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1、Did you know? In the decimal number system (base 10) ten different digits, 0 to 9, are used to write all the numbers. In the binary number system (base 2) two different digits are used, i.e. 0 and 1.
Which one of the following numbers is not a valid number in the
octal number system (base 8)?
A) 128 B) 127 C) 126 D) 125 E) 124
3、The number of diagonals that can be drawn in a regular polygon with
twenty sides (icosagon) is_____.
4、If a and b are integers, 10Ä3=1,152Ä7=3, and then 379Ä6 is equal to_____.
5、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.
The sum of the two original numbers is____.
6、The greatest number of Mondays which can occur in 45 consecutive
days is____
7、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.
8、Three girls A, B and C run in a 100 m race. When A finishes, B is 10 m
behind A and when B finishes C is 20 m behind B. How far in metres was
C from A when A finished?
(Let’s assume all the athletes run at a constant speed)
9、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.
10、 You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?
[Remember the weights may be placed on either side]
答案：1，十进制用0～9表示所有数，二进制只用0和1表示
下面哪个数在八进制下是非法的？
A)128（八进制用0～7）
3，一个二十边形内可画出多少条对角线？
170条（20选2，减去20条边）
4，如果a和b都是整数，10Ä3=1,152Ä7=3, 那么 379Ä6等于？
题目似乎有点问题，看不懂
5、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.
The sum of the two original numbers is____.
5，两个数的比例为2:3，如果分别给两个数加4，则他们的比例变为5:7。
原来的两个数的和为？
40（16和24）
6、The greatest number of Mondays which can occur in 45 consecutive
days is____
6，连续45天最多能出现多少个星期一？
6个
7、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.
7，Saul在玩一个电视游戏，击中得4分，没击中扣6分。20个回合之后他得了30分，那么他有多少次没击中？
5次（4×15-6×5=30）
8、Three girls A, B and C run in a 100 m race. When A finishes, B is 10 m
behind A and when B finishes C is 20 m behind B. How far in metres was
C from A when A finished?
(Let’s assume all the athletes run at a constant speed)
8，A,B和C三个女孩进行百米短跑比赛。A跑完的时候，B在A背后10米；B跑完的时候，C在B背后20米。那么A跑完的时候，C在A后面多少米？（假设他们一直匀速跑）
28米。（B的速度是A的90%，C是B的80%，C是A的72%）
9、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.
一个长方体盒子的三个面面积是84cm2,70cm2和30cm2。这盒子的体积是多少？
420cm3（14cm×6cm×5cm）
10、 You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?
[Remember the weights may be placed on either side]
你有1kg，3kg和9kg3个砝码和一个天平，你可以称出多少个不同的重量？（记住砝码可以放在天边两边的任意一边）
13个(1～13kg)
Which one of the following numbers is not a valid number in the
octal number system (base 8)?
A) 128 B) 127 C) 126 D) 125 E) 124
3、The number of diagonals that can be drawn in a regular polygon with
twenty sides (icosagon) is_____.
4、If a and b are integers, 10Ä3=1,152Ä7=3, and then 379Ä6 is equal to_____.
5、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.
The sum of the two original numbers is____.
6、The greatest number of Mondays which can occur in 45 consecutive
days is____
7、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.
8、Three girls A, B and C run in a 100 m race. When A finishes, B is 10 m
behind A and when B finishes C is 20 m behind B. How far in metres was
C from A when A finished?
(Let’s assume all the athletes run at a constant speed)
9、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.
10、 You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?
[Remember the weights may be placed on either side]
答案：1，十进制用0～9表示所有数，二进制只用0和1表示
下面哪个数在八进制下是非法的？
A)128（八进制用0～7）
3，一个二十边形内可画出多少条对角线？
170条（20选2，减去20条边）
4，如果a和b都是整数，10Ä3=1,152Ä7=3, 那么 379Ä6等于？
题目似乎有点问题，看不懂
5、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.
The sum of the two original numbers is____.
5，两个数的比例为2:3，如果分别给两个数加4，则他们的比例变为5:7。
原来的两个数的和为？
40（16和24）
6、The greatest number of Mondays which can occur in 45 consecutive
days is____
6，连续45天最多能出现多少个星期一？
6个
7、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.
7，Saul在玩一个电视游戏，击中得4分，没击中扣6分。20个回合之后他得了30分，那么他有多少次没击中？
5次（4×15-6×5=30）
8、Three girls A, B and C run in a 100 m race. When A finishes, B is 10 m
behind A and when B finishes C is 20 m behind B. How far in metres was
C from A when A finished?
(Let’s assume all the athletes run at a constant speed)
8，A,B和C三个女孩进行百米短跑比赛。A跑完的时候，B在A背后10米；B跑完的时候，C在B背后20米。那么A跑完的时候，C在A后面多少米？（假设他们一直匀速跑）
28米。（B的速度是A的90%，C是B的80%，C是A的72%）
9、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.
一个长方体盒子的三个面面积是84cm2,70cm2和30cm2。这盒子的体积是多少？
420cm3（14cm×6cm×5cm）
10、 You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?
[Remember the weights may be placed on either side]
你有1kg，3kg和9kg3个砝码和一个天平，你可以称出多少个不同的重量？（记住砝码可以放在天边两边的任意一边）
13个(1～13kg)
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1、In 2004, 16 June falls on a Wednesday. On what day of the week will 16 June fall in 2010?
2、 In a magic square the sum of the numbers in each row, in each diagonal and in each column are equal. In this magic square the value of x is:
3、If half of a number is 30, then three-quarters of that number is____.
4、The sum of the digits of the following product
999×555
5、Three positive integers have a sum of 28. The greatest possible product that these integers can have is_____.
6、Jack was trying to tessellate regular pentagons. He managed the
following figure.
The size of angle .a. is______.
7、If the area of the shaded region of the regular hexagon in the diagram
below is 36 cm2, the area of the whole hexagon in cm2 is_____.
8、In what follows, □ and Δ are different numbers.
When 503 is divided by □ the remainder is 20.
When 503 is divided by Δ the remainder is 20.
When 493 is divided by □ x Δ the remainder is_____.
9、A lady, her brother, her son and her daughter (all related by birth) played
volleyball. The worst player's twin (who is one of the four players) and the
best player are of opposite sex.
The worst player and the best player are of the same age.
Who cannot be the worst player(s)?
A) brother only B) daughter only
C) son and daughter only D) lady and daughter only
E) lady only
10、If you continue the given number pattern, in what row and in what
position in that row will the number 320 be?
1 -------------- row 1
2 3 -------------- row 2
4 5 6 -------------- row 3
7 8 9 10 -------------- row 4
The answers are given in the order of row ; position.
参考答案
1、Wednesday
2、12
3、45
4、27（求数位上上的数字之和）
5、28=9+9+10，因此答案为810
6、36度
7、108
8、503-20=483 483=3×7×23＝21×23，因此□ x Δ＝483，因此此题余数是10.
9、D
10、25，20
2、 In a magic square the sum of the numbers in each row, in each diagonal and in each column are equal. In this magic square the value of x is:
3、If half of a number is 30, then three-quarters of that number is____.
4、The sum of the digits of the following product
999×555
5、Three positive integers have a sum of 28. The greatest possible product that these integers can have is_____.
6、Jack was trying to tessellate regular pentagons. He managed the
following figure.
The size of angle .a. is______.
7、If the area of the shaded region of the regular hexagon in the diagram
below is 36 cm2, the area of the whole hexagon in cm2 is_____.
8、In what follows, □ and Δ are different numbers.
When 503 is divided by □ the remainder is 20.
When 503 is divided by Δ the remainder is 20.
When 493 is divided by □ x Δ the remainder is_____.
9、A lady, her brother, her son and her daughter (all related by birth) played
volleyball. The worst player's twin (who is one of the four players) and the
best player are of opposite sex.
The worst player and the best player are of the same age.
Who cannot be the worst player(s)?
A) brother only B) daughter only
C) son and daughter only D) lady and daughter only
E) lady only
10、If you continue the given number pattern, in what row and in what
position in that row will the number 320 be?
1 -------------- row 1
2 3 -------------- row 2
4 5 6 -------------- row 3
7 8 9 10 -------------- row 4
The answers are given in the order of row ; position.
参考答案
1、Wednesday
2、12
3、45
4、27（求数位上上的数字之和）
5、28=9+9+10，因此答案为810
6、36度
7、108
8、503-20=483 483=3×7×23＝21×23，因此□ x Δ＝483，因此此题余数是10.
9、D
10、25，20
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