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

Question

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

Source:   Nova GMAT  
Difficulty Level:   500

IvanW · Accepted Answer

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....

Bunuel · Answer

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.

GMAT40 · Answer

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

b2bt · Answer

This can be termed as a property of the squares of the prime numbers....

jkher · Answer

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?

Bunuel · Answer

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

Temurkhon · Answer

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

yoysufpolash · Answer

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

ydmuley · Answer

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

zahinsarwar · Answer

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

Bunuel · Answer

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.

ehsan090 · Answer

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

780gmatpossible · Answer

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   / 12

Answer E

Bunuel · Answer

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

bumpbot · Answer

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

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