A, B, C are points on a line. M is the midpoint of AB. N is the midpoi

Question

A, B, C are points on a line (in that order). M is the midpoint of AB. N is the midpoint of BC. AB = 3BC. What is AB:MN?

A. 3:1
B. 2:1
C. 3:2
D. 2:3
E. 1:2

Source is handout by Mitul Gada's classes.

pushpitkc · Answer

Consider the number line.
Since M is the mid point of AB, AM = BM = x
Similarly, since N is the mid point BC, BN = CN = y

It has been given that AB = 3BC. If BC = 2, AB = 6
Therefore, we can calculate value of x,y
x - 3 and y - 1

MN = BM + BN = x + y = 3 + 1 = 4
AB:MN = 6:4 = 3:2

Hope that helps you!

generis · Answer

Does a verifiable source tell you that those are the two options for the answer?

Does the problem specify that the points are in alphabetical order?

I get two answers. I used the same numbers as  pushpitkc  for one version. Here they are on the number line, where A______B__C

Let AB = 6
Then BC = 2
AC= 8
M = 3
N = on number line is 7

A________M_________B__N__C
0________3__________6__7__8

AB = 6
MN = (7-3) = 4
Ratio is 6:4 or 3:2

Different order: A_______C___B

Let AB = 18
Put C between A and B
BC = length = 6
M = 9
Number line values: 
C is 12, N is 15

A_____________M_______C___N___B
0_____________9_______12__15__18

MN = 15 - 9 = 6
AB = 18
AB:MN --> 18:6 = 3:1

Is either of those answers a choice?

Farina · Answer

i have got 3:1 answer, not sure if it is correct?

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