◆算术（Arithmetic）

1. The population of City X decreased by 5 percent while the population of City Y decreased by 7.5 percent

Quantity A: The loss of population by City X

Quantity B: The loss of population by City Y

【答案】D

【解析】由于题目中没有给出X城和Y城的具体人数，因此无法比较Quantity A和Quantity B的大小关系。

2.For all real numbers P and Q, P*Q=P+Q–PQ.

Quantity A: 4*1

Quantity B: 4*2

【答案】A

【解析】根据题干中给出的计算规则可得，4*1=4+1-4×1=0，而4*2=4+2-4×2=-2，因此Quantity A大。

3. A bookshelf contains 16 books written in French and 8 books written in Italian and no other books.75% of the books written in French and 50% of the books written in Italian are removed from the bookshelf.

Quantity A: The proportion of the original number of books remaining on the shelf

Quantity B: 2/3

【答案】B

【解析】根据题意，移除的法语书为16×0.75=12本，意大利语书为8×0.5=4本，那么移除后，书架上还剩下（16+8）-(12+4)=8本书，所以，剩余的书占原来的8/24=1/3，显然，Quantity B要大。

4.Quantity A: The number of primes of which 11 is an integer multiple

Quantity B: The number of primes of which 13 is an integer multiple

【答案】C

【解析】题干比较的是11和13的质数整数倍数，由于11和13本身都是质数，那么它们的质数整数倍数的个数相等，均为1个（即它们本身）。

5. Mr. Norwalk borrowed $1,000 for one year. Mr. Palisano borrowed $ 500 for two years.

Quantity A: The amount of interest Mr. Norwalk owes on his loan

Quantity B: The amount of interest Mr. Palisano owes on his loan

【答案】D

【解析】由于题目没有给出贷款利率，因此无法计算两人贷款的利息。

6. The sum of a group of numbers is 4,550. The average of the group of numbers is 325.

Quantity A: The number of numbers in the group

Quantity B: 15

【答案】B

【解析】根据题干信息可知数值共有4550÷325=14＜15，因此Quantity B大。

7. Two students spent a total of 35 hours on a school project. One of the students spent 25% fewer hours on the project than the other.

Quantity A: The difference in the number of hours spent by each

Quantity B: 6

【答案】A

【解析】根据题干中的数量关系可知，两个学生在项目上所用时间的差值为25%×35=8.75，显然Quantity A要大于QuantityB。

8. Quantity A: The least number greater than 12 that is divisible by 12 but not by 8

Quantity B: 48

【答案】B

【解析】根据题意可知，符合要求的Quantity A为36，显然要小于Quantity B。

9.Mary has $ 5 less than Sam, and Mark has half as much money as Sam.

Quantity A: Amount of money that Mary has

Quantity B: Amount of money that Mark has

【答案】D

【解析】由于题目中没有给出Sam的钱数，因此无法得知Mary和Mark的钱数。

10.Quantity A: The greatest prime factor of 243

Quantity B: The greatest prime factor of 180

【答案】B

【解析】243=3×3×3×3×3，因此Quantity A=3；而180=3×3×2×2×5，所以Quantity B=5.

11. An apartment building has 5 floors, one of which has only 2 apartments. Each of the other floors has 4 apartments.

Quantity A: 3 times the number of floors in the building

Quantity B: The number of apartments in the building

【答案】B

【解析】根据题干信息可得，Quantity A=3×5=15；Quantity B=2+4×4=18.

12. Quantity A: The time it takes Jimmy to drive 300 miles at a rate of 52 miles per hour

Quantity B: The time it takes Bobby to drive 240 miles at a rate of 40 miles per hour

【答案】B

【解析】根据题干信息，Quantity A=300÷52≈5.77小时；Quantity B=240÷40=6小时。

13. The weight of package x is more than twice the weights of packages y and z combined.

Quantity A: The weight of package z

Quantity B: the weight of package x

【答案】D

【解析】题干并没有给出各个包裹的具体重量，因此无法计算Quantity A和Quantity B的数值。

14.Quantity A: the ratio 3:13

Quantity B: the ratio 13:51

【答案】B

【解析】把两个分数同时乘以分母13和51的最小公倍数663，经比较可知，Quantity B大于Quantity A。

15． 63% of a is 72

Quantity A: 2a

Quantity B: 250

【答案】B

【解析】根据题干信息可得，a=72÷63%≈114，因此2a=228＜250.

16. Quantity A Quantity B

　  .

【答案】A.

【解析】化简A=9/2，B=5/2，所以A大于B，故本题选A项。

17.Quantity: A: 5-2

Quantity B: 10-1

【答案】B

【解析】A5 -2=， B =10 -1=0.1，所以A小于B，故本题选B项。

18.Quantity A:

Remainder when 1,003 is divided by 4

Quantity B:

Remainder when 1,004 is divided by 3

【答案】A

【解析】经计算，Quantity A=3，而Quantity B=2，因此，Quantity A大。

19.George scored higher on his science midterm than Mark did.

Quantity A: George’s score on the test

Quantity B: Three times Mark’s score on the test

【答案】D

【解析】题目没有给出两人的具体得分，因此无法确定Quantity A和Quantity B的关系。

20. Quantity A:

Quantity B:

【答案】B

【解析】由于小于，那么就大于，即Quantity B 大于Quantity A。

21.Quantity A: （30% of 50）+40

Quantity B: (50% of 40) +30

【答案】 A.

【解析】简单计算可得答案.

22.Quantity A:

24÷6×4

Quantity B:

12

【答案】A

【解析】根据运算法则，从左往右计算得Quantity A=16＞12（即Quantity B）。

23.Quantity A

400% of 3

Quantity B

300% of 4

【答案】C

【解析】Quantity A: 400% of 3 =4×3 =12；

Quantity B: 300% of 4 =3×4 =12.

24.Quantity A

The price of a television when it is on sale at 25% off

Quantity B

The price of that television when it’s on sale at $25 off

【答案】D

【解析】由于不知道电视机的具体价格，因此没法比较两数值的大小。

25.There are the same number of boys and girls in a club.

The average weight of the boys is 150 pounds. The average weight of the girls is 110 pounds.

Quantity A

The number of boys weighing over 150

Quantity B

The number of girls weighing over 110

【答案】D

【解析】由于根据题干中的已知条件无法判断每个男生或女生的体重，因此无法比较两树脂的大小。

26. A school group charters three identical buses and occupies 4/5 of the seats. After 1/4 of the passengers leave, the remaining passengers use only two of the buses.

Quantity A

The fraction of the seats on the two buses that are now occupied

Quantity B

9/10

【答案】C

【解析】为了计算简便，可以假设每辆汽车上共有20个座位；那么最初占用的座位数是48，然后四分之一（12位）乘客下车后，还剩下36位乘客；因此这36位乘客占用的座位所占的比例为36∕40=9∕10，可见Quantity A与Quantity B相等。

27.Quantity: A (-8)8

Quantity B: (-9)9

【答案】A

【解析】计算可得，Quantity A为-64，而Quantity B为-81；-64＞-81，因此，Quantity A大于Quantity B。

28.The price of a large pizza is 30% more than the price of a small pizza.

Quantity A:

The price of a large pizza when it is on sale for30% off

Quantity B:

The price of a small pizza

【答案】B

【解析】为了计算简便，假设小披萨的价格为10美元，那么大披萨的价格为10+10×30%=13美元；因此，Quantity A=13-13×30%=9.1美元＜10美元（Quantity B），选择B项。

29. A school group charters three identical buses and occupies of the seats. After of the passengers leave, the remaining passengers use only two of the buses.

Quantity A

The fraction of the seats on the two buses that are now occupied

Quantity B

【答案】C

【解析】为了计算简便，假设每辆汽车共有20个座位，那么3辆车共有60个座；根据题意，开始时乘客占了的座位，即48个座位，当的乘客（即12位）离开后，还剩36位乘客，占用36个座位，占两辆车座位数的36/40=，因此两数值相等。

30. At a sale, the cost of each tie was reduced by 20 percent and the cost of each belt was reduced by 30 percent.

Quantity A

The percent reduction on the total cost of 1 tie and 2 belts

Quantity B

25%

【答案】D

【解析】由于不知道领带和腰带的具体价格，因此无法计算他们的折扣程度。

31.Quantity A

The average (arithmetic mean) of all the positive multiples of 5 less than 26

Quantity B

The average (arithmetic mean) of all the positive multiples of 7 less than 26

【答案】A

【解析】符合题干要求的5的倍数有: 5,10,15,20,25，7的倍数有7,14,21，显然Quantity A要大于Quantity B。

32.Quantity A: a 20% pay raise followed by a 15% pay cut

Quantity B: a 15% pay cut followed by a20% pay raise

【答案】C

【解析】设原价为100，故A=100*(1+20%)*(1-15%)=102，B=100*(1-15%)*(1+20%)=102，故AB相等，本题选C项。

33.Quantity A: 15 percent of 90

Quantity B: 90 percent of l5

【答案】C

【解析】计算可知两数相等，选择C项。

34.A windmill makes one revolution every 8 seconds.

Quantity A: 23 

Quantity B: The number of revolutions made in 3 minutes

【答案】A.

【解析】根据题目中的数量关系，风车3分钟转的圈数为（3×60）÷8=22.5＜23。所以，Quantity A 大于Quantity B。

35.Quantity: A – (4) 2　

Quantity B: (-4) 2

【答案】 B

【解析】简单计算即可得出答案，注意负号的位置。

36.Quantity: A 90,000　

Quantity B: (298.89) 2 

【答案】A

【解析】由于90,000=（300）2  >(298.89) 2 ，所以Quantity A大于Quantity B。

37. Quantity A

Price of a $30,000 car after a 10% discount and 10% sales tax

Quantity B

Price of a $ 30,000 car after a 7% discount and 7 % sales tax

【答案】B

【解析】Quantity A=$30,000×90%+$30,000×90%×10%=$29,700；

Quantity B=$30,000×93%+$30,000×93%×7%=$29,853，显然Quantity B大。

38.Quantity A

Quantity B

【答案】A

【解析】比较可知，Quantity A大于Quantity B.

39.Quantity A

The number of prime numbers between 70 and 76

Quantity B

The number of prime numbers between 30 and 36

【答案】A

【解析】根据题意，Quantity A=2，Quantity B=1.

40. Carol’s age, in years, can be expressed by reversing the digits in her father’s age, in years. The sum of the digits in each age is 10.

Quantity A

The positive difference between Carol’s age, in years, and her father’s age, in years

Quantity B

36

【答案】D

【解析】根据已知条件无法计算Carl和他父亲的各自年龄，因此无法比较Quantity A和Quantity B的大小。

41. As two wheels－A and B－roll across the ground, they both rotate at a rate of 60 revolutions per second. The radius of wheel A is 3. The radius of wheel B is 1.5.

Quantity A

The distance wheel A travels per minute

Quantity B

The distance wheel B travels per second

【答案】A

【解析】根据题干中的已知条件，Quantity A=60×60×2π×3=21600π，Quantity B=60×2π×1.5=180π，因此Quantity A大。

42.A buyer pays a $1.00 tax on an item that costs $10.00 after the tax is added.

Quantity A

The percentage rate of the tax

Quantity B　

11%

【答案】A

【解析】根据题意计算可得，Quantity A大于Quantity B。

43.Quantity A

The ninth number in the following sequence:

{3, 3, 4, 6,9,13...}

Quantity B

31

【答案】C

【解析】观察Quantity A中的数列可知，3比3大0，4比3大1，6比4大2，9比6大3，13比9大4....按照这一规律可得第九个数值为31；因此两数值相等。