Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 19 May 2013, 10:53

# x and y are positive integers. If x is a prime factor of y^2

Author Message
TAGS:
Manager
Joined: 14 Mar 2010
Posts: 84
Followers: 2

Kudos [?]: 16 [0], given: 42

x and y are positive integers. If x is a prime factor of y^2 [#permalink]  21 Apr 2012, 23:05
00:00

Question Stats:

88% (02:37) correct 11% (00:00) wrong based on 1 sessions
x and y are positive integers. If x is a prime factor of y^2 , which of the following MUST be true?

A. x is even
B. x=y^2
C. y/x is even
D. x/y <=1
E. x+1 is also the prime factor of y^2

GMAT Club Tests: m02 q17
[Reveal] Spoiler: OA

_________________

MGMAT CAT MATH mgmat-cat-math-144609.html
MGMAT SC SUMMARY: mgmat-sc-summary-144610.html

 Kaplan Promo Code Knewton GMAT Discount Codes Veritas Prep GMAT Discount Codes
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11515
Followers: 1791

Kudos [?]: 9535 [0], given: 826

Re: M02#17 [#permalink]  21 Apr 2012, 23:10
If x and y are positive integers and x is a prime factor of y^2, then which of the following MUST be true?

A. x is even
B. x=y^2
C. \frac{y}{x} is even
D. \frac{x}{y}\leq{1}
C. x+1 is also a prime factor of y^2

Given: x=prime, y=positive \ integer and x is a prime factor of y^2. Now, as x is a prime factor of y^2 and y is an integer then x must be a factor of y as well (how else could x appear in the prime factorization of y^2=y*y if it's not a factor of y). Next, as x is a factor of y (and y is a positive integer) then x\leq{y} --> \frac{x}{y}\leq{1}, so D must be true.

Another approach:
Note that we are asked "which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

A. x is even --> not necessarily true: x=3=odd and y=3;
B. x=y^2 --> never true, as x=prime then it can not equal to square of another integer;
C. \frac{y}{x} is even --> not necessarily true: if x=3 and y=3 then \frac{y}{x}=1=odd;
D. \frac{x}{y}\leq{1} is less than or equal to 1 --> always true as shown above or by POE;
E. x+1 is also a prime factor of y^2 --> not necessarily true: if x=2 and y=2 then x+1=3 and 3 is not a factor of y^2=4.

_________________
Re: M02#17   [#permalink] 21 Apr 2012, 23:10
Similar topics Replies Last post
Similar
Topics:
x and y are positive integers. x is a prime factor of y, is 7 27 Jun 2005, 20:38
If x is a positive integer, is y^2 (x^3 - x + 1) 4 02 Oct 2008, 00:00
If x and y are positive integers, is x - y > (x+y)/2 ? 2 25 Oct 2009, 05:03
If x and y are positive integers and x^2 + y^2 = 100 3 18 Aug 2012, 15:22
If x and y are positive integers such that x^2+y^2 is a prim 1 27 Feb 2013, 14:19
Display posts from previous: Sort by