优质解答
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 ***.
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
英语数学题
1、An ant covers a distance of 90 metres in 3 hours. The average speed of the ant in decimetres per minute is____.
2、
3、In a certain town some people were affected by a ’flu’ epidemic. In the first month 20% of the population contracted the flu whilst 80% were healthy.
In the following month 20% of the sick people recovered and 20% of the healthy people contracted the disease.
What fraction of the population is healthy at the end of the second month?
4、Mpho, Barry, Sipho, Erica and Fatima are sitting on a park bench.
Mpho is not sitting on the far right. Barry is not sitting on the far left.
Sipho is not sitting at either end. Erica is sitting to the right of Barry,
but not necessarily next to him. Fatima is not sitting next to Sipho.
Sipho is not sitting next to Barry.
Who is sitting at the far right?
5、Of the 28 T–shirts in a drawer, six are red, five are blue, and the rest are white. If Bob selects T–shirts at random whilst packing for a holiday, what is the least number he must remove from the drawer to be sure that he has three T–shirts of the same colour?
6、In an alien language, jalez borg farn means “good maths skills”. Nurf klar borg means “maths in harmony” and darko klar farn means “good in gold”.
What is “harmony gold” in this language?
7、Five children, Amelia, Bongani, Charles, Devine and Edwina, were in the
classroom when one of them broke a window. The teacher asked each of them to make a statement about the event, knowing that three of them always lie and two always tell the truth. Their statements were as follows:
Amelia: “Charles did not break it, nor did Devine.”
Bongani: “I didn’t break it, nor did Devine.”
Charles: “I didn’t break it, but Edwina did.”
Devine: “Amelia or Edwina broke it.”
Edwina: “Charles broke it.”
Who broke the window?
8、Did you know? A palindrome is a number which reads the same forwards as backwards e.g. 35453. Next year 2002 is an example of a palindromic number. What is the difference between 2002 and the number of the previous palindromic year?
9、If a Åb = (3×b) then the value of 2+(2×a) Å(3 Å5) is____. 10、Two ants start at point A and walk at the same pace. One ant walks around a 3 cm by 3 cm square whilst the other walks around a 6 cm by 3 cm
rectangle. What is the minimum distance, in centimetres, any one must
cover before they meet again?
参考答案：
1、 单位换算,注意单词,90×10÷（3×60）＝5
2、 46
3、 0.68
4、 Erica
5、 抽屉原则 7
6、 注意一一对应,borg= maths, farn=good, jalez=skills. Klar=in, Nurf=harmony, darko=gold. 答案是Nurf darko.
7、 Charles
8、 1001
9、 67
10、 108
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
2、The number of diagonals that can be drawn in a regular polygon with
twenty sides (icosagon) is_____.
3、If a and b are integers, 10ÄÄand then 379Ä6 is equal to_____.
4、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、The greatest number of Mondays which can occur in 45 consecutive
days is____
6、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、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、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.
9、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]
参考答案：
1、A 考察我们学过的简单的进制问题,显然8进制中没有8出现
2、170 找规律,公式为n×（n-3）÷2
3、1 定义新运算,就是求379÷6的余数.
4、40,16和24
5、7
6、5
7、28米,根据距离比求出速度比,三者的速度比为1：9/10：18/25
8、420 分解质因数
9、13种
1. Two numbers differ by 57. Their sum is 185. Find the numbers. Choices for the smaller number:54 64 74.
2.A bus went 318 km farther than a car. The car went one third as far as the bus. How far did each vehicle travel? Choices for the smaller number: 147 151 159
3.one number is four times another number. The larger number is also 87 more than the smaller number. Find the numbers. Choices for the smaller number: 29 30 33
4.A clown weights 60 lb more than a trapeze artist. The trapeze artist weighs two thids as much as the clown. How much does each weigh? choices for the weight of the trapeze artist : 110 120 125
5. The U.S. Senate has 100 memebers, all Democrats or Republicans. Recently there were 12 more Democrats than Republicans. How many Senators from each political party were there at that time? Choices for the number of Republicans: 38 42 44
6.The ninth grade class has 17 more girls than boys. there are 431 students in all. how many boys are there? how many girls are there? Choices for the number of boys: 191 202 207
7. Elena has one and a half times as much money as Ramon.Together they have 225. how much money does each have?
Choices for Ramom's amount;80 90 95
8. Western state college is 18 years older than southern state. western is also 2 and the half times as old as southern. how old is each? Choice for southern state's age:12 14 18
answers: 1.设较小数为x. x+x+57=185 x=64.
2.设轿车行驶了x千米. 318+x=3x x=159千米
轿车行驶了159千米,公车行驶了318+159=477千米.
3.设较小数为x. 4x=x+87 x=29.
4.60+x=3x/2 x=120
5.Let the number of Republicans be x. x+x+12=100 x=44
6.设有x名男生 x+x+17=431 x=207名
有男生207名,女生431-207=224名.
7.设Ramom有x元. x+3x/2=225 x=90元
8.设southern states college 有x年历史. x+18=5x/2 x=12年.
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 ***.
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
英语数学题
1、An ant covers a distance of 90 metres in 3 hours. The average speed of the ant in decimetres per minute is____.
2、
3、In a certain town some people were affected by a ’flu’ epidemic. In the first month 20% of the population contracted the flu whilst 80% were healthy.
In the following month 20% of the sick people recovered and 20% of the healthy people contracted the disease.
What fraction of the population is healthy at the end of the second month?
4、Mpho, Barry, Sipho, Erica and Fatima are sitting on a park bench.
Mpho is not sitting on the far right. Barry is not sitting on the far left.
Sipho is not sitting at either end. Erica is sitting to the right of Barry,
but not necessarily next to him. Fatima is not sitting next to Sipho.
Sipho is not sitting next to Barry.
Who is sitting at the far right?
5、Of the 28 T–shirts in a drawer, six are red, five are blue, and the rest are white. If Bob selects T–shirts at random whilst packing for a holiday, what is the least number he must remove from the drawer to be sure that he has three T–shirts of the same colour?
6、In an alien language, jalez borg farn means “good maths skills”. Nurf klar borg means “maths in harmony” and darko klar farn means “good in gold”.
What is “harmony gold” in this language?
7、Five children, Amelia, Bongani, Charles, Devine and Edwina, were in the
classroom when one of them broke a window. The teacher asked each of them to make a statement about the event, knowing that three of them always lie and two always tell the truth. Their statements were as follows:
Amelia: “Charles did not break it, nor did Devine.”
Bongani: “I didn’t break it, nor did Devine.”
Charles: “I didn’t break it, but Edwina did.”
Devine: “Amelia or Edwina broke it.”
Edwina: “Charles broke it.”
Who broke the window?
8、Did you know? A palindrome is a number which reads the same forwards as backwards e.g. 35453. Next year 2002 is an example of a palindromic number. What is the difference between 2002 and the number of the previous palindromic year?
9、If a Åb = (3×b) then the value of 2+(2×a) Å(3 Å5) is____. 10、Two ants start at point A and walk at the same pace. One ant walks around a 3 cm by 3 cm square whilst the other walks around a 6 cm by 3 cm
rectangle. What is the minimum distance, in centimetres, any one must
cover before they meet again?
参考答案：
1、 单位换算,注意单词,90×10÷（3×60）＝5
2、 46
3、 0.68
4、 Erica
5、 抽屉原则 7
6、 注意一一对应,borg= maths, farn=good, jalez=skills. Klar=in, Nurf=harmony, darko=gold. 答案是Nurf darko.
7、 Charles
8、 1001
9、 67
10、 108
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
2、The number of diagonals that can be drawn in a regular polygon with
twenty sides (icosagon) is_____.
3、If a and b are integers, 10ÄÄand then 379Ä6 is equal to_____.
4、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、The greatest number of Mondays which can occur in 45 consecutive
days is____
6、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、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、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.
9、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]
参考答案：
1、A 考察我们学过的简单的进制问题,显然8进制中没有8出现
2、170 找规律,公式为n×（n-3）÷2
3、1 定义新运算,就是求379÷6的余数.
4、40,16和24
5、7
6、5
7、28米,根据距离比求出速度比,三者的速度比为1：9/10：18/25
8、420 分解质因数
9、13种
1. Two numbers differ by 57. Their sum is 185. Find the numbers. Choices for the smaller number:54 64 74.
2.A bus went 318 km farther than a car. The car went one third as far as the bus. How far did each vehicle travel? Choices for the smaller number: 147 151 159
3.one number is four times another number. The larger number is also 87 more than the smaller number. Find the numbers. Choices for the smaller number: 29 30 33
4.A clown weights 60 lb more than a trapeze artist. The trapeze artist weighs two thids as much as the clown. How much does each weigh? choices for the weight of the trapeze artist : 110 120 125
5. The U.S. Senate has 100 memebers, all Democrats or Republicans. Recently there were 12 more Democrats than Republicans. How many Senators from each political party were there at that time? Choices for the number of Republicans: 38 42 44
6.The ninth grade class has 17 more girls than boys. there are 431 students in all. how many boys are there? how many girls are there? Choices for the number of boys: 191 202 207
7. Elena has one and a half times as much money as Ramon.Together they have 225. how much money does each have?
Choices for Ramom's amount;80 90 95
8. Western state college is 18 years older than southern state. western is also 2 and the half times as old as southern. how old is each? Choice for southern state's age:12 14 18
answers: 1.设较小数为x. x+x+57=185 x=64.
2.设轿车行驶了x千米. 318+x=3x x=159千米
轿车行驶了159千米,公车行驶了318+159=477千米.
3.设较小数为x. 4x=x+87 x=29.
4.60+x=3x/2 x=120
5.Let the number of Republicans be x. x+x+12=100 x=44
6.设有x名男生 x+x+17=431 x=207名
有男生207名,女生431-207=224名.
7.设Ramom有x元. x+3x/2=225 x=90元
8.设southern states college 有x年历史. x+18=5x/2 x=12年.