Roosevelt 1927 10K Gold Pin S Arrow Hallmark School ? College ?

Description

Offered for eBay is an old gold pin with the word Roosevelt, and an attached chain with the numbers 27. The backside of Roosevelt portion is hallmarked with 10K, a S with an arrow through it (no feathers on arrow tail). The number 27 portion does not appear to be gold.
I purchased this pin many years back at the estate sale of a doctor in a neighboring Illinois community.  The "Roosevelt" may be the medical school/college he attended. He had many pins affiliated with military and fraternal organizations that I purchased at the time.
All parts in very good used condition. No dents or repairs. Pin has been stored for many years and has not been recently cleaned or polished.
Please see included photos for details.  All included photos are considered a very important part of the description, please view them carefully to determine condition for yourself.
I
tems are from a clean non smoking home.
Please read measurements as some of the photos have been enlarged to show detail.
Please ask questions if you have concerns
.  I am not a professional.
Thank you for looking and have a wonderful day.