule out -ve integer. If x is -ve, then the answer is "E- none of the above"

If x is positive then:
If x is even (E), then
SQRT(E)*E is even and E-E is also even. and so a is even and it is positive.

x= 2 then 2*sqrt(2)-2 = not integer, but if we consider sqrt (2) as an irrational number then a has to be positive.
x= 16 then 16*sqrt(16)-16 = 16*4-16 = 48 - +ve and even.

If x is odd (O), then
SQRT(O)*O is odd and O-O is even. So a is even and again it is positive.
x=3, then 3*sqrt(3)-3 = not integer, but a has to be positive again {sqrt (3) is irrational}.
x=9, then 9*sqrt(9)-9 = 18 --> +ve and even.

So if one considers sqrt of 2 and 3 are irrational numbers then we can have choice B (a is positive).
Otherwise, among the choices the answer is D (I & II - i.e. a is even and positive).

Let me know whether I am correct or not.
Intern
Intern
avatar
Joined: 01 Jul 2009
Posts: 3
Followers: 0

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

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 10 Aug 2009, 18:04
I think the correct answer is "E" because if x=1, a=0 and 0 is not a positive.
If x=2, \sqrt{2} - 1 is not a integer or even.
Manager
Manager
avatar
Joined: 02 Oct 2009
Posts: 93
Followers: 1

Kudos [?]: 4 [0], given: 2

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 16 Oct 2009, 04:48
Should we rule out the possibilty of X != -1 if it is not explicitly mentioned here?
What is the final answer..I will go with E..
CIO
CIO
avatar
Joined: 02 Oct 2007
Posts: 1218
Followers: 87

Kudos [?]: 656 [0], given: 334

GMAT ToolKit User GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 16 Oct 2009, 09:00
The answer is E. It's stated in the second post.
KocharRohit wrote:
Should we rule out the possibilty of X != -1 if it is not explicitly mentioned here?
What is the final answer..I will go with E..

_________________

Welcome to GMAT Club! :)
Facebook TwitterGoogle+LinkedIn
Want to solve GMAT questions on the go? GMAT Club iPhone app will help.
Please read this before posting in GMAT Club Tests forum
Result correlation between real GMAT and GMAT Club Tests
Are GMAT Club Test sets ordered in any way?

Take 15 free tests with questions from GMAT Club, Knewton, Manhattan GMAT, and Veritas.

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 12 Oct 2009
Posts: 84
Followers: 1

Kudos [?]: 10 [0], given: 1

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 18 Oct 2009, 06:33
As stated by the founder, the key of this question is to show that a is not an integer, if so, a non integer number can not be even nor odd and therefore one is left to prove whether a is positive or negative. Since 0 is and integer and mathematically speaking it has not sign convention i.e. zero has no distance, then given that in this case a = 0, and one can not tell what the sign of a is, then the right answer must be E.
Manager
Manager
avatar
Joined: 24 Jul 2009
Posts: 193
Location: Anchorage, AK
Schools: Mellon, USC, MIT, UCLA, NSCU
Followers: 4

Kudos [?]: 22 [0], given: 10

GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 11 Jan 2010, 21:00
bb wrote:
Explanation:
Rating:

Official Answer: E

If we prove that a is not an integer for any x, we'll be able to rule out A, C, and D. \sqrt{x} * x - x = a can be rewritten as x(\sqrt{x}-1)=a. If x=2 the expression turns into 2(\sqrt{2}-1)=a. It's clear that a is not an integer as (\sqrt{2}-1) is not an integer. Now we need to prove that a is not necessarily positive. If x=0, the equation turns 0=a. 0 is neither positive, nor negative. We're left with E as the answer.


Thanks for the explanation. Got correct answer but did more work than necessary. 1) Didn't rephrase; 2) plugged in 0, 1, 4, and 3. Had I just plugged in 2 and 0 (with the intention of ruling out answer choices), would have gotten to E much faster. Didn't spend a lot of time on it. Nonetheless, my goal should be to get the correct answer as quickly as possible.
_________________

Reward wisdom with kudos. ;)

Intern
Intern
avatar
Joined: 31 Aug 2009
Posts: 17
Schools: University of Warwick
Followers: 0

Kudos [?]: 18 [0], given: 3

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 16 Feb 2010, 06:38
LUGO wrote:
As stated by the founder, the key of this question is to show that a is not an integer, if so, a non integer number can not be even nor odd and therefore one is left to prove whether a is positive or negative. Since 0 is and integer and mathematically speaking it has not sign convention i.e. zero has no distance, then given that in this case a = 0, and one can not tell what the sign of a is, then the right answer must be E.


i always thought zero was positive...since it was 1 less than "1"
anyhow...thanks for this note.
Director
Director
avatar
Joined: 21 Dec 2009
Posts: 588
Concentration: Entrepreneurship, Finance
Followers: 15

Kudos [?]: 249 [0], given: 20

GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 02 Apr 2010, 03:42
1st I factorized: x(\sqrt{x} - 1) = a
the stem did not specified whether x is +ve /-ve; odd or even integer.
\sqrt{9} - 1 => even; but \sqrt{1/9) - 1 = 1/3 - 1 = -2/3
=> the result could be either even, rational, or -ve. So, I, II & III out.
Hence, E.
_________________

KUDOS me if you feel my contribution has helped you.

Forum Moderator
Forum Moderator
User avatar
Status: doing good things...
Joined: 02 Jul 2009
Posts: 1233
Concentration: Entrepreneurship, Finance
GMAT 1: Q V
GMAT 2: 690 Q49 V35
GPA: 3.77
WE: Corporate Finance (Other)
Followers: 152

Kudos [?]: 500 [0], given: 527

GMAT ToolKit User GMAT Tests User Premium Member Reviews Badge
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 23 Apr 2010, 08:25
What if x=25 or x=36 ?
than : 25*(5-1)=100 - even
36*(6-1)=180 - even

based on these examples I have been lured away.
_________________

Follow me, if you find my explanations useful.

Audaces fortuna juvat!

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 09 Feb 2011
Posts: 1
Followers: 0

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

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 09 Feb 2011, 04:03
I think the best solution is :

if u notice in the question it is written that x is an integer i.e it can have any value from minus infinity to plus infinity.
now if we take x as a negative number (for ex : -5)then the solution turns out be
a=-5*sqrt(-5)+(-5)

we allknow that sqrt of -ve number is an imaginary value which can neither be positive ,nor even nor an integer.

Artabandhu(Its my first post feel free to post comments)
Manager
Manager
avatar
Joined: 16 Mar 2011
Posts: 179
Followers: 1

Kudos [?]: 21 [0], given: 13

GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 24 May 2011, 13:39
Is it also possible to solve this one without factoring? \sqrt{x} * x - x = a and say for every x you put in you'd have to multiply it with zero thus making the outcome none of the one mentioned in the answers? :S
Intern
Intern
avatar
Joined: 27 Sep 2011
Posts: 2
Followers: 0

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

Re: GMAT Diagnostic Test Question 3 [#permalink] New post 28 Sep 2011, 10:27
if x = 4 we get sqrt of 4 x 4 - 4 = 2 x 4 - 4 = 8 - 4 = 4. Which is positive, even and an integer. Am i missing something? I saw you guys trying it with 2 and 3 and 0, but when you try it with an integer that has a sqrt root then you dont get this answer... can SOME PLEASE ASSIST?
Expert Post
Founder
Founder
User avatar
Affiliations: UA-1K, SPG-G, HH-D
Joined: 04 Dec 2002
Posts: 12079
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
WE: Information Technology (Hospitality and Tourism)
Followers: 2231

Kudos [?]: 8336 [0], given: 3643

GMAT ToolKit User Premium Member CAT Tests
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 28 Sep 2011, 10:33
Expert's post
Djdieg007 wrote:
if x = 4 we get sqrt of 4 x 4 - 4 = 2 x 4 - 4 = 8 - 4 = 4. Which is positive, even and an integer. Am i missing something? I saw you guys trying it with 2 and 3 and 0, but when you try it with an integer that has a sqrt root then you dont get this answer... can SOME PLEASE ASSIST?



The answer has to work in 100% of the situation, so even though 4 works, the equation does not work with others, and therefore, the answer is E. You have to try multiple numbers and if even one of them works, it is out.
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

Have a blog? Feature it on GMAT Club!

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 01 Nov 2010
Posts: 194
Location: India
Concentration: Technology, Marketing
GMAT Date: 08-27-2012
GPA: 3.8
WE: Marketing (Manufacturing)
Followers: 5

Kudos [?]: 20 [0], given: 28

GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 29 Sep 2011, 20:45
Djdieg007 wrote:
if x = 4 we get sqrt of 4 x 4 - 4 = 2 x 4 - 4 = 8 - 4 = 4. Which is positive, even and an integer. Am i missing something? I saw you guys trying it with 2 and 3 and 0, but when you try it with an integer that has a sqrt root then you dont get this answer... can SOME PLEASE ASSIST?



HERE, you have considered only one case.

answer should fulfill all the case.
Consider X= 2 , 8 ,10, all are even but for these values, a is neither odd nor Even. a is not even an integer.
same is applicable if you consider X = 2,3,5,6,7,8,10,11,12,13,14,15....
you can generalize it by saying that any value of X, which is not perfect square irrespective of odd or even , will yield a as decimal form (not Integer).

So, the Ans is E.

Hope it ll help.
you can post here still you have any doubt.
_________________

kudos me if you like my post.

Attitude determine everything.
all the best and God bless you.

Intern
Intern
avatar
Joined: 24 May 2010
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 6

GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 04 Oct 2011, 04:48
bb wrote:
GMAT Diagnostic Test Question 3
Field: Arithmetic, Roots
Difficulty: 700-750
Rating:



If x is an integer and \sqrt{x} * x - x = a , which of the following must be true?
I. a is Even
II. a is Positive
III. a is an Integer

A. I only
B. II only
C. III only
D. I and II
E. None of the above


x (\sqrt{x} -1) = a

I. a is even when X= 9, but a is fraction when X=5 (say, 5 (\sqrt{5} -1). So no
II. a is positive when X=9, but a is "0" when X=1. so no
III. a is not an integer when X=5. so no

E is my pick.
Manager
Manager
avatar
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 19 [0], given: 1

GMAT Tests User
Re: GMAT Diagnostic Test Question 3 [#permalink] New post 28 Oct 2011, 21:38
Take x=1 => 1\sqrt{1}-1=0

Since 0 is neither +ve nor -ve so option b is out.

now take x=2 => 2\sqrt{2}-2 => neither an integer nor an even.

So ans=E
Re: GMAT Diagnostic Test Question 3   [#permalink] 28 Oct 2011, 21:38
    Similar topics Author Replies Last post
Similar
Topics:
19 Experts publish their posts in the topic GMAT Diagnostic Test Question 13 bb 23 06 Jun 2009, 21:14
18 Experts publish their posts in the topic GMAT Diagnostic Test Question 10 bb 45 06 Jun 2009, 21:04
7 Experts publish their posts in the topic GMAT Diagnostic Test Question 6 bb 30 06 Jun 2009, 20:39
7 Experts publish their posts in the topic GMAT Diagnostic Test Question 2 bb 26 06 Jun 2009, 18:03
27 Experts publish their posts in the topic GMAT Diagnostic Test Question 1 bb 30 05 Jun 2009, 21:30
Display posts from previous: Sort by

GMAT Diagnostic Test Question 3

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 34 posts ] 

Moderators: Bunuel, WoundedTiger



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.