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

 It is currently 23 May 2019, 08:01

### 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

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

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Jul 2013
Posts: 312
If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

Updated on: 20 Aug 2013, 12:34
2
4
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:03) correct 12% (01:11) wrong based on 302 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
Joined: 02 Sep 2009
Posts: 55266
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

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.

_________________
Intern
Joined: 17 May 2013
Posts: 39
GMAT Date: 10-23-2013
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

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
Manager
Joined: 25 Sep 2012
Posts: 237
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

23 Aug 2013, 02:20
This can be termed as a property of the squares of the prime numbers....
Intern
Joined: 05 Jun 2011
Posts: 12
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

02 Sep 2013, 15:01
2
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
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

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
Joined: 02 Sep 2009
Posts: 55266
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

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".
_________________
Director
Joined: 23 Jan 2013
Posts: 549
Schools: Cambridge'16
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

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

### Show Tags

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
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

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 $$4$$.

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

### Show Tags

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.

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
Joined: 02 Sep 2009
Posts: 55266
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

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.

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.
_________________
Manager
Joined: 08 Oct 2016
Posts: 202
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

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
Intern
Joined: 25 Jul 2012
Posts: 27
Location: India
Concentration: Finance, Marketing
GMAT 1: 660 Q44 V37
If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

01 Oct 2018, 06:16
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.

x^2-y^2
since x and y are greater than 2, I have taken x=7 and y=5

x^2-y^2 = (x+y)(x-y)
Now, x+y = 12

Thus [(x+y)(x-y)] / 12

_________________
If you like my post, consider giving me KUDOS
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

### Show Tags

01 Oct 2018, 06:59
780gmatpossible 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.

x^2-y^2
since x and y are greater than 2, I have taken x=7 and y=5

x^2-y^2 = (x+y)(x-y)
Now, x+y = 12

Thus [(x+y)(x-y)] / 12

Hope it helps.
_________________
Re: If x and y are prime numbers such that x > y > 2, then x^2 −   [#permalink] 01 Oct 2018, 06:59
Display posts from previous: Sort by