Ann and Bob have a large number of sweets which they agree to share according to the following rules. Ann will take one sweet, then Bob will take two sweets and then taking turns, each person takes one more sweet than what the other person just took. When the number of sweets remaining is less than the number that would be taken on that turn, the last person takes all that are left. To their amazement, when they finish, they each have the same number of sweets

They decide to do the sharing again, but this time, they first divide the sweets in two equal piles and then thay repeat the process above with each pile. Ann going first both times. They still finish with the same number of sweets each. 

What is the maximum number of sweets less than 1000 they could have started with ?

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.

        The cause of tooth decay is acid, which is produced by bacteria in the mouth. The acid removes minerals from tooth enamel, allowing tooth decay to begin; the saliva in your mouth encourages remineralization and neutralizes the acid. The rate at which bacteria in the mouth produce acid depends on the amount of plaque on the teeth, the composition of the microbial flora, and whether the bacteria of the plaque have been "primed" by frequent exposure to sugar. To keep your teeth healthy, a regular dental hygiene program should be followed.
        Removing plaque with a toothbrush and dental floss temporarily reduces the numbers of bacteria in the mouth and thus reduces tooth decay. It also makes the surfaces of the teeth more accessible, enabling saliva to neutralize acid and remineralize lesions. If fluoride is present in drinking water when teeth are forming, some fluoride is incorporated into the enamel of the teeth, making them more resistant to attack by acid. Fluoride toothpaste seems to act in another way, by promoting the remineralization of early carious lesions.
In addition to a regular dental hygiene program, a good way to keep your teeth healthy is to reduce your intake of sweet food. The least cavity-causing way to eat sweets is to have them with meals and not between. The number of times you eat sweets rather than the total amount determines how much harmful acid the bacteria in your saliva produce. But the amount of sweets influences the quality of your saliva. Avoid, if you can, sticky sweets that stay in your mouth a long time. Also try to brush and floss your teeth after eating sugary foods. Even rinsing your mouth with water is effective. Whenever possible, eat foods with fiber, such as raw carrot sticks, apples, celery sticks, etc., that scrape off plaque, acting as a toothbrush. Cavities can be greatly reduced if these rules are followed when eating sweets.

According to the passage, all of the following statements about plaque are true EXCEPT ___________.

A. It consists of acid producing bacteria

B. It is not affected by eating sweet

C. It can be removed from teeth by brushing and flossing

D. It reduces the positive effect of saliva

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions from 35 to 42.

        The main cause of tooth decay is acid, which is produced by bacteria in the mouth. The acid removes minerals from tooth enamel, allowing tooth decay to begin; the saliva in your mouth encourages remineralization and neutralizes the acid. The rate at which bacteria in the mouth produce acid depends on the amount of plaque on the teeth, the composition of the microbial flora, and whether the bacteria of the plaque have been “primed” by frequent exposure to sugar. To keep your teeth healthy, a regular dental hygiene program should be followed.

        Removing plaque with a toothbrush and dental floss temporarily reduces the numbers of bacteria in the mouth and thus reduces tooth decay. It also makes the surfaces of the teeth more accessible, enabling saliva to neutralize acid and remineralize lesions. If fluoride is present in drinking water when teeth are forming, some fluoride is incorporated into the enamel of the teeth, making them more resistant to attack by acid. Fluoride toothpaste seems to act in another way, by promoting the remineralization of early carious lesions.

                   In addition to a regular dental hygiene program, a good way to keep your teeth healthy is to reduce your intake of sweet food. The least cavity-causing way to eat sweets is to have them with meals and not between. The number of times you eat sweets rather than the total amount determines how much harmful acid the bacteria in your saliva produce. But the amount of sweets influences the quality of your saliva. Avoid, if you can, sticky sweets that stay in your mouth a long time. Also try to brush and floss your teeth after eating sugary foods. Even rinsing your mouth with water is effective. Whenever possible, eat foods with fiber, such as raw carrot sticks, apples, celery sticks, etc., that scrape off plaque, acting as a toothbrush. Cavities can be greatly reduced if these rules are followed when eating sweets.

According to the passage, all of the following statements about plaque are true EXCEPT _________.

A. It consists of acid producing bacteria

B. It is not affected by eating sweets

C. It can be removed from teeth by brushing and flossing

D. It reduces the positive effect of saliva

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions from 35 to 42.

        The main cause of tooth decay is acid, which is produced by bacteria in the mouth. The acid removes minerals from tooth enamel, allowing tooth decay to begin; the saliva in your mouth encourages remineralization and neutralizes the acid. The rate at which bacteria in the mouth produce acid depends on the amount of plaque on the teeth, the composition of the microbial flora, and whether the bacteria of the plaque have been “primed” by frequent exposure to sugar. To keep your teeth healthy, a regular dental hygiene program should be followed.

        Removing plaque with a toothbrush and dental floss temporarily reduces the numbers of bacteria in the mouth and thus reduces tooth decay. It also makes the surfaces of the teeth more accessible, enabling saliva to neutralize acid and remineralize lesions. If fluoride is present in drinking water when teeth are forming, some fluoride is incorporated into the enamel of the teeth, making them more resistant to attack by acid. Fluoride toothpaste seems to act in another way, by promoting the remineralization of early carious lesions.

                   In addition to a regular dental hygiene program, a good way to keep your teeth healthy is to reduce your intake of sweet food. The least cavity-causing way to eat sweets is to have them with meals and not between. The number of times you eat sweets rather than the total amount determines how much harmful acid the bacteria in your saliva produce. But the amount of sweets influences the quality of your saliva. Avoid, if you can, sticky sweets that stay in your mouth a long time. Also try to brush and floss your teeth after eating sugary foods. Even rinsing your mouth with water is effective. Whenever possible, eat foods with fiber, such as raw carrot sticks, apples, celery sticks, etc., that scrape off plaque, acting as a toothbrush. Cavities can be greatly reduced if these rules are followed when eating sweets.

What can be concluded from the passage about sweets?

A. All sweets should be avoided.

B. Sweets should be eaten with care.

C. It is better to eat sweets a little at a time throughout the day.

D. Sticky sweets are less harmful than other sweets.

Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions.

        The cause of tooth decay is acid, which is produced by bacteria in the mouth. The acid removes minerals from tooth enamel, allowing tooth decay to begin; the saliva in your mouth encourages remineralization and neutralizes the acid. The rate at which bacteria in the mouth produce acid depends on the amount of plaque on the teeth, the composition of the microbial flora, and whether the bacteria of the plaque have been "primed" by frequent exposure to sugar. To keep your teeth healthy, a regular dental hygiene program should be followed.
        Removing plaque with a toothbrush and dental floss temporarily reduces the numbers of bacteria in the mouth and thus reduces tooth decay. It also makes the surfaces of the teeth more accessible, enabling saliva to neutralize acid and remineralize lesions. If fluoride is present in drinking water when teeth are forming, some fluoride is incorporated into the enamel of the teeth, making them more resistant to attack by acid. Fluoride toothpaste seems to act in another way, by promoting the remineralization of early carious lesions.
In addition to a regular dental hygiene program, a good way to keep your teeth healthy is to reduce your intake of sweet food. The least cavity-causing way to eat sweets is to have them with meals and not between. The number of times you eat sweets rather than the total amount determines how much harmful acid the bacteria in your saliva produce. But the amount of sweets influences the quality of your saliva. Avoid, if you can, sticky sweets that stay in your mouth a long time. Also try to brush and floss your teeth after eating sugary foods. Even rinsing your mouth with water is effective. Whenever possible, eat foods with fiber, such as raw carrot sticks, apples, celery sticks, etc., that scrape off plaque, acting as a toothbrush. Cavities can be greatly reduced if these rules are followed when eating sweets.

What can be concluded from the passage about sweets?

A. All sweets should be avoided.

B. Sweets should be eaten with care.

C. It is better to eat sweets a little at a time throughout the day

D. Sticky sweets are less harmful than other sweets.