41

2014 MATH Olympiad [Grade 2]

【Sol】31. 19+5=2432. 15-7=833. 22-4=1834. 23-7=1635. 7+5-3=936. 47+36=8337. 75+88=16338. 75-28=4739. 29×7=20340. 9×56=504

No. Answer No. Answer No. Answer No. Answer No. Answer

1 25 11 19 21 140 31 24

2 21 12 21 22 607 32 8 42 63 7 13 8 23 802 33 18 43 34 7 14 9 24 35 34 16 44 23 28

5 8 15 16 25 667 35 9 45

6 5 16 3 26 268 36 83 46 3

7 17 17 9 27 98 37 163 48

8 27 18 15 28 228 38 47 47 +12 or add 12

9 17 19 23 29 4,963 39 203 49 ③

10 27 20 113 30 5,312 40 504 50or

2014 MATH Olympiad [Grade3]

【Sol】48.31. 22-5=17

32. 54+72=12633. 42-5=3734. 376-192=18435. 205-138=6736. 6×8=4837. 56×4=22438. 275×6=1650

49.39. 42÷7=640. 486÷9=54

50.41. A : B :

43.

There are 12 shaded triangles.

No. Answer No. Answer No. Answer No. Answer No. Answer

1 119 11 2 21 476 31 17 41 A : B :

2 130 12 5 22 460 32 126 42 11

3 643 13 27 23 432 33 37 43 6

4 599 14 18 24 2,952 34 184 44 Michael

5 901 15 323 25 4,134 35 67 45 5

6 1,040 16 316 26 29,136 36 48 461 and 72 and 63 and 5

7 74 17 469 27 4R2 37 224 48

8 37 18 487 28 6R3 38 1,650 47B-A=C-Bor A+C=B×2 or A+C=B+B

9 7 19 3,744 29 26R18 39 6 49

10 37 20 216 30 18R28 40 54 50 12

17 15

13

2014 MATH Olympiad [Grade4]

【Sol】46. (1) A=1 (2) A=231. 41×4=164

32. 25×32=800 1 233. 43÷5=8R3 ⇒8, 3

8 11 8 1134. 28÷7=435. 72÷6=12

7 10 6 936. 396÷9=44(No) (No)37. 185÷21=8R17 ⇒ 8, 17

38. 6×4÷8=3(3) A=3

39. or 0.75⇒

or 0.753

40. 3.44-1.92=1.528 11

5 842. $30÷5(boxes)=$6(box)

(Yes)$144÷$6(box)=24(boxes)

47.

45.

No. Answer No. Answer No. Answer No. Answer No. Answer1 288 11 28R1 21 35R3 31 164 41 ①

2 657 12 16R3 22 54R15 32 800 42 24

3 2,736 13 10R4 23 7R27 33 8, 3 43 ①

4 3,783 14 11R6 24 26 34 4 44 41

5 15,136 15 18R3 25 36 35 12 45

6 177,933 16 11R7 26 62 36 44 46 8

7 13 17 14R4 27

37 8, 17

8 13 18 137 28

38 3 48C=A+A+Bor C=A×2+Bor C-B=A×2

9 15 19 124R7 29 10.38 39 or 0.7549 ②

10 14 20 847R4 30 22.68 40 1.52 50 orThe answer can be various.

○ △ ○

△ △

□

△ ○ ○

○ △ □

2014 MATH Olympiad [Grade5]

No. Answer No. Answer No. Answer No. Answer No. Answer1 19 11 21 21 48 31 525 41 ④

2 27 12 37 22 80 32 8 42 13

3 23 13 32 23 48 33 6 43 21

4 19 14 12 24 11 34 5 44 24

5 18 15 13 25 5 35 34 45 30

6 14 16 92 26 11 36 72 46 7

7 83 17 255 27 489 37 17 47 ③

8 112 18 119 28 516 38 14 48 21

9 146 19 730 29 7 39 29 49 22

10 741 20 5 30 12 40 31 50 9

【Sol】46. Available numbers are 5, 6, 7, 8.31. 35×15=525

Since B=8, A+D=12, C+D=11, then D=5,32. 98÷9=10R8 ⇒ 8A=7, C=633. 126÷21=6

34. 127÷29=4R11 ⇒ 5 335. 1234÷60=20R34 ⇒ 34

B A36. 6×7+5×6=42+30=7237. 40-(14÷7+3×7)=40-23=17 D4 C

38. ⇒ 14

48. We can find the rule as below39. 7.52-7.23=0.29 ⇒ 293×3-2=7, 5×5-4=21, 4×4-5=11,

40.

⇒ 31

3×3-7=2, 5×5-10=15Rule : B×B-A=C or A+C=B×B

42. Let the length of the shortest log be □ cm.□ + □ + □ + 7 = 46 49.

therefore, □ is 13.→ are 4 groups

43. 11 + 21 + 2 + 3 →���

are 4×3=12 groups1 + 2 + 3 + 4 + 5 + 6

44. Complete the table.→ are 2 groups

Number of cuts 1 2 3

Number of pieces 2 3 4

Time (min) 8 16 24 →

are 2×5=10 groups45. 101, 111, … , 191 (10)Therefore, groups of 2 squares are 22.202, 212, … , 292 (10)

303, 313, … , 393 (10)

50.

The Possible scores : 3, 4, 5, 6, 7, 8, 9, 10, 12The number of Possible scores : 9

Number of arrows that could hit each ring

1 points 3 2 2 1 1 1 0 0 0 0

2 points 0 1 0 2 1 0 3 2 1 0

4 points 0 0 1 0 1 2 0 1 2 3

Total score 3 4 6 5 7 9 6 8 10 12

2014 MATH Olympiad [Grade6]

【Sol】42. The number of squares increases by 3 when the29. (16+10)×13÷2=26×13÷2=169

order increases by 1.30. (4+(4+8+4))×12÷2-(8×8)=120-64=5631. 80÷3=26R2

32. 1932÷21=92

33. 15-(24÷2)=15-12=3

34. 20-(6÷3)×9=2

35. (3hr 17min 30sec)+(3hr 47min 50sec)

=7hr 5min 20sec ⇒ 7+5+20=32 43. The 1st Monday is 6th.Therefore, Monday is 6th, 13th, 20th, 27th.36. ×

□

□ □ 6/24 = 1/4 44. The following shows the place of each animal

in the race.37. ⇒ 5

38. ⇒ ⇒24

39.

⇒ 101

Therefore, Cougar is 8cm ahead of Kangaroo.40.

⇒ 41

45. Make the table as below.

41. Complete the table to show the ones placevalues.

Therefore, ♡ ◇ and ♡◇

No. Answer No. Answer No. Answer No. Answer No. Answer

1 15 11 26 21 11 31 2 41 1

2 15 12 7 22 3 32 92 42 26

3 18 13 12 23 8 33 3 43 27

4 21 14 80 24 8 34 2 44 8

5 9 15 343 25 17 35 32 45 16

6 342 16 852 26 2 36 1/4 46 315

7 4 17 24 27 1 37 5 47 6

8 26 18 58 28 13 38 24 48 34

9 31 19 85 29 169 39 101 49 5

10 20 20 9 30 56 40 41 50 8

order 1 2 3 4 5 6 7 8

Thenumber

ofsquares

3×1+2=5

3×2+2=8

3×3+2=11

3×4+2=14

3×5+2=17

3×6+2=20

3×7+2=23

3×8+2=26

♡ 9 10 11 12 13

◇ 1 2 3 4 5

♡×◇ 9 20 33 48 65Time

multiplied1 2 3 4 5 6 7 8 9 10 11 12

Onesplacevalue

7 9 3 1 7 9 3 1 7 9 3 1

-1)

ven dd

46. …

The pairs having a sum of 30 are(5, 25), (6, 24), … , (14, 16).

There are 10 pairs and 15 alone.Therefore, the sum is 30×10+15=315.

47. Since the ones places is 2, 3-digit evennumbers can be made as below;352, 372, 532, 572, 732, 752

48.

□×(□ △

e (even)÷2o ((odd+1)÷2)

∴ A+B+C=2+12+20=34

49. 3 9 7 9 goes between 3 and 7.B+C=16 ⇒ (B, C) = (6, 10)

D or (10, 6)BD+E=12 ⇒ (D, E) = (4, 8)

C A E or (8, 4)Then, available number A is 5.

50. We can calculate step by step as below.

Since A=4, B=4, the value of A+B is 4×4=16

2014 MATH Olympiad [Grade 7]

【Sol】

× 28. 41.

4 bags of cookies 2 bags of cookies(2 bags of cookies) -×

= 3 carton of milk 3 carton of milk

$61 ― $ 41 = $20×

÷ ÷

Therefore, the value of 1 bag of cookies is $10.

42.29. 8×3÷2=24÷2=12

2nd stair 1st stair30. 14×10-(6×4÷2+8×6÷2+8×6÷2+6×4÷2)=140-(12+24+24+12)=140-72=68

31. (3+40)-10=33

32.

⇒ 8

exposed faces : 16 exposed faces : 2433. 153.9-62.78=91.12 ⇒ 12

34. ⇨ Maximum number of people (other sol) Top & Botton view side view ÷

The number of pencil is 3.35. ⇨ 2×3=6

9×2 6×2

36.

⇒ 31 Front & Back view

37.

⇒ 26

38. ×

×

5×239. 12.3×30=369 The total number of faces is40. (9×2)+(6×2)+(5×2)=40.× ×

× ÷ ÷

No. Answer No. Answer No. Answer No. Answer No. Answer1 48 11 72 21 19 31 33 41 10

2 2 12 96 22 55 32 8 42 40

3 35 13 42 23 28 33 12 43 4

4 15 14 15 24 7 34 3 44 933

5 53 15 12 25 30 35 6 45 ③

6 5 16 11 26 83 36 31 46 ④

7 988 17 7 27 12 37 26 47 6

8 3 18 6 28 9 38 7 48 10

9 14 19 11 29 12 39 369 49 30

10 4 20 9 30 68 40 45 50 18

② ③ ④

43. We can draw 4 lines of symmetry as below 50. The blocks with 2 painted faces in shownbelow.

(1st stair) (2

nd stair)

44.⇒ (10+8)blocks

The only number that makes the ones placevalue 7 multiplied by 3 is 9. Therefore □ is 9.Therefore, the 3-digit number □△○ is 933.

46. We can make each cube as below

①

47. Hundreds Tens Ones6 6 7 … 667

7 6 … 6767 … 677

7 6 6 … 7667 … 767

7 6 … 776

48. Number pattern

Rule: A×C=B+6Therefore, missing numbers are 6 and 4.

49.

Total number of ways : 8+6+4+2+4+3+2+1=30

2014 MATH Olympiad [Grade8]

【Sol】× × × × 29. 41.

⇒ 35.7×10=357 42. We can draw the given set of blocks as below.30. Base area ;

Top

× ×

Surface area ;× × × ×

× × × Side

Front

31. 18=2×□×□ Therefore, the number of blocks is 6.9=□×□□=3 43.32.

⇒6

33.

⇒ 43

34. × ⇒ 3

35. ÷

⇒ 6544. True statement is (4)

36. 29÷12.5=2R4 ⇒437. 4.75×2.8×10=13.3×10=13338. (5.4-0.5)÷0.7=7

45. Let Danny have x pieces of candy in the39.

×

×

⇒ 8 beginning, .

40. ∴ ⇨ ×

No. Answer No. Answer No. Answer No. Answer No. Answer1 13 11 1 21 22 31 3 41 49

2 8 12 9 22 192 32 6 42 6

3 1 13 7 23 386 33 43 43 ③

4 17 14 7 24 472 34 3 44 4

5 19 15 2 25 3 35 65 45 32

6 1 16 3 26 3 36 4 46 4

7 7 17 9 27 213 37 133 47 5

8 20 18 1 28 27 38 7 48 12

9 19 19 56 29 357 39 8 49 11

10 8 20 54 30 8 40 6 50 41

∴

47. Hundreds Tens Ones 3-digit number

∴ 3-digit even number :102, 110, 112, 120, 210 (5 numbers)

48. AB × , and AB ×C ≥ ⇒ C

Therefore, AB ≤ and AB ≥

AB

49.· Guess 10 correct answers and 5 incorrect

answers then Wendy earned × ×

· Guess 11 correct answers and 4 incorrectanswers then Wendy earned × ×

Therefore, Wendy answered 11 correct answers.

50.

10

2014 MATH Olympiad [Grade9]

【Sol】41. The perimeter of the map :29. From

… ①

× cm

Since the solutions of the two equations are

equal, substituting ① into

Actual perimeter : × m

42.

∴

31.

⇒ 101

32. × ÷

33. × ⇒ 2543.

34. ÷ R ⇒ 435. ÷ × ⇒ 536. ÷

÷ × ×

⇒ 51+2 1+2+3 …37. Teachers : ×

The number of squares in is

38. cm × cm cm m 1+2+3+ … +7+8=36orm × m m

39. 27=16+8+2+1 ⇒ 440. × × ×

× ××

No. Answer No. Answer No. Answer No. Answer No. Answer1 1 11 14 21 13 31 101 41 260

2 23 12 692 22 27 32 7 42 7

3 6 13 25 23 18 33 25 43 36

4 2 14 96 24 8 34 4 44 ②

5 9 15 608 25 9 35 5 45 250

6 1 16 266 26 29 36 5 46 120

7 5 17 178 27 17 37 180 47 120

8 29 18 124 28 156 38 420 48 4

9 38 19 16 29 5 39 4 49 18

10 32 20 12 30 351 40 16 50 15

Adult Children total10 1 18×10+12=1929 2 18×9+12×2=1868 3 18×8+12×3=1807 4 18×7+12×4=174

Fiqurenumber

1 2 3 4 5 …

Number of0 0 1 3 6 …

48. We can draw the symmetric line as below.

45. He spent $40 on a story book 49. In thousands place : A×4<10 ⇒A=1 or 2In ones place : D×4 is even number ⇒A=2

2 B C D

× 4

D C B 2

In ones place : D=8He saved $200 in the bank.

2 B C 8

× 4

8 C B 2∴ He had $250 in the beginning.

In hundreds place : B×4<10 ⇒B=1 or 2In tens place : C×4+3=B : odd number ⇒B=1

2 1 C 8 2 1 7 846.× 4 × 4The weight of 15 pieces of candy : ⇒

8 C 1 2 8 7 1 2 g

The weight of 40 pieces of candy :Therefore, A=2, B=1, C=7, and, D=8, then

× ÷ gA+B+C+D=18

The weight of the empty jar g

50.The sum of the numbers in 3 arrows is… .The sum of the numbers in each arrow is

47.÷ .

ones place : 101, 111, 121, …,191(Case 1)

⇒ 10 timestens place : 110, 111, 112, …,119⇒ 10 timeshundreds place : 100, 101, 102, …,199⇒ 100 times ∴

∴The numeral 1 is written 120 times.(Case 2)

∴