IMac 27-inch, Late 2013,Memory 16 GB 1600 MHz DDR3,Software OS X 10.9.2 (13C1021)

There are 4 RAM slots. 2 are taken and 2 are free. To upgrade to the maximum amount of RAM you need to place 2 sticks of 4 GB on the free slots.
DDR3 PC3-12800 • CL=11 • UNBUFFERED • NON-ECC • DDR3-1600 • 1.35V • 256MEG X 64 •

If you have difficulty doing it and you find yourself in London you can visit us https://www.computerbeing.co.uk/

Go to your Mail program, then in the top left corner, click on "Mail" then "Preferences" that will bring up your email accounts. Check the settings there to make sure everything is correct.

check the display section if the os reloading fails inbetween...

Memory


Type DDR3 SDRAM (non-ECC memory only)

Speed 1066 MHz, 1333 MHz

Connectors four

Capacity 1 GB, 2 GB, or 4 GB

Minimum memory 1 GB

Maximum memory 16 GB

see:http://h20566.www2.hp.com/portal/site/hpsc/template.PAGE/public/kb/docDisplay/?sp4ts.oid=5295969&spf_p.tpst=kbDocDisplay&spf_p.prp_kbDocDisplay=wsrp-navigationalState%3DdocId%253Demr_na-c03536888-9%257CdocLocale%253D%257CcalledBy%253D&javax.portlet.begCacheTok=com.vignette.cachetoken&javax.portlet.endCacheTok=com.vignette.cachetoken

probably no, 32 bit systems have an under 4Gb limit. looks like 2 memory slots 1,2,4 and 8Gb supported.

Memory upgrade information

• Dual channel memory architecture
  
• Two 240-pin DDR3 DIMM sockets
  
• Supports DDR3 DIMMs
  
  • PC3-10600 (1333 MHz)
    
  • PC3-12800 (1600 MHz)
    
• Non-ECC memory only, unbuffered
  
• Supports 1 GB, 2 GB, 4 GB and 8 GB DIMMs
  
• Supports up to 4 GB on 32-bit* systems
  
• Supports up to 16 GB on 64-bit systems
  

You may have tried to put too much memory (RAM) onto it.
That models maximum spec is:
Memory upgrade information:

• Four DDR3 DIMM (240-pin) sockets
  
• Supports 1 GB, 2 GB, and 4 GB DDR3 DIMMs per socket
  
• Supports Dual channel memory architecture
  
• Supported speeds
  
  • PC3-10600 @ 1333 MHz*
    
  • PC3-8500 @ 1066 MHz
    *DDR3-1333 modules run at 1066 MHz if three or more modules are installed.
    
• Non-ECC memory only, unbuffered
  
• Supports up to 16 GB on 64-bit PCs (DIMMs run at DDR3-1066)
  
• Supports up to 4 GB on 32-bit PCs
  

You can find the specs and troubleshooting help files here

This motherboard uses DDR3-SDRAM, ECC and non-ECC, unbuffered, PC3-10600(1333mhz) or PC3-8500(1066mhz), dual channel architecture (two sticks at a time), and a max memory of 8Gs.
This are the specs for your ram: 4GB 1600MHz DDR3 Non-ECC
(Kit of 2) Intel XMP HyperX = DDR3-1600
Default = DDR3-1333 CL9-9-9-27
CL9-9-9 1.65V
1.5V
In other words, Yes! This should work just fine. The ram will just run at its default speed of 1333mhz.

Manufacturer Part: 55Y3706

2 GB (installed) / 4 GB (max) - DDR3 SDRAM - 1066 MHz - PC3-8500 ( 1 x 2 GB )

So you need DDR3 SDRAM at 1066Nhz PC3-8500

If you are running 64bit Software then upgrade to 8GB (2 X 4GB sticks) otherwise your OS may not recognise any more that 2 MB

LenovoMemory - 1 GB - SO DIMM 204-pin - DDR3 - 1066 MHz / PC3-8500 - 1.5 V - unbuffered - non-ECC Manufacturer Part: 55Y3706

Memory
-4 x DIMM, Max. 16 GB, DDR3 1800(O.C.)/1600(O.C.)/1333/1066 ECC,Non-ECC,Un-buffered Memory
Memory- Dual Channel memory architecture

*Due to OS limitation, when installing total memory of 4GB capacity or more, Windows® 32-bit operation system may only recognize less than 3GB. Install a 64-bit WindowsWindows® OS when you want to install 4GB or more memory on the motherboard.
Memory- *Refer to www.asus.com or user manual for Memory QVL (Qualify Vendor List)

It should be, it says this about your memory support.

4 x 1.5V DDR3 DIMM sockets supporting up to 16 GB of system memory

DDR3 2200+/1800/1600/1333/1066/800 MHz

Here is a list of compatible memory for that motherboard
http://memoryselector.cnetchannel.com/tigerdirect/results.asp?hvhBlBE0fe0AED