If x and y are positive integers greater than 1 such that x − y and are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III
Manhattan Prep (2015-05-17). GMAT Advanced Quant (Kindle Locations 4076-4082). Manhattan Prep Publishing. Kindle Edition.
OA D. Why not E?
IMO, III always results in a positive fraction and thus is not prime always. Please let me know what am I missing.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
MGMAT Advanced quant - Hybrid problem
This topic has expert replies
-
bubbliiiiiiii
- Legendary Member
- Posts: 979
- Joined: Tue Apr 14, 2009 1:38 am
- Location: Hyderabad, India
- Thanked: 49 times
- Followed by:12 members
- GMAT Score:700
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The problem should read as shown above.If x and y are positive integers greater than 1 such that x - y and x/y are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III
III: y/xbubbliiiiiiii wrote: IMO, III always results in a positive fraction and thus is not prime always. Please let me know what am I missing.
If x=4 and y=2, then y/x = 2/4 = 1/2.
Since 1/2 is not a non-prime INTEGER, III does not have to be true.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If x and y are positive integers greater than 1 such that x - y and x/y are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III
==> x/y=even, x=y*even=even, x-y=even,even-y=even, y=even-even=even therefore x=y=even. Since x/y=x/even=even, x=even*even=a multiple of 4. Therefore, x=4n, y=2m(n,m are integers).
I. x ==> x=4n=multiple of 4, therefore is not a prime number
II. x + y ==> x+y=4n+2m=2(2n+m)=even, therefore it is not a prime number.
III. y/x ==> y/x=2m/4n=m/2n is NOT integer therefore it is not a prime number (since we need non-prime integers)
Therefore the answer is D.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
If x and y are positive integers greater than 1 such that x - y and x/y are both even integers, which of the following numbers must be non-prime integers?
I. x
II. x + y
III. y/x
(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III
==> x/y=even, x=y*even=even, x-y=even,even-y=even, y=even-even=even therefore x=y=even. Since x/y=x/even=even, x=even*even=a multiple of 4. Therefore, x=4n, y=2m(n,m are integers).
I. x ==> x=4n=multiple of 4, therefore is not a prime number
II. x + y ==> x+y=4n+2m=2(2n+m)=even, therefore it is not a prime number.
III. y/x ==> y/x=2m/4n=m/2n is NOT integer therefore it is not a prime number (since we need non-prime integers)
Therefore the answer is D.
www.mathrevolution.com
l The one-and-only World's First Variable Approach for DS and IVY Approach for PS that allow anyone to easily solve GMAT math questions.
l The easy-to-use solutions. Math skills are totally irrelevant. Forget conventional ways of solving math questions.
l The most effective time management for GMAT math to date allowing you to solve 37 questions with 10 minutes to spare
l Hitting a score of 45 is very easy and points and 49-51 is also doable.
l Unlimited Access to over 120 free video lessons at https://www.mathrevolution.com/gmat/lesson
Our advertising video at https://www.youtube.com/watch?v=R_Fki3_2vO8
