If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A)5
B)5(x - y)
C)20x
D)20y
E)35x
OAC
Greatest common divisor
This topic has expert replies
-
- Legendary Member
- Posts: 510
- Joined: Thu Aug 07, 2014 2:24 am
- Thanked: 3 times
- Followed by:5 members
- 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
C: 20xj_shreyans wrote:If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A)5
B)5(x - y)
C)20x
D)20y
E)35x
Dividing 35x by 20x, we get:
35x/20x = 7/4.
Since 35x/20x = non-integer, 20x is not a factor of 35x.
Thus, it is not possible for 20x to be the greatest common divisor of 35x and 20y.
The correct answer is C.
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
The wording of the question tells us that 4 of the answer choices CAN be the greatest common divisor (GCD) of 35x and 20y, and one of them cannot.If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A) 5
B) 5(x - y)
C) 20x
D) 20y
E) 35x
So, might BEGIN by eliminating those answer choices that CAN be the greatest common divisor of 35x and 20y
A) 5
5 is a DIVISOR of both 35x and 20y, but can it be the GCD of 35x and 20y?
YES. If x = 1 and y = 1, then 5 is the GCD of 35x and 20y.
ELIMINATE A
B) 5(x - y)
CAN 5(x - y) be the GCD of 35x and 20y?
YES. If x = 3 and y = 2, then 5(x - y) = 5, 35x = 105 and 20y = 40
Since 5 is the GCD of 105 and 40, we can ELIMINATE B
Aside: It can be tough finding values such that 4 of the answer choices are, indeed, the GCD of 35x and 20y. So, we should also be looking for another approach that shows that an answer choice CANNOT be the GCD of 35x and 20y
C) 20x
CAN 20x be the GCD of 35x and 20y?
NO!
How do we know this?
20x cannot be the greatest common DIVISOR of 35x and 20y, because 20x isn't even a DIVISOR of 35x
Notice that 35x/20x = 35/20 = 7/4
This tells us that 20x cannot be a DIVISOR of 35x, which means 20x cannot be the GCD of 35x and 20y.
Answer: C
Cheers,
Brent