A good way to minimize size is when exporting as pdf (or within Acrobat) to make it only compatible with newer versions of pdf readers.   

See this screenshot for where that option is located:

http://www.greenerprinter.com/grp/b-images/PDFPrep_InDesign3.gif

I think by default it is compatible with versions of acrobat from many years ago.  A quick google will tell you when versions came out and you can make the decision for how far back you think you should go.

Hey, I have exactly the same problem. I found out that what makes my file heavy is vector linework from Illustrator and pdfs. On the other hand vectors look sharp and nice, unlike bitmap jpgs. Do you know if there is some solution which would somehow keep the small size and nice linework?

By the way- I was told that the best way of exporting&small size is Pdf - Interactive- that's what I am doing already, maybe it will help someone too

For vector linework in Illustrator:

Keep your artboard sizes small. If your diagrams are too big, scale them down and adjust your lineweights accordingly. Save all the diagrams as separate PDFs and choose "Smallest File Size" and disable all editing options. Link these to your InDesign file. Should shave off a few MBs.

For raster images in Photoshop:

Always start off with a ppi of 300. At that pixel density, you don't have to go beyond a resolution of 3500 x 2500 even for a full size A4 image. For smaller images which won't cover your whole page, reduce your resolution but preserve the ppi. While saving, save it as JPG and choose a quality between 8-12, depending on the density of information. If it's just flat colors, you can even get away with 6.

InDesign:

When you're saving your final PDF, choose "Smallest File Size" and in the Compression tab to the left, downsample anything above 225 dpi to 175 dpi for online PDFs. Keep Compatibility at Acrobat 1.7 or newer. If you're printing, preserve the 300 dpi.

Use the print function to create the PDF rather than the export function. This should help.

thanks guys, I'll try those things out

Me too guys! Sounds like a good start!

For all of you saying that I should export my file as a compatible file with Acrobat 1.7 or newer, are we sure that the admissions' computers have adobe 1.7 or newer? :)

Or are we going to end up with a small pdf, what won't be able to be seen? 

The original version 1.7 of the PDF format was released November 2006.

Ok good to know Spoons! Thank you all for your support! Hope the best to fellow applicants