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

 It is currently 19 May 2013, 20:36

# M02 Q17

Author Message
TAGS:
Manager
Status: Preparing for GMAT - March 2011
Joined: 21 May 2010
Posts: 150
Location: London
Schools: INSEAD, RSM, HEC, St. Gallen, IF, IESE
WE 1: Finance 6 years
Followers: 5

Kudos [?]: 8 [0], given: 0

M02 Q17 [#permalink]  05 Jan 2011, 03:57
00:00

Question Stats:

92% (02:04) correct 7% (01:28) wrong based on 4 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 is less than or equal to 1
(c)X+1 is also a prime factor of Y^2

Please need a good explanation for this.
[Reveal] Spoiler: OA

_________________

In The World Full Of Duplicates,, I Am The Only Masterpiece..
Girl Power
beat-the-beast-with-non-native-speaker-108349.html

GMAT Club team member
Joined: 02 Sep 2009
Posts: 11516
Followers: 1792

Kudos [?]: 9537 [0], given: 826

Re: M02 Q17 [#permalink]  05 Jan 2011, 05:55
tirupatibalaji wrote:
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 is less than or equal to 1
(c)X+1 is also a prime factor of Y^2

Please need a good explanation for this.

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. y/x is even --> not necessarily true: if x=3 and y=3 then \frac{y}{x}=1=odd;
D. x/y 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.

Hope it's clear.
_________________
Manager
Status: Preparing for GMAT - March 2011
Joined: 21 May 2010
Posts: 150
Location: London
Schools: INSEAD, RSM, HEC, St. Gallen, IF, IESE
WE 1: Finance 6 years
Followers: 5

Kudos [?]: 8 [0], given: 0

Re: M02 Q17 [#permalink]  05 Jan 2011, 06:46
Thanks Bunuel.
You are genius.
_________________

In The World Full Of Duplicates,, I Am The Only Masterpiece..
Girl Power
beat-the-beast-with-non-native-speaker-108349.html

Manager
Joined: 26 Mar 2007
Posts: 89
Schools: Thunderbird '15
Followers: 1

Kudos [?]: 10 [0], given: 8

Re: M02 Q17 [#permalink]  06 Jan 2011, 03:26
Bunuel has explained it well. Ans must be D
Re: M02 Q17   [#permalink] 06 Jan 2011, 03:26
Similar topics Replies Last post
Similar
Topics:
1 Factoring...? (m02 #8) 5 27 Feb 2008, 22:50
14 m02#8 15 03 Nov 2008, 16:24
12 m02#24 16 05 Nov 2008, 08:21
4 m02 #21 26 14 Nov 2008, 13:33
18 M02 #19 26 26 Dec 2008, 18:28
Display posts from previous: Sort by