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

It is currently 20 Oct 2014, 03:49

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

If x^2 = y + 5 , y = z - 2 and z = 2x , is x^3 + y^2 + z

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2008
Posts: 273
Followers: 3

Kudos [?]: 56 [1] , given: 22

If x^2 = y + 5 , y = z - 2 and z = 2x , is x^3 + y^2 + z [#permalink] New post 13 Jun 2010, 08:11
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

42% (02:39) correct 58% (01:59) wrong based on 362 sessions
If x^2 = y + 5 , y = z - 2 and z = 2x , is x^3 + y^2 + z divisible by 7?

(1) x \gt 0
(2) y = 4
[Reveal] Spoiler: OA
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23331
Followers: 3599

Kudos [?]: 28590 [7] , given: 2803

Re: Divisibility by 7 [#permalink] New post 13 Jun 2010, 08:33
7
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
study wrote:
If x^2 = y + 5, y = z - 2 and z = 2x, is x^3 + y^2 + z divisible by 7?

1. x \gt 0
2. y = 4


We have system of equations with three distinct equations and three unknowns, so we can solve it. As x is squared we'll get two values for it and also two values for y and z: two triplets. Hence we'll get two values for x^3 + y^2 + z, one divisible by 7 and another not divisible by 7. Each statement is giving us the info to decide which triplet is right, thus both statement are sufficient on its own.

Given:
x^2 = y + 5
y = z - 2 --> y=2x-2.
z = 2x

x^2 =2x-2+ 5 --> x^2-2x-3=0 --> x=3 or x=-1

x=3, y=4, z=6 - first triplet --> x^3 + y^2 + z=27+16+6=49, divisible by 7;
x=-1, y=-4, z=-2 - second triplet --> x^3 + y^2 + z=-1+16-2=13, not divisible by 7.

(1) x \gt 0 --> we deal with first triplet. x^3 + y^2 + z=27+16+6=49, divisible by 7. sufficient.
(2) y = 4 --> --> we deal with first triplet. x^3 + y^2 + z=27+16+6=49, divisible by 7. sufficient.

Answer: D.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2008
Posts: 273
Followers: 3

Kudos [?]: 56 [0], given: 22

Re: Divisibility by 7 [#permalink] New post 13 Jun 2010, 09:04
excellent explanation..thanks. kudos
Intern
Intern
avatar
Joined: 10 Jun 2010
Posts: 46
Followers: 0

Kudos [?]: 10 [0], given: 2

Re: Divisibility by 7 [#permalink] New post 21 Jul 2010, 08:21
shouldn't the answer be B? when x=1 or x=2, the answer is not divisible by 7, while when x=3, it is. Hence A is insufficient.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23331
Followers: 3599

Kudos [?]: 28590 [0], given: 2803

Re: Divisibility by 7 [#permalink] New post 21 Jul 2010, 08:33
Expert's post
anandnat wrote:
shouldn't the answer be B? when x=1 or x=2, the answer is not divisible by 7, while when x=3, it is. Hence A is insufficient.


Pleas read the solution above.

What are the values of z and y when x=1 or x=2? What is the value of x^3+y^2+z when x=1 or x=2?

x=1 and x=2 do not satisfy the system of equations given in the stem, hence are not the valid solutions for x.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Director
Director
avatar
Joined: 28 Jul 2011
Posts: 582
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1

Kudos [?]: 53 [0], given: 16

Arithmetic [#permalink] New post 07 Jan 2012, 02:10
Can anyone help me in solving the below problem in 2 min
Attachments

Arithmetic.jpg
Arithmetic.jpg [ 72 KiB | Viewed 4404 times ]


_________________

+1 Kudos If found helpful..

1 KUDOS received
Manager
Manager
avatar
Status: Meh, I can't take the GMAT before 2017.
Joined: 20 Aug 2011
Posts: 152
Followers: 3

Kudos [?]: 67 [1] , given: 0

Re: Arithmetic [#permalink] New post 07 Jan 2012, 02:37
1
This post received
KUDOS
X^2=Y+5
Y=Z-2=2X-2
Z=2X

X^2=2X=3
X^2-2X-3=0
X=3, -1
Y=4,-4
Z=6,-2
X^3+Y^2+Z

1.
X>0
X=3, Y=4, Z=6
X^3+Y^2+Z= Some value we don't care about but can determine whether or not the value is divisible by 7.

Sufficient

2.
y=4, X=3, Z=6
X^3+Y^2+Z= Some value we don't care about but can determine whether or not the value is divisible by 7.

Sufficient

Hence D
_________________

Hit kudos if my post helps you.
You may send me a PM if you have any doubts about my solution or GMAT problems in general.

Director
Director
avatar
Joined: 28 Jul 2011
Posts: 582
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1

Kudos [?]: 53 [0], given: 16

Re: Arithmetic [#permalink] New post 07 Jan 2012, 02:52
blink005 wrote:
X^2=Y+5
Y=Z-2=2X-2
Z=2X

X^2=2X=3
X^2-2X-3=0
X=3, -1
Y=4,-4
Z=6,-2
X^3+Y^2+Z

1.
X>0
X=3, Y=4, Z=6
X^3+Y^2+Z= Some value we don't care about but can determine whether or not the value is divisible by 7.

Sufficient

2.
y=4, X=3, Z=6
X^3+Y^2+Z= Some value we don't care about but can determine whether or not the value is divisible by 7.

Sufficient

Hence D


Thanks i made things complex........
_________________

+1 Kudos If found helpful..

Manager
Manager
User avatar
Joined: 29 Jul 2011
Posts: 111
Location: United States
Followers: 3

Kudos [?]: 36 [0], given: 6

Re: Arithmetic [#permalink] New post 07 Jan 2012, 14:39
Rephrase the stem:
x^2 = y + 5
x^2 - y + 5 = 0
x^2 -(z-2) + 5 = 0
x^2 - z - 3 = 0
x^2 - 2x - 3 = 0
x = 3, -1
Substituting gives z = 6, -2 and y = 4, -4

Notice that both statements ask for same information, that is 1) x>0 -> x=3 and corresponding y=4 and z=6. 2) y=4 means x=3 and z=6

Substituting these values in the stem gives us 51, which is not div by 7. So, both suff.

D
_________________

I am the master of my fate. I am the captain of my soul.
Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution.
PS - Always look at the answers first
CR - Read the question stem first, hunt for conclusion
SC - Meaning first, Grammar second
RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2782
Followers: 206

Kudos [?]: 42 [0], given: 0

Premium Member
Re: If x^2 = y + 5 , y = z - 2 and z = 2x , is x^3 + y^2 + z [#permalink] New post 21 Sep 2013, 14:07
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

Manager
Manager
avatar
Joined: 10 Mar 2014
Posts: 106
Followers: 1

Kudos [?]: 18 [0], given: 6

CAT Tests
Re: Divisibility by 7 [#permalink] New post 27 Apr 2014, 05:17
Bunuel wrote:
study wrote:
If x^2 = y + 5, y = z - 2 and z = 2x, is x^3 + y^2 + z divisible by 7?

1. x \gt 0
2. y = 4


We have system of equations with three distinct equations and three unknowns, so we can solve it. As x is squared we'll get two values for it and also two values for y and z: two triplets. Hence we'll get two values for x^3 + y^2 + z, one divisible by 7 and another not divisible by 7. Each statement is giving us the info to decide which triplet is right, thus both statement are sufficient on its own.

Given:
x^2 = y + 5
y = z - 2 --> y=2x-2.
z = 2x

x^2 =2x-2+ 5 --> x^2-2x-3=0 --> x=3 or x=-1

x=3, y=4, z=6 - first triplet --> x^3 + y^2 + z=27+16+6=49, divisible by 7;
x=-1, y=-4, z=-2 - second triplet --> x^3 + y^2 + z=-1+16-2=13, not divisible by 7.

(1) x \gt 0 --> we deal with first triplet. x^3 + y^2 + z=27+16+6=49, divisible by 7. sufficient.
(2) y = 4 --> --> we deal with first triplet. x^3 + y^2 + z=27+16+6=49, divisible by 7. sufficient.

Answer: D.

Hope it helps.


Hi bunnel,

In second statement y=4 if we replace we found x^2 = 4+5 = 9

so can we write x= +3 and -3. if we replace x= -3 then sum will be -24+16+6 = -1. then how it can be divisible by 7

Please clarify

Thanks.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23331
Followers: 3599

Kudos [?]: 28590 [0], given: 2803

Re: Divisibility by 7 [#permalink] New post 28 Apr 2014, 01:41
Expert's post
PathFinder007 wrote:
Bunuel wrote:
study wrote:
If x^2 = y + 5, y = z - 2 and z = 2x, is x^3 + y^2 + z divisible by 7?

1. x \gt 0
2. y = 4


We have system of equations with three distinct equations and three unknowns, so we can solve it. As x is squared we'll get two values for it and also two values for y and z: two triplets. Hence we'll get two values for x^3 + y^2 + z, one divisible by 7 and another not divisible by 7. Each statement is giving us the info to decide which triplet is right, thus both statement are sufficient on its own.

Given:
x^2 = y + 5
y = z - 2 --> y=2x-2.
z = 2x

x^2 =2x-2+ 5 --> x^2-2x-3=0 --> x=3 or x=-1

x=3, y=4, z=6 - first triplet --> x^3 + y^2 + z=27+16+6=49, divisible by 7;
x=-1, y=-4, z=-2 - second triplet --> x^3 + y^2 + z=-1+16-2=13, not divisible by 7.

(1) x \gt 0 --> we deal with first triplet. x^3 + y^2 + z=27+16+6=49, divisible by 7. sufficient.
(2) y = 4 --> --> we deal with first triplet. x^3 + y^2 + z=27+16+6=49, divisible by 7. sufficient.

Answer: D.

Hope it helps.


Hi bunnel,

In second statement y=4 if we replace we found x^2 = 4+5 = 9

so can we write x= +3 and -3. if we replace x= -3 then sum will be -24+16+6 = -1. then how it can be divisible by 7

Please clarify

Thanks.


Given: x^2 = y + 5, y = z - 2 and z = 2x.

(2) y = 4:

y = z - 2 --> z=6;
z = 2x --> x=3.

So, x cannot be -3.

Does this make sense?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Divisibility by 7   [#permalink] 28 Apr 2014, 01:41
    Similar topics Author Replies Last post
Similar
Topics:
6 Experts publish their posts in the topic If x^2 = y + 5, y = z - 2 and z = 2x, is x^3 + y^2 + z keiraria 2 29 Apr 2012, 01:29
Set A is {x,2x+y,2y,y+z,x+z}. If x,y, and z are positive jeeteshsingh 2 11 Mar 2010, 05:40
1) x^2 + y^2 > Z^2 X^2, Y^2, Z^2 are always positive Aleehsgonji 6 23 Jul 2009, 19:29
if X^2=y+5 , y=z-2 , z=2x Is x^3 + y^2 +z divisible by 7 a) FN 5 13 Sep 2007, 13:36
if X^2=y+5 , y=z-2 , z=2x Is x^3 + y^2 +z divisible by 7 a) saurabhmalpani 7 02 May 2007, 16:37
Display posts from previous: Sort by

If x^2 = y + 5 , y = z - 2 and z = 2x , is x^3 + y^2 + z

  Question banks Downloads My Bookmarks Reviews Important topics  


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®.