Finding lost partitions

Question

I am resetting my sister's MBP late 2010 to factory defaults. It's all backed up. I'm reinstalling from the recovery partition currently. Before I started working on it today, it had the very descriptive problem: "wouldn't boot."

I previously had installed Ubuntu on this since she wanted to try it, and it was run as a dual boot system for about a year. Now, the disk space needs to be brought back into Mac, since the HDD was almost full. To top it off, Grub/rEFInd seem to have gotten lost at some point along the way during an upgrade, so Ubuntu is functionally gone anyway.

I did some research, took it into safemode, which did boot, backed up, and then booted into recovery (command + r), opened up disk utility, formatted, and clicked the - button on the three Linux partitions (boot, swap, and file system, I believe).

Now, when I look in Disk Utility, on my 320GB HDD I see a ~200GB Macintosh HD (which I have erased and formatted), a Recovery HD, and there's over 100GB missing. There's no other partitions, and I can't expand the Macintosh HD partition.

Immediately after removing the partitions, I had a Partition Table error when I ran Verify on the HDD. Repair kept failing, so I rebooted into recovery mode and ran repair. Now there's no error, but still no drives.

When click on the HDD and go to the Partition tab, I can choose 1 Partition, which does correctly show 320GB. Otherwise, I can't find the lost 100GB. I tried enabling debug mode (something like defaults write com.apple.DiskUtility DUDebugMenuEnabled 1) and checking making everything visible, but the partitions still are not visible.

My questions:

1. Is it possible to reinstall without the disks (not my machine, no idea where the disk is) if I change the drive to 1 partition and format it? Am I going to be able to do this from Recovery Tools?
2. Following Unable to increase partition size with subsequent blocking partition, I believe after reinstalling OSX I will be able to use a 3rd Party utility, probably gParted, to move stuff around on the drive. Can I use gParted from an Ubuntu live disk for this?
3. Is there a way to make the partitions reappear is disk utility so that I can at least format them?

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After reinstall finished:

Edit: Per the comment, here's the output of sudo gpt -r show /dev/disk0

      start       size  index  contents
          0          1         PMBR
          1          1         Pri GPT header
          2         32         Pri GPT table
         34          6         
         40     409600      1  GPT part - C12A7328-F81F-11D2-BA4B-00A0C93EC93B
     409640  423215696      2  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
  423625336    1269544      3  GPT part - 426F6F74-0000-11AA-AA11-00306543ECAC
  424894880    1269536      4  GPT part - 48465300-0000-11AA-AA11-00306543ECAC
  426164416  198977999         
  625142415         32         Sec GPT table
  625142447          1         Sec GPT header

And a screenshot of DiskUtility's output. As you can see, my 320.07GB HDD has a partition just shy of 217GB Macintosh HD. The Recovery HD partition is 654MB, leaving 102GB lost.

Answer 1

As the gpt command reveals you have two recovery partitions (and a lot of unallocated disk space after partition 4):

• partition 3 with a wrong size (1269544 blocks) and a correct partition type (426F6F74-0000-11AA-AA11-00306543ECAC)
• partition 4 with the correct size (1269536 blocks) and a wrong partition type & visibility

The second Recovery HD (slightly visible below the Macintosh HD in your screenshot) is blocking the expansion of the volume Macintosh HD. The easiest procedure to solve your problem is to boot to Internet Recovery Mode and completely reformat the internal drive and reinstall OS X:

According to this Apple support document your MacBook Pro (Mid 2010)* can be upgraded to use Internet Recovery after applying a firmware upgrade. Since the firmware upgrade was published in 2012 I assume that it was applied already.

So to answer the first part of your first question: After booting to Internet Recovery Mode you may install Mac OS X Lion. In Internet Recovery Mode usually the Mac OS X the Mac originally was shipped with will be installed. For Snow Leopard Macs like your MBP Mid 2010 Mac OS X Lion will be installed.

To initiate the Internet Recovery Mode restart your Mac and press alt cmd R.
The prerequisites for an Internet Recovery are listed here: Recovery/Internet Recovery. In a few words you need the latest firmware update installed, either ethernet or WLAN (WPA/WPA2) and a router with DHCP activated for a successful internet recovery.
On a 50 Mbps-line it takes about 4 min (presenting a small animated globe) to boot into the Recovery Netboot image which is loaded from an Apple server.

After booting successfully open Disk Utility and repartition your disk to 1 JHFS+ partition with a GUID partition table. Quit Disk Utility and start 'Reinstall OS X'. Depending on your internet connection the reinstall will take some time.

The second part of question 1 as well as the questions 2 and 3 are obsolete after following the above instructions and successfully reinstalling Mac OS X Lion.

*: A MacBook Pro (Late 2010) never was produced/sold, so I assume it's a MacBook Pro (Mid 2010)