AMO 2027 Grades 6-7 SET 11 - Self-study

Find the next number in the following sequence:

3, 9, 6, 12, 9, 15, 12, 18, ...

A. 9
B. 12
C. 15
D. 18
E. None of the above

Tom is 6 years older than Nina. Five years from now, the sum of their ages will be 52. How old are both of them?

**Editorial input note:** Enter Tom’s age then Nina’s age, using numbers only, separated by a semicolon with no spaces.

A rectangular tank, 45cm long, 36cm wide was filled with water to the brim. If there was 25.92l of water in the tank, what was its height?

Suppose $p\ast q=2p+2q-pq$, where p and q are positive integers. If $8\ast x=4$, then what is the value of x?

A. 1
B. 2
C. 3
D. 4
E. None of the above

Danzel’s age is 2/9 of his mother’s age. Three years ago, his mother was 42 years old. In how many years’ time will Danzel’s age be 2/7 of his mother’s age?

The ratio of the difference, the sum and the product of two numbers is 1 : 7 : 24. The product of the two numbers is ...

A. 24
B. 48
C. 72
D. 96
E. None of the above

In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.

a) How many students like only tea?

b) How many students like only coffee?

c) How many students like neither tea nor coffee?

d) How many students like only one of tea or coffee?

e) How many students like at least one of the beverages?

**Editorial input note:** Enter the five counts for (a)–(e), in order, separated by semicolons with no spaces.

Study the pattern below. In which will you find the number 300?

Express the following numbers as product of prime numbers.

a) 512

b) 299

c) 1001

d) 2010

The average age of 5 boys is 13 years 6 months. A 16-year-old boy joins them. Find the average age of the 6 boys.

Ellen takes a trip that is y miles long in total, where y > 20. She travels the first 15 miles at an average speed of 30 miles per hour and the rest of the trip at an average speed of 40 miles per hour. Which of the following represents the total time of the trip, in hours?

A. $\frac12+\frac{y-15}{40}$

B. $2+\frac{y-15}{40}$

C. $\frac12+40y-15$

D. $2+40(y-15)$

E. $\frac12+40(y-15)$

Harry has $\$50$. Helen has $\$110$. How much money must Harry give to Helen so that the amount of money Helen has is 3 times more than what Harry has?

The figure below shows a square ABCD with two shaded triangles inside. Given that the total area of the shaded triangles is 242cm², find the length, in cm, of AB.

Susan jogged from home to the sports complex at a constant speed of 6 km/h. 10 minutes later, her sister, Susie, started riding a bicycle along the same route toward the sports complex at a constant speed of 18 km/h. If they arrived at sports complex at the same time, how many seconds does it take Susan to jog from home to the sports complex?

In the quadrilateral AECF below, AB = 3cm, CE = 4cm and CD = AF = 2cm. Find the area (in cm²) of the quadrilateral ABCD.