What is the greatest common factor of x and y ?
(1) x and y are both divisible by 4
(2) x - y = 4
What if y=0 and x=4.
In that case there is no greatest common factor of x and y.
Shouldn't the answer be (E)?
DS Question
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 63
- Joined: Sat May 17, 2014 9:01 am
- Followed by:1 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
On the GMAT, problems about factors are invariably constrained to POSITIVE INTEGERS.
The problem above should read as follows:
Options for x and y:
4, 8, 12, 16, 20, 24, 28...
If x=4 and y=4, then the GCF of x and y is 4.
If x=8 and y=8, then the GCF of x and y is 8.
Since the GCF can be different values, INSUFFICIENT.
Statement 2: x-y = 4
If x=5 and y=1, then the GCF of x and y is 1.
If x=6 and y=2, then the GCF of x and y is 2.
Since the GCF can be different values, INSUFFICIENT.
Statements combined:
Statement 1 yields the following options for x and y:
4, 8, 12, 16, 20, 24, 28...
Statement 2 indicates that the difference between x and y is 4.
Implication:
x and y must be equal to two consecutive values in the list above.
If we select any pair of consecutive values -- 4 and 8, 8 and 12, 12 and 16, 16 and 20 -- the GCF in every case is 4.
SUFFICIENT.
The correct answer is C.
The problem above should read as follows:
Statement 1: x and y are both divisible by 4What is the greatest common factor of POSITIVE INTEGERS x and y?
(1) x and y are both divisible by 4
(2) x - y = 4
Options for x and y:
4, 8, 12, 16, 20, 24, 28...
If x=4 and y=4, then the GCF of x and y is 4.
If x=8 and y=8, then the GCF of x and y is 8.
Since the GCF can be different values, INSUFFICIENT.
Statement 2: x-y = 4
If x=5 and y=1, then the GCF of x and y is 1.
If x=6 and y=2, then the GCF of x and y is 2.
Since the GCF can be different values, INSUFFICIENT.
Statements combined:
Statement 1 yields the following options for x and y:
4, 8, 12, 16, 20, 24, 28...
Statement 2 indicates that the difference between x and y is 4.
Implication:
x and y must be equal to two consecutive values in the list above.
If we select any pair of consecutive values -- 4 and 8, 8 and 12, 12 and 16, 16 and 20 -- the GCF in every case is 4.
SUFFICIENT.
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 Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
One worthwhile additional note here: the GCF of two positive integers x and y is itself a factor of the difference between x and y. (Algebraically, we'd say GCF(x,y) is a factor of (x - y).)
So S2 tells us _something_: the GCF of x and y is either 1, 2, or 4, since the GCF of x and y must be a factor of (x - y), or 4.
Combining the two statements, then, we know that 4 is the GCF, since it's already a common factor of the two numbers (i.e. 4 is a factor of x and 4 is a factor of y) and it's the greatest of the three potential common factors (1, 2, and 4).
So S2 tells us _something_: the GCF of x and y is either 1, 2, or 4, since the GCF of x and y must be a factor of (x - y), or 4.
Combining the two statements, then, we know that 4 is the GCF, since it's already a common factor of the two numbers (i.e. 4 is a factor of x and 4 is a factor of y) and it's the greatest of the three potential common factors (1, 2, and 4).