If a, b and c are positive integers and c is odd, are both a and b divisible by c ?
(1) a + b is divisible by c.
(2) a - b is divisible by c.
The OA is C.
Can any expert help me with this DS question please? Thanks.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
If a, b and c are positive...
This topic has expert replies
-
BTGmoderatorLU
- Moderator
- Posts: 2207
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 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
Statement 1: a+b is divisible by cLUANDATO wrote:If a, b and c are positive integers and c is odd, are both a and b divisible by c ?
(1) a + b is divisible by c.
(2) a - b is divisible by c.
Case 1: a=1, b=1, c=1, with the result that a+b=2 is divisible by c=1
In this case, a and b are both divisible by c.
Case 2: a=2, b=1, c=3, with the result that a+b=3 is divisible by c=3
In this case, a and b are NOT both divisible by c.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statement 2: a-b is divisible by c
Case 1: a=1, b=1, c=1, with the result that a-b=0 is divisible by c=1
In this case, a and b are both divisible by c.
Case 2: a=4, b=1, c=3, with the result that a-b=3 is divisible by c=3
In this case, a and b are NOT both divisible by c.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.
Statements combined:
Case 1: c=3
Let a+b = 9 and a-b = 3, with the result that a+b and a-b are both divisible by c=3.
Adding together a+b = 9 and a-b = 3, we get:
(a+b) + (a-b) = 9 + 3
2a = 12
a = 6.
Since a=6 and a+b = 9, b=3.
In this case, both a=6 and b=3 are divisible by c=3.
Case 2: c=5
Let a+b = 45 and a-b = 15, with the result that a+b and a-b are both divisible by c=5.
Adding together a+b = 45 and a-b = 15, we get:
(a+b) + (a-b) = 45 + 15
2a = 60
a = 30.
Since a=30 and a+b = 45, b=15.
In this case, both a=30 and b=15 are divisible by c=5.
Case 3: c=7
Let a+b = 105 and a-b = 63, with the result that a+b and a-b are both divisible by c=7.
Adding together a+b = 105 and a-b = 63, we get:
(a+b) + (a-b) = 105 + 63
2a = 168
a = 84.
Since a=84 and a+b = 105, b=21.
In this case, both a=84 and b=21 are divisible by c=7.
In every case, a and b are both divisible by c, with the result that the answer to the question stem is YES.
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
-
Mo2men
- Legendary Member
- Posts: 712
- Joined: Fri Sep 25, 2015 4:39 am
- Thanked: 14 times
- Followed by:5 members
Hi,LUANDATO wrote:If a, b and c are positive integers and c is odd, are both a and b divisible by c ?
(1) a + b is divisible by c.
(2) a - b is divisible by c.
The OA is C.
Can any expert help me with this DS question please? Thanks.
What is the source of this question?
