ABACUS International Math Challenge
for
3rd and 4th graders
November, 2007
A.601. Hen Samantha had 10 more baby chickens
than her neighbor, Hen Diana. But last night 5 eggs hatched at both households,
and now Samantha has twice as many baby chickens as Diana. How many baby
chickens does each hen have?
A.602. In a car race the # 5 car started
the race from the one before last place. It passed 7 cars in the first part
of the course, but on a downhill section 2 cars passed it. In the next section
of the race it passes 8 cars, but then it slid out in turn and 4 cars passed
it. This way it finished in 9th place. How many cars started the race if
all of them finished it?
A.603. A fifth of the course of the car
race is a narrow road in the forest, a third of which ( an 8 km long section)
is very muddy. How long is the course?
A.604. The final result of the car race
was that Adam, Tom and Dave finished in the first three places in some order.
One of them drove a Honda, the other drove a Ford, and the third drove a
Renault racing car. We have the following information about them:
- Tom's friend, who drove a Ford, finished in third place.
- The one who drove the Honda did not win the race.
- Adam never set in a Renault or a Honda.
- Tom did not race in a Honda.
Find out the finishing places and the types of cars of these three guys.
A.605. When you multiply half of a number
by the third of it, you get 54. What number are we talking about?
A.606. On the night section of the car
race in a very dangerous part, at and between the 78th and the 85th kilometer
stones, they posted signal poles at every 20 meters on both sides of the
road. How many signal poles did they post?
A.607. In average a race car uses 12 liters
of gasoline on every 50 km. On a difficult road that is curvy or on an uphill,
the cars use 1/3 more. How many liters of gasoline do they use on a 450-km
course of which 2/3 are difficult?
A.608. The organizers made a course more
difficult by changing the surface of the road. 1/3 of the course is rocky,
half of it is dirt road, and the last 12 km is in deep sand. How long is
this course?
Please, send your solutions to: