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

It is currently 17 Oct 2019, 00:56

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

If x, y, and z are positive integers, where x > y and

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 24 Jul 2009
Posts: 65
Location: United States
GMAT 1: 590 Q48 V24
If x, y, and z are positive integers, where x > y and  [#permalink]

Show Tags

New post Updated on: 13 Jun 2013, 05:51
3
19
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (02:50) correct 61% (03:00) wrong based on 353 sessions

HideShow timer Statistics

If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

(1) x + y = 8z +1
(2) x – y = 2z – 1

Originally posted by ctrlaltdel on 15 Nov 2009, 22:47.
Last edited by Bunuel on 13 Jun 2013, 05:51, edited 1 time in total.
OA added.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58427
Re: Are x and y consecutive perfect squares  [#permalink]

Show Tags

New post 16 Nov 2009, 08:40
17
7
Economist wrote:
What is the source?? This is a heck of a problem. Plugging numbers is painful. Do we have any algebraic approach?


Here you go.
If \(x\) and \(y\) are consecutive perfect squares, then \(\sqrt{y}\) and \(\sqrt{x}\) must be consecutive integers.

So, the question: is \(\sqrt{y}=\sqrt{x}-1\)?

Square both sides: \(y=x-2\sqrt{x}+1\)?

(1) \(x+y=8z+1\)
\(x+y=8\sqrt{x}+1\)
\(y=8\sqrt{x}+1-x\)

So basically question transforms to is \(8\sqrt{x}+1-x=x-2\sqrt{x}+1\)?
\(10\sqrt{x}=2x\)?
\(5\sqrt{x}=x\)?
\(\sqrt{x}=5\)?
\(x=25\)?

If x=25 then yes, if not then no. But we don't know the value of x, hence insufficient.

(2) \(x-y=2\sqrt{x}-1\)
\(y=x-2\sqrt{x}+1\), which is exactly what we are asked in the question. Hence sufficient.

Answer: B.
_________________
General Discussion
Manager
Manager
avatar
Joined: 30 Aug 2009
Posts: 227
Location: India
Concentration: General Management
Re: Are x and y consecutive perfect squares  [#permalink]

Show Tags

New post 16 Nov 2009, 01:27
2
1
ctrlaltdel wrote:
If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

(1) x + y = 8z +1
(2) x – y = 2z – 1

Happy Solving


B

1. x+ y = 8z+1
the values of x and y satisfying this equation is 25 and 16 which are consecutive perfect squares
the values of x and y satisfying this equation is 64 and 1 which are NOT consecutive perfect squares
Hence insuff

2. x -y = 2z-1
the values x and y satisfying this equation will be all consecutive perfect squares (be it [4,1] [9,4][2500,2401]
non consecutive perfect squares will not satisfy the equation
hence suff
Manager
Manager
avatar
Joined: 24 Jul 2009
Posts: 65
Location: United States
GMAT 1: 590 Q48 V24
Re: Are x and y consecutive perfect squares  [#permalink]

Show Tags

New post 16 Nov 2009, 01:42
Spoiler: :: OA
B
Kudos to kp1811
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 650
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Are x and y consecutive perfect squares  [#permalink]

Show Tags

New post 16 Nov 2009, 07:55
What is the source?? This is a heck of a problem. Plugging numbers is painful. Do we have any algebraic approach?
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 650
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Are x and y consecutive perfect squares  [#permalink]

Show Tags

New post 16 Nov 2009, 10:08
Thanks Bunuel :) ! Great job..+1K
Manager
Manager
avatar
Joined: 16 Apr 2009
Posts: 214
Re: Are x and y consecutive perfect squares  [#permalink]

Show Tags

New post 17 Nov 2009, 20:07
bunuel - sometimes i wonder how easily you solve these questions - you are awesome :)
_________________
Always tag your question
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1571
Concentration: Finance
GMAT ToolKit User
Re: If x, y, and z are positive integers, where x > y and  [#permalink]

Show Tags

New post 11 Mar 2014, 18:31
IM BACK!

The difference of perfect squares can be expressed as an odd number. Or viceversa, an odd number can be expressed as the difference of two consecutive perfect squares

Namely,

(k+1)^2 - (k)^2 = 2k + 1

Hope this clarifies
Manager
Manager
avatar
Joined: 03 May 2013
Posts: 67
Re: If x, y, and z are positive integers, where x > y and  [#permalink]

Show Tags

New post 30 Apr 2015, 19:18
If x, y, and z are positive integers, where x > y and z=x^(1/2), are x and y consecutive perfect squares? (A perfect square is defined as the square of an integer. For example, 36 is a perfect square since it equals 6 squared, while 38 is not a perfect square since it is not equal to the square of any integer.)

(1) x + y = 8z +1
(2) x – y = 2z – 1

Alt way

2. z^2-2z+1 =y
(z-1)^2 = y, z-1 = y^1/2, z=y^1/2+1, since z=X^1/2 , x^1/2 and y^1/2 are consecutive
1. z^2-8z-1 =-y NO solution
Hence B
Manager
Manager
avatar
S
Joined: 20 Jun 2013
Posts: 50
Location: India
Concentration: Economics, Finance
GMAT 1: 430 Q39 V25
GPA: 3.5
WE: Information Technology (Other)
GMAT ToolKit User
Re: If x, y, and z are positive integers, where x > y and  [#permalink]

Show Tags

New post 30 May 2017, 05:05
thanks that was a good one... pretty weak in ds got a get the basics first i guess
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13204
Re: If x, y, and z are positive integers, where x > y and  [#permalink]

Show Tags

New post 30 Sep 2018, 10:15
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 Club Bot
Re: If x, y, and z are positive integers, where x > y and   [#permalink] 30 Sep 2018, 10:15
Display posts from previous: Sort by

If x, y, and z are positive integers, where x > y and

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





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