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AMO 2027 Grades 6-7 SET 8 - Self-study

Question 1

Find the next term of the following sequence:

2, 12, 1112, 3112, 132112, ...

A. 332112
B. 422112
C. 432112
D. 1113122112
E. None of the above

Question 2

A survey was given to residents of all 50 states asking if they had earned a bachelor’s degree or higher. The results from 7 of the states are given in the table above. The median percent of residents who earned a bachelor’s degree or higher for all 50 states was 26.95%. What is the difference between the median percent of residents who earned a bachelor’s degree or higher for these 7 states and the median for all 50 states?

Percent of Residents Who Earned a Bachelor’s Degree or Higher
State | Percent of residents
State A | 21.9%
State B | 27.9%
State C | 25.9%
State D | 19.5%
State E | 30.1%
State F | 36.4%
State G | 35.5%

A. 0.05%
B. 0.95%
C. 1.22%
D. 7.45%
E. None of the above

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Question 3

Tank A, when full, holds 555 gallons of water. Tank B, when full, holds 680 gallons of water. If Tank A is only 2/3 full and Tank B is only 2/5 full, how many more gallons of water are needed to fill both tanks to capacity?

Question 4

Two positive integers have a sum of 13. Find the greatest possible product of these two positive integers.

A. 13
B. 24
C. 30
D. 42
E. None of the above

Question 5

Find the smallest value of □ and △ in the equation below.

25 × △ × 18 = □ × 15

Question 6

Find the digits represented by a and b in $\overline{a7889b}$ so that it is divisible by 15.

Question 7

Evaluate:

a) A = 1 + 2 + 3 + 4 + 5 + ... + 2020.

b) B = 2 + 4 + 6 + 8 + ... + 2020.

c) C = 1 + 3 + 5 + 7 + ... + 2019.

d) D = 1 + 2 + 4 + 8 + 16 + 32 + ... + 2048.

e) E = 1 + 3 + 9 + 27 + 81 + ... + 2187.

**Editorial input note:** Enter the values of A, B, C, D, and E in that order, separated by semicolons, with no spaces or thousands separators.

Question 8

A number is a palindrome if its digits are the same when written forward or backward.. For example, the numbers 7, 11111 and 302203 are palindromes. How many integers between 1 and 1003 inclusive are palindromes?

Question 9

The following pattern is made up of matchsticks. How many triangles are there when there are 101 matchsticks?

Question illustration

Question 10

A small community consists of 10 women, each of whom has 3 children. If one woman and one of her children are to be chosen as mother and child of the year, how many different choices are possible?

Question 11

1/12 of Bob’s marbles and 0.75 of Dan’s marbles are equal to 34. If both of them have 88 marbles altogether, how many marbles does each boy have?

**Editorial input note:** Enter Bob’s count followed by Dan’s count, using numbers only. Separate them with a semicolon followed by one space; use no space before the semicolon.

Question 12

The average number of seeds in a package cucumber seed is 25. The number of seeds in the package can vary by three. What are the maximum and minimum number of seeds that could be in a package?

**Editorial input note:** Enter the maximum followed by the minimum, using numbers only. Separate them with a semicolon followed by one space; use no space before the semicolon.

Question 13

The number of English books in a library is 326 more than the number of Chinese books and 634 more than the number of Malay books. The average number of English, Chinese and Malay books in the library is 1080. Find the average number of Chinese and Malay books in the library.

Question 14

The area of triangle ABC is 231 square inches, and point P is marked on side AB so that AP : PB = 3 : 4. What are the areas of triangles APC and BPC?

**Editorial input note:** Enter the areas of APC and BPC in that order, in square inches, using numbers only. Separate them with a semicolon followed by one space; use no space before the semicolon.

Question 15

Kim, Jane and Mark shared a sum of money. Kim’s share was 0.5 of the amount received by Jane and Mark. Jane’s share was 0.25 of the sum of money. If Kim received $\$45$ more than Jane, what was the total amount of money they shared?