Olimpiade Matematika (IMSO/IMC)

The sum of the numbers A, B and C is 390. Given that A is 3 times of B and A is one third of C, find the value of C.

• 90

• 130

• 260

• 270

A palindrome is a number which reads the same backwards as forwards. A car odometer read 26962 km. After two hours driving the odometer showed the next palindrome. What was the average speed of the car, in km per hour?

• 55

• 57

• 65

• 75

Class A has 10 students and class B has 15 students. In a test, the average grade for class A is 60, and the average grade for class B is 66. A new student writes the test in the office. If he is put in class A, its average will become 62. If he is put in class B, what will its average become?

• 66

• 67

• 76

• 77

Two years ago, Steve was three times as old as Bill, and in three years he will be twice as old as Bill. Find the sum of their ages.

• 16

• 20

• 24

• 28

Dad walks at 6 km per hour when alone and mom walks at 4 km per hour when alone. When they walk together, they compromise at 5 km per hour. They leave home to go to the store 1 km away. Six minutes after leaving home, dad has to return for the shopping list while mom goes on. How long does mom have to wait in the store, in minutes, before dad arrives with the shopping list?

• 6,5

• 7,3

• 7,5

• 7,7

A says, ``I ate it.''

B says, ``The one who ate it was either C or D.''

C says, ``Exactly one of A and B is lying.''

D says, ``C did not eat it.''

If exactly two of them are lying, who ate it?

• A

• B

• C

• D

Bag A has twice the number of beads in bag B. 12% of beads in bag A are removed and transferred to bag C. 20% of beads in bag B are removed and transferred to bag C. After removing and transferring beads, there are now 488 beads in bag C which is 22% more than the original number of beads in bag C. How many beads were there in the bag A at the beginning?

• 240

• 300

• 360

• 400

City P is 625 kilometers from City Q. M departed from City P at 5:30 a.m. travelling at 100 kilometers per hour, and arrived at City Q. Fifteen minutes after M left, N departed from City Q and arrived at City P travelling at 80

kilometers per hour. At what time did M and N meet together?

• 8.05

• 8.55

• 9.05

• 9.15

Alan has 80% more stamps than Billy. Billy has 3/5 of the number of Charlie's stamps. If Billy gave 150 stamps to Charlie, then Charlie would now have three times the number of Billy’s remaining stamps. What is the total number of stamps they have altogether?

• 1800

• 2000

• 2010

• 2020

X is a 2-digit number whose value is 13/4 of the sum of its digits. If 36 is added to X, the result will contain the same digits but in reverse order. Find X.

• 24

• 26

• 28

• 32