It is currently 19 Sep 2017, 05:01

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

For positive integers x and y, which of the following can

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 121

Kudos [?]: 1109 [1], given: 17

For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 11 Jun 2013, 03:55
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:07) correct 38% (01:22) wrong based on 132 sessions

HideShow timer Statistics

For positive integers x and y, which of the following can be written as y^2?

A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Last edited by Bunuel on 11 Jun 2013, 06:00, edited 1 time in total.
Edited the question.

Kudos [?]: 1109 [1], given: 17

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41597

Kudos [?]: 123964 [0], given: 12070

Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 11 Jun 2013, 06:04

Kudos [?]: 123964 [0], given: 12070

Intern
Intern
avatar
Joined: 02 Feb 2012
Posts: 29

Kudos [?]: 14 [0], given: 35

GPA: 4
Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 11 Jun 2013, 06:12
Bunuel wrote:
emmak wrote:
For positive integers x and y, which of the following can be written as y^2?

A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!


Plug values: if x=5, then x^2-9=16=4^2.

Answer: C.


How the solution can be made easy? I was plugging in smaller numbers than 5 and in such cases even (C) fails. As the time was running out, I made an educated guess as (C) and it turned out to be right !!!!

Kudos [?]: 14 [0], given: 35

Intern
Intern
User avatar
Joined: 08 May 2013
Posts: 11

Kudos [?]: 27 [0], given: 31

GMAT ToolKit User
Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 12 Jun 2013, 17:24
Bunuel wrote:
emmak wrote:
For positive integers x and y, which of the following can be written as y^2?

A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!


Plug values: if x=5, then x^2-9=16=4^2.

Answer: C.


Although I understood the explanation, but it would fail if I put x=4. In other words, why did you select x=5?

Kudos [?]: 27 [0], given: 31

Manager
Manager
avatar
Joined: 09 Apr 2013
Posts: 208

Kudos [?]: 80 [0], given: 40

Location: United States
Concentration: Finance, Economics
GMAT 1: 710 Q44 V44
GMAT 2: 740 Q48 V44
GPA: 3.1
WE: Sales (Mutual Funds and Brokerage)
Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 12 Jun 2013, 17:35
The question is asking "Which of these equations could equal a perfect square?"

If you're familiar with number properties regarding perfect squares, you should be able to rule out everything except the correct answer.

the fact that 5^2 - 4^2 is equal to 3^2 should be a pattern that you have memorized (esp. with regards to right triangles)
also, another one you might see often is some form of 13^2-5^2=12^2

Kudos [?]: 80 [0], given: 40

1 KUDOS received
Manager
Manager
avatar
Joined: 04 Feb 2010
Posts: 196

Kudos [?]: 22 [1], given: 8

CAT Tests
Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 12 Jun 2013, 22:57
1
This post received
KUDOS
1
This post was
BOOKMARKED
The way I solved this is by process of elimination.

First, all factorials should be written off. A factorial would never be a perfect square since the last prime in the series would be the only single factor of its kind in the factorial. (i.e. 11! would have an 11 as one of its factor, but would not have another 11 as another factor, hence making it impossible for it to be a perfect square). A, B and E are out.

Second, D is never going to be a perfect square, since a perfect square plus one is never going to be a perfect square.

This leaves us with C.

Kudos [?]: 22 [1], given: 8

Intern
Intern
avatar
Joined: 27 May 2013
Posts: 2

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

Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 14 Jun 2013, 07:16
but if we assume in option c, X=10 than it is= 100-9=91 (which is not a square root). how option c is valid?


Bunuel wrote:
emmak wrote:
For positive integers x and y, which of the following can be written as y^2?

A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!


Plug values: if x=5, then x^2-9=16=4^2.

Answer: C.

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41597

Kudos [?]: 123964 [0], given: 12070

Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 14 Jun 2013, 07:18
poojamittal63 wrote:
but if we assume in option c, X=10 than it is= 100-9=91 (which is not a square root). how option c is valid?


Bunuel wrote:
emmak wrote:
For positive integers x and y, which of the following can be written as y^2?

A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!


Plug values: if x=5, then x^2-9=16=4^2.

Answer: C.


The question asks "which of the following CAN be written as y^2". If x=5, then x^2−9 CAN be written as 4^2.
_________________

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 [?]: 123964 [0], given: 12070

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17559

Kudos [?]: 270 [0], given: 0

Premium Member
Re: For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 13 Apr 2015, 10:41
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 [?]: 270 [0], given: 0

Director
Director
User avatar
Joined: 04 Jun 2016
Posts: 648

Kudos [?]: 346 [0], given: 36

GMAT 1: 750 Q49 V43
For positive integers x and y, which of the following can [#permalink]

Show Tags

New post 24 Jul 2016, 23:01
1
This post was
BOOKMARKED
For positive integers x and y, which of the following can be written as y^2?
A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!

It is worth while to remember that the only factorial that are perfect square is 0 and 1. {0!=1 and 1!=1 and \(1=1^2}\)
If you know this fact then you can figure out that the answer is C
But just to reconfirm I will solve this question.
Now lets attack the problem.

A. (x+1)! = OHHHH ! so close, If x= 0 then this could have been our answer, \({0+1=1^2}\)but question stem tells us that x and y are +ve integer. 0 is not a positive integer.

B. (x+9)! = Cannot be a perfect square. No factorial except 1 is a perfect square

C. x^2−9 = Yes ! this can be ; take \(x= 3; 3^2-9 = 0-0 = 0 ; y= 0^2\) ||||| take \(x=5; 5^2-9=16 ; Y^2=4^2\)

D. x^2+1 = NO ! if you add 1 to a perfect square you cannot another perfect square; exception is 0 ; \(0^2+1 = 1 = 1^2\)

E. ((x+1)^2)!= Again so close if x= 0 then we could have a perfect square but x cannot be zero; so this expression cannot be a perfect square.





emmak wrote:
For positive integers x and y, which of the following can be written as y^2?

A. (x+1)!
B. (x+9)!
C. x^2−9
D. x^2+1
E. ((x+1)^2)!

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 346 [0], given: 36

For positive integers x and y, which of the following can   [#permalink] 24 Jul 2016, 23:01
    Similar topics Author Replies Last post
Similar
Topics:
3 EXPERTS_POSTS_IN_THIS_TOPIC If positive integers x and y are not both odd, which of the following Madelaine88 7 15 May 2016, 05:03
2 EXPERTS_POSTS_IN_THIS_TOPIC If v, w, x, y, and z are positive integers, which of the following cou Bunuel 2 25 Apr 2016, 10:48
3 EXPERTS_POSTS_IN_THIS_TOPIC If x = y^2, and x and y are positive integers, which of the following Bunuel 5 25 May 2017, 12:02
64 EXPERTS_POSTS_IN_THIS_TOPIC If x and y are positive integers, which of the following cul3s 19 12 Jul 2017, 01:12
39 EXPERTS_POSTS_IN_THIS_TOPIC If x and y are positive integers, which of the following CAN priyanka116 14 15 May 2016, 09:36
Display posts from previous: Sort by

For positive integers x and y, which of the following can

  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®.