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Friday, May 18, 2007

ALGEBRA QUESTION OF THE DAY

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

8 comments:

Anonymous said...: B; May 18, 2007 at 1:13 PM
Unknown said...: b; May 20, 2007 at 8:46 PM
Unknown said...: B; May 21, 2007 at 10:38 PM
Anonymous said...: explain; May 22, 2007 at 10:30 AM
Anonymous said...: for ex...5>3>2...thn B is correct
Bt if 4>3>2...thn...16-9=7 !!!
thn wats the ans here....?; May 22, 2007 at 10:31 AM
Anonymous said...: can some1 explain?; May 23, 2007 at 7:53 AM
Aditya`s take said...: the question says prime no.

so we take 2 prime nos..

for eg 5 and 3.....5*5-3*3=16 divisible by 4

aand if we take 7*7-3*3 =40 its again divisible by 4.....so the answer is ...b; May 23, 2007 at 11:27 PM
Vishal Naidu said...: Let X and Y be the primes......

since both X & Y are !=2

X & Y are both odd numbers...
trivial evens can't be primes....
so let X = 2m+1
Y = 2n+1

=> X^2 - Y^2 = (X+Y) (X-Y)
= (2m+2n+2)(2m-2n)
= 4 (m+n+1)(m-n)

so definitely divisible by 4 :); May 31, 2007 at 6:41 AM