My solution

// Start with a score of zero
var score = 0;

// Ask all the questions, storing the answers in new variables
var q1    = prompt("How many hours are there in a day?");
var q2    = prompt("Pick any number from 1 to 10.");
var q3    = prompt("Type either \"A\" or \"B\"");
var q4    = prompt("Is London the capital of England?");
var q5    = prompt("What is 10 + 10?");

// Check the first answer is correct.
if(parseInt(q1) === 24) {

  // If the answer is correct, add 1 to the score.
  score = score + 1;
}

/*
  Check the second answer is correct.
  We're checking that the answer is both more than (or equal to) 1,
  AND that 10 is more than (or equal to) the answer.

  IF this is true, add 1 to the score variable.
*/
if(parseInt(q2) >= 1 && 10 >= parseInt(q2)) {
  score = score + 1;
}

/*
  Check the third answer is correct.
  We're checking that the answer is simply either "A" OR "B".

  IF this is true, add 1 to the score variable.
*/
if(q3 === "A" || q3 === "B") {
  score = score + 1;
}

/*
  Check the fourth answer is correct.
  We're converting the answer to uppercase, and then allowing for a couple of different answers.

  IF this is true, add 1 to the score variable.
*/
if(q4.toUpperCase() === "YES" || q4.toUpperCase() === "Y" || q4.toUpperCase() === "YES IT IS") {
  score = score + 1;
}

/*
  Check the fifth answer is correct.
  We're looking for an answer of 20 (integer) OR "TWENTY" (string).

  IF this is true, add 1 to the score variable.
*/
if(parseInt(q5) === 20 || q5.toUpperCase() === "TWENTY") {
  score = score + 1;
}

// Create an empty new variable for the crown prize.
var crown;

// IF they didn't score anything (score is zero), write it to the document.
if (score === 0) {
  document.write("<p>Your score was " + score + ". You didn't win anything this time.</p>");

// ELSE if the score WASN'T zero, set the prize based on the score value.
} else {

  // IF the score is less than (or equal to) 2, the crown variable is changed to "Bronze".
  // Don't worry if the score was zero - that would have been handled in the first statement, and we wouldn't have gotten to this one.
  if(score <= 2) {
    crown = "Bronze";

  // ELSE IF the score is less than (or equal to) 4, the crown variable is changed to "Silver".
  } else if(score <= 4) {
    crown = "Silver";

  // ELSE IF the score is equal to 5, the crown variable is changed to "Gold".
  } else if(score === 5) {
    crown = "Gold";
  }

  // Write the winner's message to the document, telling them their final score along with their prize (using the crown variable).
  document.write("<p>Your score was " + score + "! You win the " + crown + " Crown!</p>");
}