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

It is currently 24 Sep 2018, 14:29

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 and y are prime numbers such that x > y > 2, then x^2 −

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

Hide Tags

Senior Manager
Senior Manager
avatar
Joined: 10 Jul 2013
Posts: 315
If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post Updated on: 20 Aug 2013, 12:34
2
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:06) correct 12% (01:03) wrong based on 237 sessions

HideShow timer Statistics

If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?

(A) 3
(B) 4
(C) 5
(D) 9
(E) 12

_________________

Asif vai.....


Originally posted by Asifpirlo on 20 Aug 2013, 12:29.
Last edited by Bunuel on 20 Aug 2013, 12:34, edited 1 time in total.
Edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49430
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 20 Aug 2013, 12:36
4
Asifpirlo wrote:
If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?

(A) 3
(B) 4
(C) 5
(D) 9
(E) 12


If x=5 and y=3, then x^2-y^2=16 and 16 is divisible only by 4 from the options, thus it must be correct.

Answer: B.
_________________

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

Intern
Intern
avatar
Joined: 17 May 2013
Posts: 41
GMAT Date: 10-23-2013
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 22 Aug 2013, 20:38
y can take values like 3, 5, 7, 9
x can take values like 5, 7, 9
Square of their diff is divisible by 4
Ans: B

PS : Numbers have to be PRIME
Current Student
User avatar
Joined: 25 Sep 2012
Posts: 259
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
GMAT ToolKit User Reviews Badge
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 23 Aug 2013, 02:20
This can be termed as a property of the squares of the prime numbers....
Intern
Intern
avatar
Joined: 05 Jun 2011
Posts: 14
Schools: Kellog, Stern, Stanford, Booth,HBS, Wharton
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 02 Sep 2013, 15:01
1
1
In addition to what has already been stated, this is a number properties question, without testing any numbers (not sure if that's faster or slower) but:

x>y>2 and noting that they are prime means that X and y are odd.

also

X^2 - y^2= (x+y)(x-y) so now you have (odd+odd)(odd-odd) which = even * even, which means that at minimum the numbers have 2 powers of 2 in them so it must be divisible by 4.

Just how I thought of it....
Intern
Intern
avatar
Joined: 21 Jul 2013
Posts: 2
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 10 Sep 2013, 01:14
if we take x=7 and y=5 then x2-y2 is 49-25=24 and this is divisible by 3,4 and 12, something is wrong with this question?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49430
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 10 Sep 2013, 01:17
jkher wrote:
if we take x=7 and y=5 then x2-y2 is 49-25=24 and this is divisible by 3,4 and 12, something is wrong with this question?


The question asks "x^2 − y^2 must be divisible by which one of the following numbers" not "could be divisible".
_________________

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

Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 590
Schools: Cambridge'16
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 02 Jan 2015, 04:48
1
we have

(x-y)*(x+y)=x^2-y^2

3,5,7,11,13,17,19,23,27,31......

difference is only 2 or 4 and when it is 2 the sum is always divisible by 4.

It is B
Intern
Intern
avatar
B
Joined: 20 Apr 2017
Posts: 13
Location: Bangladesh
GPA: 3.74
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 29 Jun 2017, 04:40
Asifpirlo wrote:
If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?

(A) 3
(B) 4
(C) 5
(D) 9
(E) 12


X^2 - Y^2
= ( X + Y ) * ( X –Y )
= ( odd + odd ) * ( odd – odd )
= even * even
= 2x * 2x
= 4 x^2 which must be divisible by 4
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 961
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 29 Jun 2017, 05:13
Asifpirlo wrote:
If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?

(A) 3
(B) 4
(C) 5
(D) 9
(E) 12


Lets take some examples:

\(x = 5 & y = 3\)

\(= 5^2 - 3^2\)

\(= 25 - 9\)

\(= 16\)

Similarly you take any other prime numbers you will get a difference which is always divisible by \(4\).

Hece, Answer is B
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Intern
Intern
User avatar
B
Joined: 16 Mar 2017
Posts: 9
Location: Bangladesh
Concentration: Finance, Accounting
GMAT 1: 610 Q47 V27
GPA: 3.71
WE: Accounting (Other)
GMAT ToolKit User
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 07 Jul 2017, 06:13
Bunuel wrote:
Asifpirlo wrote:
If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?

(A) 3
(B) 4
(C) 5
(D) 9
(E) 12


If x=5 and y=3, then x^2-y^2=16 and 16 is divisible only by 4 from the options, thus it must be correct.

Answer: B.



Hi, what if x = 7 and y = 5, then x^2-y^2 = 49 -25 = 24 which is divisible by 12 (answer no. E)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49430
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 07 Jul 2017, 06:17
zahinsarwar wrote:
Bunuel wrote:
Asifpirlo wrote:
If x and y are prime numbers such that x > y > 2, then x^2 − y^2 must be divisible by which one of the following numbers?

(A) 3
(B) 4
(C) 5
(D) 9
(E) 12


If x=5 and y=3, then x^2-y^2=16 and 16 is divisible only by 4 from the options, thus it must be correct.

Answer: B.



Hi, what if x = 7 and y = 5, then x^2-y^2 = 49 -25 = 24 which is divisible by 12 (answer no. E)


The question ask x^2 − y^2 MUST be divisible by which one of the following numbers, not COULD be divisible by which one of the following numbers. It COULD be divisible by 12 but it MUST be divisible only by 4 (from the options). So, it will ALWAYS be divisible by 4, and will be divisible by 12 only in specific cases.
_________________

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

Manager
Manager
avatar
S
Joined: 08 Oct 2016
Posts: 205
Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE: Engineering (Telecommunications)
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 15 Jul 2017, 08:23
Choice:B
Time taken=1:26
In this case I took 2 choices
first: x=5,y=3
x^2-y^2
25-9
16 only choice B satisfies
Second: x=7,y=5
x^2-y^2
49-25
24
Now A,B and E satisfies
So B is correct choice
_________________

Got Q42,V17
Target#01 Q45,V20--April End

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8174
Premium Member
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

Show Tags

New post 02 Sep 2018, 06:08
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

GMAT Club Bot
Re: If x and y are prime numbers such that x > y > 2, then x^2 − &nbs [#permalink] 02 Sep 2018, 06:08
Display posts from previous: Sort by

If x and y are prime numbers such that x > y > 2, then x^2 −

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

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.