SOAL-SOAL LATIHAN OLIMPIADE MATEMATIKA DALAM BAHASA INGGRIS - Arsip MKKS

1. F i n d t h e l e a s t common m u l t i p l e o f t h e f i r s t 8 n a t u r a l numbers.
2. Number t h e 8 corners o f a cube from 1 t o 8 so t h a t t h e sum o f any
f o u r numbers a t t h e corners o f each f a c e i s 18.

3. The value o f a machine declines 10% o f i t s c u r r e n t value f o r each
year o f use. I f t h e o r i g i n a l c o s t o f t h e machine was $5,000, a f t e r
a minimum o f how many f u l l years w i l l i t s value be l e s s than 50% o f
i t s o r i g i n a l value?

4. Two numbers are r e l a t i v e l y prime i f t h e i r g r e a t e s t common f a c t o r i s 1.
F i n d t h e number o f n a t u r a l numbers g r e a t e r than 1 b u t l e s s than 51
which are r e l a t i v e l y prime t o 51.
5. The l a r g e s t c i r c l e p o s s i b l e i s c u t from a square piece o f paper.
The l a r g e s t square p o s s i b l e i s then c u t from t h i s c i r c u l a r piece.
F i n d t h e r a t i o o f t h e area o f t h e smaller square t o t h e area o f
t h e l a r g e r square.
6. A t an i n t e r n a t i o n a l c o m p e t i t i o n among 24 students, t h r e e languages
were spoken (French, Spanish, and E n g l i s h ) . E i g h t o f t h e students
who spoke E n g l i s h d i d n o t speak Spanish. E i g h t o f t h e students who
spoke Spanish d i d n o t speak English. O f t h e e i g h t students who
spoke French, t h r e e spoke o n l y French. S i x spoke o n l y E n g l i s h and

t h e r e was o n l y one student a t t h e c o m p e t i t i o n who spoke a l l t h r e e
languages. How many students spoke Spanish and E n g l i s h b u t n o t
French?
7. We know t h a t

3
fi
=

2

since

23 = 8.

Compute f

i

8

.

8. F i n d t h e g r e a t e s t odd f a c t o r o f 7992.

9. Two gardeners are each given 100 f e e t o f fence and a r e asked
t o p l a n a r e c t a n g u l a r garden enclosed by t h e fence t h a t uses
a l l o f t h e fence. I f t h e dimensions must be whole numbers
and g r e a t e r than 20 f e e t , what i s t h e g r e a t e s t p o s s i b l e
d i f f e r e n c e between t h e areas o f t h e r e c t a n g u l a r gardens?
10. On t h e p l a n e t Urp most years have 180 days (18 months o f 10
days each). Once every 7 years, however, an Urp year contains
181 days ( t h e t h i r d month contains 11 days). Each Urp week i s
5 days long. The days o f t h e week, i n order o f occurrence, are
Oneday, Twoday, Threeday, Fourday and Fiveday. Duorps was born
on a Fourday, on t h e f i r s t day o f t h e f o u r t h month i n a 181-day
year. On what day o f t h e week was Duorps' 25th b i r t h d a y ?