Undertale – Is Monster Kid’s Sister Older or Younger?

There's no definitive in-game/canonical evidence as to which brother is older.

It's obvious that they both care about each other, however the Wiki entries for Sans and Papyrus just list them as 'brothers', and everything in-game pointing one of them being the older sibling is circumstantial at best - most likely played this way so as to leave it up to the player's own interpretation/head-canon.

Some parts of the story points to Sans being younger:

• Papyrus encourages & cajoles Sans for his laziness:

  IT'S BEEN EIGHT DAYS AND YOU STILL HAVEN'T... RECALIBRATED. YOUR. PUZZLES! ... YOU GET LAZIER AND LAZIER EVERY DAY!!!
  _{- Papyrus}

• Sans admires his brother

  my brother's a real star....

• Who encouraged him to take a job as a sentry:

  ...he's the person who pushed me to get this sentry job.
  _{- Sans}

Other pieces of the story point to Sans being older:

• Sans has a 'real' job & takes care of his brother/pays the bills
• Sans reads Papyrus bedtime stories and gives him presents

  Sans cares for and admires his brother. He reads him bedtime stories and gives him presents under the identity of Santa.
  _{- Undertale Wiki}

There are some other fan-theories & explanations out there, for example, that they are as old as the creation dates of the fonts the characters are based on: Comic Sans and Papyrus, but again, as these are just fan-theories and aren't confirmed in-game in any way.

Finally, it's worth mentioning that the developer of the game - Toby Fox - has also previously tweeted that Papyrus might use the Japanese word 'Aniki' (i.e. 'Older Brother' or 'Superior' in Japanese):

Papyrus would definitely use "aniki." i think. what's your take.
_{- Toby Fox. September 10, 2015 (Internet Archive)}

Again, this isn't covered in-game and Toby has since deleted this statement. Thus it shouldn't be interpreted as 'Word of God' (TV Tropes). Even if the statement hadn't been recanted, there is still enough evidence to point either way in game, thus it would still be open to interpretation.

Until (and if) we get another source of official canon material (such as a second game, comic, movie etc) that builds upon or embellishes the story, we don't have the evidence to say which brother is older than the other. It's ultimately up to you to decide.

The problem is that the more monsters you kill, the less frequent the random encounters are. This can make the last couple very tedious. However, there is a cool hack/trick that I have found to help you get the last one.

1. Go to an area that monsters definitely can spawn in. They usually don't spawn in puzzle rooms, so just go somewhere that you remember having a random encounter in.

2. If you are in fullscreen, hit F4 to go back to windowed mode.

3. Hold down an arrow key. Any arrow key, doesn't really matter, but don't walk into a wall or an object.

4. While you are still holding down the arrow key, press alt-tab. This will cause the game to lose focus. However, Frisk will continue to walk without actually moving. The game registers this as you walking.

5. Watch youtube until a random encounter happens. This shouldn't take more than 2-3 minutes at most.

This doesn't make grinding very much faster, but it definitely makes it less tedious.