44.
2013 MATH Olympiad [Grade1]
45. ① 4=1+3 , ② 6=1+5 , ④ 9=1+3+5【Sol】46.31. 12+5+4=21
32. 17-9=8→ 233. 21-9=12→ 5 ⇒ 1034. 15-4-5=6→ 335. 14+12=26
36. 82+45=12737. 235+223=458
47.38. 257-124=13339. 39×2=7840. 128×5=640
41.
48.42. 1, 2, 3 - 1, 2, 2, 3 - 1, 2, 2, ②, 343. Box-shaped figures
3, 4, 2, 11 2 3 4
No. Answer No. Answer No. Answer No. Answer No. Answer1 27 11 17 21 2 31 21 41 6
2 27 12 10 22 609 32 8 42 2
3 7 13 4 23 485 33 12 43 2
4 8 14 3 24 26 34 6 44 3, 4, 2, 1
5 9 15 18 25 184 35 26 45 ③
6 3 16 20 26 2,880 36 127 46 10
7 16 17 141 27 1,872 37 458 47
8 14 18 134 28 8 38 133 48 A=13, B=16
9 18 19 385 29 9 39 78 49 ②
10 17 20 863 30 16 40 640 50 ①
4 5
13 16
2013 MATH Olympiad [Grade2]
45.【Sol】,31. 17+5=22
32. 438+254=69233. 657+569=122634. 75-46=29
→ 146.35. 625-348=277⇒ 7→ 336. 4×8=32
37. 28×8=224 → 338. 13×34=44239. 44÷7=6R2
48. 1 and 6, 2 and 5, 3 and 4, 1,2, and 440. 128÷21=6R2 ⇒ 6
41. 4 methods
49.17
50.42. 8
43.
15
No. Answer No. Answer No. Answer No. Answer No. Answer
1 182 11 5 21 387 31 22 41
2 112 12 4 22 485 32 692 42 A=6 , B=10
3 431 13 85 23 608 33 1,226 43 15
4 847 14 8 24 24,222 34 29 44 ④
5 1,485 15 354 25 3,864 35 277 45 2
6 7,554 16 173 26 31,780 36 32 46 7
7 33 17 197 27 8R2(8.4) 37 224 47
8 11 18 35 28 26 38 442 48 4
9 57 19 3,768 29 16R12 39 6, 2 49 17
10 8 20 76 30 15R24 40 6 50 8
2013 MATH Olympiad [Grade3]
【Sol】 46. 1st : 1
2nd
: 1+2=331. 56×4=2243
rd : 1+2+3=632. 274×43=11,782���33. 57÷3=19
6th
: 1+2+3+4+5+6=2134. 67÷6=11R1 ⇒ 1235. 38÷9=4R2
48. Make a table to find the answer.36. 130+1=131 or (520÷4)+1=13137. 764÷21=36R8 ⇒ 3638. kg g kg g kg g
39. �
⇒ □=7
40. × ×since 4 hours is the same as 240 minutes, the
43. left : 4 blocks , right : 6 blocksnumber of dolls is 36.
Therefore, 2 more blocks44. Thursday is 7th , 14th , 21th , 28th
49. Even number can be made when the oned placeTherefore , the fourth Thursday is on the 28th
is 2 or 6. Therefore 2-digit even numbers are45.
12, 52, 62, 16, 26, 56.
: 4 groups of 4 squares
No. Answer No. Answer No. Answer No. Answer No. Answer1 273 11 21R2 21 15R24 31 224 41 ②
2 768 12 19R2(19.5) 22 23R14 32 11,782 42 ①
3 2,144 13 10R7 23 8R3 33 19 43 2
4 3,741 14 12R3(12.6) 24 22 34 12 44 28th
5 18,639 15 11R5 25 31 35 4, 2 45 4
6 134,232 16 12R3(12.375) 26 0 36 131 46 21
7 12 17 12R6 27
37 36 47
8 14 18 182 28
38 12, 740 48 36
9 18 19 115R4 29 9.55 39 7 49 6
10 12 20 862R4 30 11.86 40 3, 3 50 ③
Time(min) 40 80 120 160 200 240
Number of dolls
6 12 18 24 30 36
2013 MATH Olympiad [Grade4]
【Sol】 44. Complete the table
31. 12×60=72032. 32÷2=1633. 340÷4=8534. 800÷50=1635. 435÷46=9R21 ⇒ 936. × ×× 45. One sheep has the the same weight as 337. Megan : 1hour 45minutes 50seconds rabbits. One rabbit has the same weight as
= 105minutes 50seconds = 6,350seconds 2 squirrels. So, one sheep has the sameZack : 160minutes = 9,600seconds weight as 6 squirrels.
38. ÷ 46. Use a table to find the answer.39. ⇨ × ×
41.
Therefore, = 9 , = 5AC
48. B-A=C-B, A+C=B×2, B-A=2,C-B=2,
49.(1) + + + = 18 → + = 9
∴ Rick is drinking cola. (2) + + ( + ) = 17→ + = 8 → = 4
43. Since 1×8=2×4, the number in shaded blank (3) + =9 → = 5is 3. (4) ( + ) + + =16 → = 2
Therefore, + + + = 5+2+2+2=11
No. Answer No. Answer No. Answer No. Answer No. Answer1 18,291 11 8R11 21 11 31 720 41 Rick
2 142,450 12 6R4 22 10 32 16 42 ②
3 31R1 13 31R15 23 27 33 85 43 3
4 17R4 (17.8) 14 4R42 24 6 34 16 44 60
5 11R5 15 8R3 25
35 9 45 6
6 13R4 16 76R36 (76.8) 26
36 675 46= 9
= 5
7 65 17 284R3 27 6.193 37 Zack 47
8 162 18 75R32 28 5.519 38 100 48 A+C=B×2Answers may vary
9 112 19 714R28 29
39 12 49 11
10 847R2 (847.4) 20 40 30
40 Jason, Justin, Eric, Nina 50
Number of cuts 1 2 3 4 5
Number of pieces 2 3 4 5 6
Time (min) 12 24 36 48 60
5 6 7 8 9
1 2 3 4 5
× 5 12 21 32 45
Juice Milk Cola
Devon × ○ ×Susan ○ × ×Rick × × ○
2013 MATH Olympiad [Grade5]
【Sol】42. Using the pattern we would complete the table.29. □ × 7 ÷ 2 = 49, □ × 7 = 98, □ = 14
30.
+3 +5 +7 +9 +11
⇒ 5 × 5 + 5 × 9 = 25 +45 =70(cm2)43.
31. 82÷7=11R5 3 bags of cookies 2 bags of cookies 1 bags of cookies- =4 cartons of milk 3 cartons of milk 1 cartons of milk32. 243÷37=6R21
33. (18÷3)-(24÷6)=6-4=2 $29 - $21 = $834. (10÷5)×3+25+7=38 44.35. 360÷(20×2)=360÷40=9 : exposed faces of 2
nd stair : 12
36.
: exposed faces of 1st stair : 2637.
38. 153.8-62.78=91.02∴ 12+26 = 38
39.
45. ×
40.
×
46. condition
41. There are 20 numbers as below.505, 515, 525, … , 595 condition
606, 616, 626, … , 696
condition
No. Answer No. Answer No. Answer No. Answer No. Answer
1 12R5 11 47 21
31 11, 5 41 20
2 10R8 12 11 22
32 6, 21 42 6
3 17R6 13 7 23
33 2 43 8
4 88R48 14 2 24
34 38 44 38
5 302R6 15 2km 880m 25
35 9 45 30
6 30R156 16 7kg 790g 26
36
46
7 40 17 11L 300mL 27
37 47
8 27 18 5hr 8min 20sec 28
38 91.02 48 A=1, B=2, C=120
9 50 19 1hr 34min 35sec 29 14 39
49 18
10 7 20
30 70 40 18 50 7
Figure number
Number of 4 7 12 19 28 39
47.
48. First, we find the values that belong in theblank spaces from 1st row to 4th row.Next, we find the values that belong in theblank spaces from 4th row to 7th row.
120
1
Therefore, A=1, B=2, C=120
49. ÷
50.
The Possible scores : 3, 5, 7, 9, 11, 13, 15The number of Possible scores : 7
3 1 2 52 1 3
1 23
6 203
12 10
2 5
Number of arrows that could hit each ring
1points 3 2 2 1 1 1 0 0 0 0
3points 0 1 0 2 1 0 3 2 1 0
5points 0 0 1 0 1 2 0 1 2 3
Total score 3 5 7 7 9 11 9 11 13 15
2013 MATH Olympiad [Grade 6]
38.
÷
【Sol】29. (7 + □) × 10 ÷ 2 = 110
(7 + □) × 10 = 220 39. Standard amount: 300, comparing amount: 75(7 + □) = 22, The value of the ratio
□ = 1540. width : length30.
A × ÷ m
B × ÷ m 41. ones place is 1 → 31
ones place is 2 → 62 ⇒ 31, 62, 93C × ÷ m
ones place is 3 → 93A B C m
31. ÷ × ÷×42. using the pattern, there are 36 dots in
× ×
32. ×□
□ ÷
33.
34. ⇨ Greatest common factor +5 +5 +5 +5 +5 +5 ×
43.The number of students is 6. If the value of A is 1, If the value of A is 2,
35. Sam : 16=2×2×2×2 ⇒ seat No. 2
James : 27=3×3×3 ⇒ seat No. 3
Heather : 24=2×2×2×3 ⇒ seat No. 6 36.
(No) (Yes)
37.
Therefore, the value of A, B, and C is2, 7, and 10.
No. Answer No. Answer No. Answer No. Answer No. Answer
1 81 11 5 21
31 51 41 31, 62, 93
2 7 12 75 22
32 6 42 36
3 29.07 13 96 23
33 3.83 43A=2, B=7,C=10
4 6.201 14 42 24 6 34 6 44 12
5 0.448 15
25
35② : Sam③ : James⑥ : Heather
45 30
6 2.173 16
26
36
46 6
7 26.838 17
27
37
47
8 0.031 18
28
38
48 11
9 12 19
29 15 39 49 300
10 2 20
30 36 40 50A=7, B=9,C=10, D=5
Number
Numberof dots
6 11 16 21 26 31 36
44.
⇒ There are 4×3=12 different ways.
45.2 cuts (It takes 6 minutes
to make 1 cut.)
: 5 cuts
Therefore, it takes 30 minutes to make 5 cuts.
46. ÷
48. There are 12 red marbles.There are 15 yellow marbles.There are 11 blue marbles
49.⇒ 300m2 of the orchard
are does not have anytrees.
50. (A+B+C)+D=31, (A+B+C)+C=36 ⇒ C=D+5(B+C)+(B+C)=38, B+C=19
⇒ B=A+2(A+C)+(B+C)=36, A+C=17
A+(B+C+D)=31, (B+C+D)+D=29 ⇒ A=D+2B=A+2 , A=D+2 ⇒ B=D+4
Since A+B+C+D = (D+2)+(D+4)+(D+5)+D= D× 4+11=31,
then D=5, A=7, B=9, C=10.
2013 MATH Olympiad [Grade7]
【Sol】32.
hours29. +
= (Arc length of the 12m half circle)+ (Arc length of the 8m half circle)
m 33. + (Arc length of the 4m half circle)
× ×
34.
×
× km
× ×
× × 35.
÷ × kg m
30. Base radius ; 36. m
× × × × × 37. Total number of visitors per day
∴ cm
÷ ×
Surface area ;
Total number of male students per day× × ×
× ×
× ×
cm
38. ×
31. You must frist find the greatest common factor ×
of 8 and 24 × ÷ ÷ � factor of 8 : 1, 2, 4, 8
� factor of 24 : 1, 2, 3, 4, 6, 8, 12, 24 � common factor of 8 and 24 : 1, 2, 4, 8� The greatest common factor of 8 and 24 : 8 39. ÷ × × cm
No. Answer No. Answer No. Answer No. Answer No. Answer
1
11
21 9 31 8 41 8
2
12
22
32
42 169
3
13 28 23 1448.4 33
43 5
4
14
24 1.0005 34 20 44 9
5
15
25 6.9 35 3 45 A+B=C×2 Answers may vary
6
16 4 26 16.05 36 111.9 46 =1, =5
7
17
27 11.4 37 500 47
8
18 30 28
38 7 48 31, 19
9
19
29 12π(=37.68)m 39 20 49 63
10 20
30
144π
(=452.16)cm40 144 50 162
)
☆
☆☆
40. 49. Pattern of the perimeters.� The width of a tile ;
1st 2nd 3rd 4th … 10th
cm cm cm cm
⇨ ×
� The number of tiles needed to fill the wall The perimeters of 10th figure : 9+6×9=63(cm)horizontally ÷
� The number of tiles needed to fill the wall50.
vertically ÷ 4th 3rd 2nd 1st original� Total number of tiles needed to fill the entire cm cm cm cm cm
wall ×
×
×
×
×
41. Numbers are below340, 342,
Therefore, original height of the ball is 162cm402, 403, 420, 423, 430, 432 (8 number)
42. 1+3+5+ … + 23+25 = 13×13 = 169
43. The number of households which have eithercows or horses is 24+18-10=32.Therefore, 5 households have neither cows norhorses.
44. From (4) , 19 × 4 = 76From (3) , 76 - 13 = 63From (2) , 63 ÷ 7 = 9Therefore, the secret number is 9.
45. A+B=C×2, A+B=C+C ,A+B-C=C, (A+B)÷2=C
1 346.
5 6 651 61 5
1
48. Complete the table.
Number of rabbits 10 20 19 18
Number of sparrows 40 30 31 32
Number of legs 120 140 138 136
Therefore, there are 31 sparrows and 19 rabbits.
2013 MATH Olympiad [Grade8]
30. From … ①【Sol】Since the solutions of the two equations are27. (Area of the 6m radius half circle)quual, substituting ① into - (Area of the 4m radius half circle) - (Area of the 2m radius half circle)
× × ×
∴
× × ×
× × ×
31.
⇒ 6 cm
32.
÷ ÷
L 28. Base area ;
33. × L × ÷ cm
34. ÷ R Lateral area ;
× cm
÷
× Height ; ÷ ÷ cm ×
35. 29. Base area ; ×
× × m
Volumn of cylinder ; ×
÷
÷
] × m
Mass of water ;36. (Helen) : (Susan) = 4 : 3 = 8 : 6 = 12 : 9
× kg= 16 : 12 = 20 : 15
kg t (Susan) : (Lily) = 5 : 4 = 10 : 8 = 15 : 12∴(Helen) : (Susan) : (Lily) = 20 : 15 : 12
No. Answer No. Answer No. Answer No. Answer No. Answer
1 18.84 11 8 21
31 6 41 6
2 1266.88 12
22 4 32
42
3 1.0005 13
23
33 0.75 43 4
4 0.15892 14
24
3414, 0.02 or
44 6, 12, 18
5 9.64 15
25 35 44 45 31, 32, 33
6 5.2 16 10 26 36 46 7
7 3.2 17
27 8π(=25.12)cm2 37John:$150,000Joan:$250,000Jill:$350,000
47
8 6.74 18 15 28 26, 7 38
48 14
9
19 12 29 18,840,00018,840 39 6, 6 49 ③
10
20 1 30 40 45 50 160
…
37. John : ×
44.
Joan : ×
⇒ The numbers belonging to A and B areJill : ×
6, 12, 18.
45. Possible combination of scores are as below.
L 38.
39.
⇨ Greatest common factor:
× cm Therefore, the Possible scores Henry can get are
31, 32, 33.The length of an edge of the cube is cm .Also, the number of cubes that fit along the 46.length of the given box is ÷
And the number of cubes that fit along thewidth of the given box is ÷
The number of cubes that make up the height The 15th
skip is the 9th
skip and the 6th
skip.of given box is ÷ . After the 15
th skip is reached numeral location 7
Therefore, the total number of cubes is× × . 48.
40. × g
× ×
41.
1 0 (10) 3 0 (30) 5 0 (50)1 (31) 1 (51)
50.3 (53)
42. The numerator : … ⇒ Total money : $72
The denominator :□=(72÷3)×2=48
Therefore, the 12th
number is□=120÷3=40
…
∴ Andy had $160 before she went shopping.43.
4 lines
9 Points 2 1 18 Points 1 2 17 Points 1 1 2
Total 33 32 31
Number of skips 1 2 3 4 5 6 7 8 9Numeral location 5 9 4 8 3 7 2 6 1
Figurenumbers
… 14
Area 1cm2 3cm2 6cm2 10cm2 15cm2 … 105cm2
Pattern +2 +3 +4 +5