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

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2
4 00:00

Difficulty:   5% (low)

Question Stats: 88% (01:03) correct 12% (01:11) wrong based on 302 sessions

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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

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

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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.
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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]

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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]

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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]

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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]

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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?
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Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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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".
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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]

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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
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Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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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
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Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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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
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Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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

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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.
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Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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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
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Target#01 Q45,V20--April End
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GMAT 1: 660 Q44 V37 If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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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.

Bunuel can you please help what is wrong in the below approach :

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

Answer E
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Posts: 55266
Re: If x and y are prime numbers such that x > y > 2, then x^2 −  [#permalink]

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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.

Answer: B.

Bunuel can you please help what is wrong in the below approach :

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

Answer E

I addressed your doubt here: https://gmatclub.com/forum/if-x-and-y-a ... l#p1883647

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
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