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Lizzie gets 20% on a 10-problem test, 80% on a 20-problem test and 90% on a 30− problem test. If the three tests are combined into one 60-problem test, what percentage is her overall score?

A number is called a palindrome if it reads the same backwards as forwards. For example, 13931 is a palindrome. What is the difference between the least 5-digit palindrome number and the greatest 6-digit palindrome number?

1 Answer

3 votes

Answer:

Question #1: 75%

Question #2: 989998

Explanation:

Question #1: Lizzie's overall score:

First, we can calculate Lizzie's overall score

Let's calculate Lizzie's overall score first:

1. Lizzie's score on the 10-problem test:

Percentage = 20%

Number of correct answers = 20% of 10 = 0.2 * 10 = 2

Thus, Lizzie answered 2 our of 10 questions correctly.

2. Lizzie's score on the 20-problem test:

Percentage = 80%

Number of correct answers = 80% of 20 = 0.8 * 20 = 16

Thus, Lizzie answered 16 out of 20 questions correctly.

3. Lizzie's score on the 30-problem test:

Percentage = 90%

Number of correct answers = 90% of 30 = 0.9 * 30 = 27

Thus, Lizzies answered 27 out of 90 questions correctly.

Now, let's add the number of correct answers for all three tests:

2 + 16 + 27 = 45.

The total number of problems in the combined test is 60, which means Lizzie got 45 out of 60 problems correct overall

Now, we can calculate the percentage score using the following formula:

Overall Percentage = (Number of correct answers / Total number of problems) * 100

Overall Percentage = (45 / 60) * 100 = 75%

Therefore, Lizzie's overall score is 75%.

Question #2: Difference between the least 5-digit palindrome number and the greatest 6-digit palindrome number:

Now let's find the difference between the least 5-digit palindrome number and the greatest 6-digit palindrome number:

The least 5-digit palindrome number is 10,001 (reads the same backward and forward).

The greatest 6-digit palindrome number is 999,999 (the highest possible palindrome number with six digits).

Difference = 999,999 - 10,001 = 989998

Therefore, the difference between the least 5-digit palindrome number and the greatest 6-digit palindrome number is 989998.

User E LaRoche
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