Problem Solving

If x is a prime number greater than 5, y is a positive integer, and 5y=x^2+x, then y must be divisible by which of the following?

A) 5
B) 2x
C) x+1

(Note: more than one statement can be true)

y = x(x+1)/5
As x is a prime and hence would not be divisible by 5, (x+1) must be divisible by 5 in order to get an integer value for y.
So, x+1 should end with 5 or 0. But we can rule out 5 here as in that case x ends with 4, which is not possible for a prime number 'x'
=> x+1 ends with '0'
=> possible values of x are: 19,29,59,... all primes ending with '9'
Each time 5 goes in x+1 leaving a multiple of '2' such that y is a multiple of 2x
Answer is only 'B'

bryan88 wrote:If x is a prime number greater than 5, y is a positive integer, and 5y=x^2+x, then y must be divisible by which of the following?

A) 5
B) 2x
C) x+1

(Note: more than one statement can be true)

IMO its B..
Here is the explanation-

y = (x^2+x)/5
= x(x+1)/5

Now since x is a prime greater than 5 and y is an integer=> x+1 must be divisible by 5.
Thus x can have either 4 or 9 at unit place. Fox x to be prime 9 is the only choice!

Now if x has 9 at units that means x+1 is of the form 10*n, where n is an integer.

Thus,
y= x*10*n/5
= x*2*n

Hence y is divisible by 2x and not by 5 and x+1.

As an example, let x=29

=> y = 29*30/5 = 29*6 = 174.

174 is not divisible by 5 and 30 (x+1) but divisible by 2*x= 29*2.

Thus B.