Full quant section #1 Q:18

GRE Quant Problem Solving
1

I did the Full quant section for practice and found Q 18 a bit boggling, saw the video explanation were a student answered how she solved it but it didn’t really understand it.

q18 gregmat quant
q18 gregmat quant1836×1010 103 KB

What i don’t really get is how she directly implied BM = 3x and MC= X, then she used that same ratio for the other side.

Any light i can get for this is greatly appreciated.

2

hi, well I am sure this method is confusing a bit i would suggest u to go for alternative method which is choosing numbers.

where they said BM=3CM so lets assume cm =3 and so BM will be 9 and since its similar triangle we can see the change of difference from one side and use it for other side .By doing so we can find NC is 2.5 so the total length of AC will be 7.5+2.5=10.

Do let me know if u have any doubt above

3

By Side Splitter Theorem, we can say " if a line is parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally. "

Thus, we get :

\frac{CN}{NA}= \frac{CM}{MB}

Also, we know BM = 3CM and NA = 7.5,

\frac{CN}{7.5}= \frac{CM}{3 \cdot CM} => \frac{CN}{7.5}= \frac{\cancel{CM}}{3 \cdot \cancel{CM}}
\frac{CN}{7.5} = \frac{1}{3} \text{ or } CN = 7.5/3=2.5
1 Like
4

\Delta CMN and \Delta CBA are similar.

5

Thanks!! your post made me realize that the “CM” in BM = 3CM was not talking about centimeters. I know they usually don’t talk about units in this types of questions but i got confused.

This can be a trap for metric system users lol.

6

I also thought this was centimetres, thanks for pointing it out, was really stuck on this