On a number line, if AC is 5 and BC is 20. Does C lie between A and B?

a. AB = 25
b. A is to the left of B

correct ans is a.?

i thought e. pls help and explain.

thx
P

Hi poonamchiK,
Okay, please draw a number line. Put points A and C on the line and designate that they are five units apart. To help us illustrate this let's say that A is at 20 on the number line and C is at 25.

We know from B to C is 20 units. So let's look at two options:
a) B is at point 5, A is at point 20, and C is at point 25
OR
b) B is at point 45, C is at point 25, and A is at point 20.
Put both of these potential Bs on your number line so you can see the two options.

How will we know which it is? Well, if we know how far apart AC is we know which option it is.

Statement #1 tells me that AB is 25 spaces apart. Sufficient! We clearly have the second option above, and we know that C is between A and B.

On your grid, keep AD and cross off BCE.

Statement #2 tells me A is to the left of B. Remember BC is 20 units apart and AB is five. Let's let C be 20 and B be 40. Since A has to be to the left of B I need to put C to the left of B. But I could have two scenarios (draw on your number line):
a) A is 25
b) A is 15
So these scenarios do not conclusively show that C is always in the middle of A and B. The first scenario is no and the second is yes. Insufficient.

The answer is A.

_________________
Jamie Nelson
ManhattanGMAT Instructor

there are 4 ways this number line can be drawn

A-------5-------C-------------20--------------B

B----------------15----------------A-------5-------C

B---------------------20-----------------------C-----5-----A

C-----5-----A------------------15------------------B


from a) only the 3rd line fulfils the criteria of AB = 25 and C is in between A and B , sufficient

b) A is to the left of B in lines 1 and 4, we can't decide if C is in between A and B, INSUFFICIENT

hence A is the answer

Thank you atul. I like your diagram which is helpful.

_________________
Jamie Nelson
ManhattanGMAT Instructor