If 2a - b = 3c, where a, b, and c are integers, which of the following could be the average (arithmetic mean) of a and b?
a. -2
b. 0
c. 1
d. 10
e. 12
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Average of a,b
This topic has expert replies
-
debmalya_dutta
- Master | Next Rank: 500 Posts
- Posts: 385
- Joined: Sun Jul 12, 2009 10:16 pm
- Thanked: 29 times
- Followed by:2 members
- GMAT Score:710
a+b / 2 = m
a+b=2m
a= 3c+b / 2
substitute a into above equation
3c+b / 2 + 2b/2= 2m
= 3c+3b / 2 = 2m
= c+b=4m/3
therefore m has to be divisible by 3
only number among answer choices that contains factor of 3 is 12
answer e
a+b=2m
a= 3c+b / 2
substitute a into above equation
3c+b / 2 + 2b/2= 2m
= 3c+3b / 2 = 2m
= c+b=4m/3
therefore m has to be divisible by 3
only number among answer choices that contains factor of 3 is 12
answer e
-
hardik.jadeja
- Legendary Member
- Posts: 535
- Joined: Fri Jun 08, 2007 2:12 am
- Thanked: 87 times
- Followed by:5 members
- GMAT Score:730
0 is also one of the possible answer.
2a - b = 3c
b = 2a - 3c
a + b = 3a - 3c ......... (adding a to both sides)
(a + b)/2 = (3/2) (a - c) ........... (diving both sides by 2)
Now if a = c then a = -b and in that case arithmetic mean is 0
Correct me if i am missing something. What is the source of this problem?
2a - b = 3c
b = 2a - 3c
a + b = 3a - 3c ......... (adding a to both sides)
(a + b)/2 = (3/2) (a - c) ........... (diving both sides by 2)
Now if a = c then a = -b and in that case arithmetic mean is 0
Correct me if i am missing something. What is the source of this problem?
