BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Master GMAT

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 120
Joined: Mon Nov 07, 2011 10:54 pm
Location: Delhi
Thanked: 5 times

Master GMAT

by bryan88 » Tue May 01, 2012 8:32 pm
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)
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 142
Joined: Thu Apr 26, 2012 3:24 am
Location: India
Thanked: 28 times

by mathbyvemuri » Tue May 01, 2012 8:43 pm
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'
Top
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Sun Mar 11, 2012 8:57 pm
Location: India
Thanked: 16 times
Followed by:1 members

by shantanu86 » Tue May 01, 2012 8:52 pm
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.
If you feel like it, hit thanks :)
Top
Post new topic Post Reply
• Page 1 of 1