AMO 2019 , Prim a7 6 (Grade 6) Contest
Question 1
Find the sum of the digits of the sum below.
93517 + 35179 + 51793
+ 17935 + 79351
Question 2
How many 4-dig it numbers have a digit sum of 5?
Question 3
Four darts are throw n at the dartboard shown. A miss scores 0
points. The four scores are added together. Find the least whole
number score that is impossible to obtain.
Question 4
is twice as old as the
The sum of the ages of three brothers is 32. Toe oldest broth er
3 years. How old is
youngest brother. The ages of the two older brothers differ by
the young est brother?
Que~ ion 5
The second
A locker combination consists of 5 differ ent single digit numbers.
the second; the fourth
numb er is twice the first; the third number is 50% more than
than the fourth . Find
numb er is 1 more than the first; and the fifth numb er is 2 more
the sum of the digits of the combination
Question 6
"5".
There is a meth od to square a numb er that ends with the digit
25 x 25
= 625 because "2" times "2 + 1" = 6 and 5 x 5 = 25.
35 x 35 = 1225 because "3" times "3 + 1" = 12 and 5 x 5 = 25.
45 x 45
= 2025 because "4" times "4 + 1" = 20 and 5 x 5 = 25.
The{ always end with a "25".
If 245 x 245
= 100 x N + 25, the the value of N.
AMO 2019, Prima ry 6 {Grade 6) Contest
Question 7
Jessica has a rectangle made of construction paper. She folds the rectan
gle in half
to form another rectangle. She folds the resulting rectangle in half to form
a 6-cmby-6-cm square. What is the area (in cm2 ) of Jessica's original rectangle?
Question 8
The people going to the event were comprised of couples. No couple could
be split
between 2 buses and no single bus could hold more than 65 people. What
is the
least numbe r of buses needed to get the 600 people to the event with
the same
number of couples on each bus?
Question 9
How many 3-digi t whole numbers have their digits in decreasing order
(reading from
left to right)?
Ques tion 10
I n the multip licatio n AB x BA = A45B, A and B represent differe nt digits,
AB and BA
are 2-digit numbe rs and A45B is a 4-digi t number. If AB less than BA,
what is the 2digit numbe r BA?
Question 11
The place cards shown are folded along the
dotted line so that only a numb er or letter is
visible. Chrissy enters the room and sees all
six place cards, some w ith numbe rs showi ng and some w ith letters
showi ng. The
numbers that she sees add up t o 11. How many differe nt sets of numb
ers are
possible?
AMO 201 9, Prima ry 6 (Gr ad e 6)
Cont.est
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Question 12
Find the ones dig it of the sum bel
ow.
2 10
+ 39
Question 13
If the area of the triangle CAB is
27 an2, find the tot al area {in
cm 2) of the two unshaded triangl
es in the triangle CAB?
L_ _ -
I____ -
C
~
7
Question 14
The 6 faces of the cube shown
at the rig ht are
each painted
black. The cube is the n cut int o
64 smaller identical cubes. Ho w
many of these 64 cubes have bla
ck paint on at least 2 faces?
Question 15
The 5-digit number 4A12B is divisib
le by 99. How many different value
s for 4A12B
are possible?
Question 16
A MOEMS-tile is shaped like an M as
shown. It is a 5 by 5
square with two 4 by 1 rectangles
removed. Jimmy is
playing a game where the object is
to place as many
MOEMS-tiles as possible on a 6 by
42 game board without
an y overlap. What is the maximum
number of tiles Jimmy
can place on this board?
AMU
LU Jr.-'f • • · · ·· - · •
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\. - · - - - - 1
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Question 17
How many digits are there in the second least multiple of 41 whose only digits are
17
Question 18
In the figure, the octagon is made up of two overlapping squares. The overlapping
region is also a square. The larger square has a side length of 6
cm. The smal ler square has one corner at the center of the larger
1
square, and the smaller square has a side length of 4 cm. Find the
I
I
I
I
_ ______,
,____
I
area (in cm 2) of the smallest square possible that can surround the
entire octagon.
Question 19
A football league has 10 teams. During the season, each of the 10 teams plays
exactly 3 games with each of the other teams. What is the total number of games
played?
Question 20
One light flashes every 7 minutes and another light flashes every 2 minutes. If both
lights flash together at 1 PM, how many minutes after 3 PM will both lights flash
together for the first time?
Question 21
A team won first 2 of their 9 games and lost 25% of the remaining games. In
they won
i of all their games. How many games did they lose?
total,
AMO 2019, Primary 6 (Grade 6) Contest
Question 22
In the cryptarithm shown, different letters represent different
digits: If two letters are the same, they represent the same digit.
DUCK
+ DUCK
What is the least value that GOO could be?
GOOSE
Question 23
In the cryptarithm shown, different letters represent different digits. If
TIC
two letters are the same they represent the same digit. When A= 5
TAC
and O = 4, what is the greatest value that WIN could be?
+TOE
WIN
Question 24
A ladder has 7 rungs. An ant is going to climb the ladder, without
B
-
retracing any part of its path, to get to the top rung of the ladder. Given
that the ant starts at A, the middle of the bottom rung, how many
different ways can the ant get to point B, the middle of the top rung?
A
Question 25
In a book, 843 digits were used to number all the pages consecutively, starting with
1. How many pages are in the book?
END OF PAPER