RedDragonl

Let's define the problem step by step to solve for the greatest possible percentage of questions Amy could have answered correctly.

### Solution By Steps

**Step 1: Analyze Amy's performance**

- Amy answered the first three questions wrong, but she answered all the other questions correctly.

- Therefore, the first three questions are incorrect for Amy, and all subsequent questions (starting from question 4) are correct.

**Step 2: Analyze Scott's performance**

- Scott answered exactly two questions wrong: the last question and the question before the last correct answer.

- This means Scott answered the second-to-last question wrong and also the last question wrong.

- All other 26 questions before these two wrong answers were correct.

**Step 3: Determine the overlap in wrong answers**

- We are told that Amy and Scott were both incorrect on exactly one common question.

- From Amy’s incorrect answers (questions 1, 2, and 3) and Scott’s incorrect answers (the last two questions), the only possible overlap occurs if Amy’s third wrong answer matches Scott's second wrong answer (i.e., the second-to-last question of the test).

- Thus, Amy's third wrong answer is the second-to-last question, which means she got question number \( n-1 \) wrong.

**Step 4: Calculate the total number of questions**

- Scott answered the last 26 questions before his last wrong answer correctly, and he got the last two questions wrong.

- Therefore, the total number of questions on the test is \( 26 + 2 = 28 \).

**Step 5: Count Amy's correct answers**

- Amy answered the first three questions wrong (questions 1, 2, and 3).

- Additionally, she also answered the second-to-last question wrong (question 27).

- Hence, Amy answered \( 28 - 4 = 24 \) questions correctly.

**Step 6: Calculate the greatest possible percentage of correct answers**

- Amy answered 24 questions correctly out of 28 total questions.

- The percentage of correct answers is calculated as:

\[
\text{Percentage} = \left( \frac{24}{28} \right) \times 100 = 85.71\%
\]

### Final Answer

The greatest possible percentage of the total number of questions that Amy could have answered correctly is **85.71%**.

Analyzing the Problem

We have a quadrilateral BCED with extended sides meeting at point A. We're given several side lengths and need to find DE.

Solution Approach

To find DE, we'll need to break down the quadrilateral into triangles and use similar triangles to establish proportions.

Breaking Down the Quadrilateral

Let's divide quadrilateral BCED into two triangles: Triangle ABC and Triangle ADE.

Using Similar Triangles

We can see that triangle ABC and triangle ADE share angle A. Additionally, angle ABC is congruent to angle ADE (alternate interior angles since BD is parallel to AE). Therefore, triangles ABC and ADE are similar.

Setting up Proportions

Since the triangles are similar, their corresponding sides are proportional. We can set up the following proportion:

AB / BD = AC / DE

Substituting Values and Solving

We know AB = 3, BD = 18, and AC = 7. Substituting these values into the proportion, we get:

3 / 18 = 7 / DE

Cross-multiplying, we get:

3 * DE = 18 * 7

DE = (18 * 7) / 3

DE = 42

Therefore, DE = 42.

The answer is phi(1200) = 600.

The answer is phi(191) = 172.

The smallest number that works is 16.

The number we're looking at is interesting because it can be expressed as a difference of squares:

1,005,010,010,005,001 = (1005^2) - (1^2)

We can use a property of difference of squares to our advantage: a^2 - b^2 = (a + b)(a - b). In this case:

(1005^2) - (1^2) = (1005 + 1)(1005 - 1) = 1006 * 1004

Now, 1006 is even (because the last digit is 6), so it's not prime. We can focus on 1004.

Looking closely at 1004, we see that the last two digits are 04, which is a multiple of 4. Therefore, 1004 is also even and not prime.

However, 1004 can be further factored: 1004 = 2 * 2 * 251. Here, 251 is odd, and a quick primality check reveals it is a prime number.

Therefore, the largest prime factor of 1,005,010,010,005,001 is 251.

The answer to the problem is sqrt(17).

For

x+y+z=17, 

xy+xz+yz=94,

xyz=168

you can look at all the factors of 168