Solution of SEAMO 2016 Paper A - Southeast Asian Mathematical Olympiads
SEAMO 2016 PAPER A
SEAMO 2016 Paper A No. 1
What is the missing number?
A. 19
B. 23
C. 17
D. 30
E. 21
Solution: Show/Hide
3 + 7 + 11 = 213 + 4 + 5 = 12
5 + 6 + 12 = 23
Answer: B
SEAMO 2016 Paper A No. 2
How many triangles are there in the figure below?
A. 10
B. 11
C. 12
D. 13
E. 14
Solution: Show/Hide
$1\Delta \to 9$$4\Delta \to 3$
$11\Delta \to 1$
Total = 9 + 3 + 1 = 13
Answer: D
SEAMO 2016 Paper A No. 3
Vanessa uses some coins to form a triangle. Each of the 3 corners of the triangle has a coin. There are 6 coins on each side of the triangle. How many coins does Vanessa use to form the triangle?
A. 12
B. 13
C. 14
D. 15
E. 16
Solution: Show/Hide
$6\times 3-3=15$Answer: D
SEAMO 2016 Paper A No. 4
What is the result of $50\times 101$?A. 1010
B. 4350
C. 5050
D. 10100
E. 50500
Solution: Show/Hide
$\begin{align}50\times 101 &= 50\times (100+1) \\ &= 50\times 100+50\times 1 \\ &= 5000+50 \\ &= 5050 \end{align}$Answer: C
SEAMO 2016 Paper A No. 5
The sum of two numbers is 80. The difference between the two numbers is 12. What is the value of the bigger number?A. 32
B. 40
C. 46
D. 48
E. 52
Solution: Show/Hide
$\frac{\begin{align}x+y &= 80 \\ x-y &= 12 \end{align}}{\begin{align}2x &= 92 \\ x &= 46 \end{align}}+$The bigger number is 46.
Answer: C
SEAMO 2016 Paper A No. 6
Find the sum of 1 + 2 + 3 + 4 + … + 18 + 19 + 20
A. 190
B. 195
C. 200
D. 210
E. 220
Solution: Show/Hide
$1+2+3+...+n=\frac{n(n+1)}{2}$$1+2+3+...+20=\frac{20(20+1)}{2}=210$
Answer: D
SEAMO 2016 Paper A No. 7
How many tiles do you need to cover the area shown below?
A. 2
B. 3
C. 4
D. 5
E. 6
Solution: Show/Hide
So, it takes 4 tiles to cover the area.
Answer: C
SEAMO 2016 Paper A No. 8
In which row is the number 47 if the numbers continue?
A. Row A
B. Row B
C. Row C
D. Row D
E. Row E
Solution: Show/Hide
47 divided by 5, remainder 247 in row B
Answer: B
SEAMO 2016 Paper A No. 9
Find the sum of2 + 22 + 222 + 2222 + 22222
A. 24680
B. 24690
C. 24700
D. 24710
E. None of the above
Solution: Show/Hide
Answer: B
SEAMO 2016 Paper A No. 10
What is the least number of colours needed to colour the petals such that no two neighboring petals have the same colour?
A. 2
B. 3
C. 4
D. 5
E. 6
Solution: Show/Hide
Answer: B
SEAMO 2016 Paper A No. 11
The time that Jennifer’s party started and ended is as shown below. How long was her party in minutes?
A. 300
B. 305
C. 310
D. 320
E. 330
Solution: Show/Hide
Started: 10.00 AMEnded: 03.10 PM
5 hours and 10 minutes
= $5\times 60+10=310\,\min $
Answer: C
SEAMO 2016 Paper A No. 12
How many ways are there to put 20 oranges into 3 baskets so that each basket has an even number of oranges?
A. 8
B. 9
C. 10
D. 11
E. None of the above
Solution: Show/Hide
There are 8 ways
Answer: A
SEAMO 2016 Paper A No. 13
Uncle Sam is going to deliver a parcel to point B, beginning his journey from point A. How many ways are there for him to reach there using the directions $\uparrow $ and $\to $ only?
A. 20
B. 21
C. 22
D. 23
E. 24
Solution: Show/Hide
Answer: A
SEAMO 2016 Paper A No. 14
How many dots are there in Figure 5?
A. 12
B. 13
C. 14
D. 15
E. 16
Solution: Show/Hide
Fig. 1: 1Fig. 2: 1 + 2 = 3
Fig. 3: 1 + 2 + 3 = 6
Fig. 5: 1 + 2 + 3 + 4 + 5 = 15
Answer: D
SEAMO 2016 Paper A No. 15
Jane wrote on piece of paper all the whole numbers from 1 to 59.1 2 3 4 5 6 7 8 9 10 11 12 … … 57 58 59
How many digits did she write altogether?
A. 107
B. 109
C. 111
D. 113
E. 115
Solution: Show/Hide
1 – 9 $\to $ 9 digits10 – 59: $\to $ (59 – 10 + 1) $\times $ 2 = 100 digits
Total = 9 + 100 = 109 digits
Answer: B
SEAMO 2016 Paper A No. 16
A file in a bookstore costs 70¢. Akshta has 5 10¢ coins, 3 20¢ coins ad 1 50¢ coin. How many ways can she pay for the file without receiving change?
A. 5
B. 6
C. 7
D. 8
E. None of the above
Solution: Show/Hide
Make a list$50+20$
$50+10+10$
$20+20+20+10$
$20+20+10+10+10$
$20+10+10+10+10+10$
5 ways
Answer: A
SEAMO 2016 Paper A No. 17
What is the missing number?1, 1, 2, 3, 5, 8, 13, ( ), 34, 35, ….
A. 18
B. 19
C. 20
D. 21
E. 22
Solution: Show/Hide
1 + 1 = 21 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
Answer: D
SEAMO 2016 Paper A No. 18
The diagram shows a dartboard. What is the leasts number throws to score 100?
A. 2
B. 3
C. 4
D. 5
E. None of the above
Solution: Show/Hide
38 + 39 + 23 = 100Answer: B
SEAMO 2016 Paper A No. 19
A number is first reduced by 8. The remainder is then multiplied by 5. The product is the increased by 8. The final results is 48. What is the number?A. 14
B. 15
C. 16
D. 17
E. None of the above
Solution: Show/Hide
48 – 8 = 4040 5 = 8
8 + 8 = 16
Answer: C
SEAMO 2016 Paper A No. 20
Given that
What is the value of “
”?A. 12
B. 20
C. 26
D. 28
E. None of the above
Answer: D
SEAMO 2016 Paper A No. 21
What is the maximum number of slices we can get by making 3 straight cuts? Each slice does not have to be equal in size.Gambar
Solution: Show/Hide
GambarAnswer: 7
SEAMO 2016 Paper A No. 22
A farmer has 17 chickens and rabbits. He counts 52 legs in all. How many chickens does he have?Gambar
Solution: Show/Hide
$a+b=17$$2a+4b=52$
$\frac{\begin{align}a+2b &= 26 \\ a+b &= 17 \end{align}}{b=9}-$
$\begin{align}a+b &= 17 \\ a+9 &= 17 \\ a &= 8 \end{align}$
Answer: 8 chickens
SEAMO 2016 Paper A No. 23
Shaun can walk 60 meters in one minute. Tim can walk 55 meters in one minute. If Tim is 35 meters a head of Shaun, how many minutes does Shaun take to catch up with Tim?Solution: Show/Hide
60 – 55 = 5 meters faster every minute$35\div 5$ = 7 minutes
Answer: 7 minutes
SEAMO 2016 Paper A No. 24
Two circles are friendly if they touch each other like the pair shown below:Gambar
How many “friendly pairs” are there in the figure below?
Gambar
Solution: Show/Hide
18 friendly pairsAnswer: 18
SEAMO 2016 Paper A No. 25
There are 5 blue balls, 4 orange balls and 2 yellow balls in a bag. Shella is blindfolded and starts to take the balls out one at a time. At least how many balls must she take out so that, for certain, she ends up with 4 balls of the same colour?Gambar
Solution: Show/Hide
- Suppose Shella draws 3 blue, 3 orange, and 2 yellow. That's 8 balls total, and she doesn't yet have 4 of any color.
- On the next (9th) ball, no matter what color it is, she will end up with 4 balls of that color.
Answer: 9
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