Re: [計量] 好多題計量請教
※ 引述《balance9235 (退伍變米蟲)》之銘言：
: 這是今天的題目，麻煩大家了！
: 1. After filling the car's fuel tank, Marie drove from city P to City Q and
: then to city R. If she spent two-fifths of the fuel driving from city P
: to city Q and another 7 gallons from city Q to city R, still having a
: quart of a tank left, how many gallons does the tank hold to capacity?
: (A) 12
: (B) 18
: (C) 20
: (D) 21
: (E) 35 ANS:(C) 算出來的數字不是整數
加滿是X
2X/5+7=3X/4(用掉3X4剩X/4) 因此7=7X/20 X=20
: 2. Machine X produces w widgets in 5 minutes. If Machine X and Machine Y,
: working at the same time, produce w widgets in 2 minutes, how long will
: it take Machine Y to work alone to produce w widgets?
: (A) 2 1/2 min.
: (B) 2 2/3 min.
: (C) 3 1/3 min.
: (D) 3 1/2 min.
: (E) 3 1/3 min. ANS:(C)
2分鐘時,X做2w/5個,所以Y在2分鐘內做3w/5個,因此Y要做w個的話要2*5/3=3 1/3 min
: 3. At a school, out of 120 seniors, 80 srniors take Calculus and 64 seniors
: take Biochemistry. ^e
: Column A Column B
: The number of seniors
: who take both Calculus 24
: and Biochemistry. ANS: D 我算80+64-120=24 C
兩者都修的人是不確定的,最高可以到64人都修兩門課,
最低是只有24人,因此是D
: 4. If 10^50-74 is written as an integer in base 10 notation, what is the sum
: of the digits in that integer?
: (A) 424
: (B) 433
: (C) 440
: (D) 458
: (E) 467 ANS:(C) 看不懂題目要問啥
┌ 共48個 ┐
10^50-74的所有位數相加為何=9999999999...999926 因此=2+6+48*9=8+432=440
: 5. In the xy-plane, point A (22,-2) and B (10,-2) lies on a circle with center
: O. If the measure of angle AOB is 120 degrees, then what is the area of the
: circle?
: (A) 12π
: (B) 24π
: (C) 36π
: (D) 48π
: (E) 60π ANS:(D)
A 跟 B位在一個圓上,角AOB是120度,因此把圖畫出來可以發現AB長12,是圓內的一個弓型
圓的半徑為2*6/√3(看成是兩個30-60-90的直角三角形,三邊比是1:√3:2)
圓的面積=π*(2*6/√3)^2=48π
: 6. For any positive integer n, the sum of the first n positive integers equals
: [(1+n)n]/2. What is the sum of all the even integers between 99 ans 300?
: (A) 19,900
: (B) 20,200
: (C) 22,650
: (D) 40,299
: (E) 45,150 ANS:(A) 我算(B)
between沒有包含兩端點,所以300不算
: 7. Running at their respective constant rates, machine A takes 2 days longer
: to produce w appliances than machine B. At their rates, if the two machines
: together produce 5/4w appliances in 3 days, how many days would it takes
^^^^ w在分母or分子要寫清楚
: machine A alone to produce 2w appliances?
: (A) 4
: (B) 6
: (C) 8
: (D) 10
: (E) 12 ANS:(E) 算出來數字不美
B生產w要X天,A要X+2天,所以B每天生產w/X個,A每天生產w/(X+2)個
現在一起生產5w/4花3天,B生產了3w/X個,A生產了3w/(X+2)個,X=4
A生產w要4+2=6天,所以生產2w要12天
: 8. In town X, 64 percent of the population are employed, and 48 percent of the
: population are employed males. What percent of the employed people in town
: X are females?
: (A) 16%
: (B) 25%
: (C) 32%
: (D) 40%
: (E) 52% AND:(B) 我算(A)
What percent of the employed people in town X are females?
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
town X裡被雇用的人中,有多少比例是女人,分母是被雇用者,分子是被雇用的女生
因此是(64-48)/64=25%,但這些題都很機車...
: 9. In a company, 50% of the male employees and 40% of the female employees are
: at least 35 years old. If 42% of all the employees are at least35 years old
: , what fraction of the employees in the company are females?
: (A) 3/5
: (B) 2/3
: (C) 3/4
: (D) 4/5
: (E) 5/6 ANS:(D) 不太會算
假設原本女性比例是X,則男生是1-X
50%(1-X)+40%(X)=42% 0.5-0.5X+0.4X=0.42 X=0.8=4/5
: 10. 252^5 is divisible by 6^z. z is a positive integer.
: Column A Column B
: The greatest value 10
: of Z. ANS: C
252^5=(4*9*7)^5=2^10*3^10*7^5=6^10*7^5 因此Z=10
: 11. How many minutes does the minute hand of a clock take to meet the hour
: hand from 8:00 to 9:00?
: (A) 460/11
: (B) 300/7
: (C) 480/11
: (D) 310/7
: (E) 480/7 ANS:(C)
分針跟時針貼在一起,還記得國中有背一個公式但忘了...
當貼在一起時,時針從8點到9點走的比例=分針從0走到60的比例
圓一圈是360度,每小時12度,分針從0開始走,時針從8點開始走
當X分時分針走X/60*360度,時針走180+60+X/60*30度
X/60*360=180+60+X/60*30 6X=240+X/2 X=480/11
: 12. A positive integer n is said to be "prime-saturated" if the product of all
: the different positive prime factors of n is less than the square root of
: n. What is the greatest two-digit "prime-saturated" integer?
: (A) 99
: (B) 98
: (C) 97
: (D) 96
: (E) 95 ANS:(D)
prime-saturated是指他全部的質因數相乘比他自己開根號還要小
99: 3,11 3*11>10>√99
98: 2,7 2*7>10>√98
97: 97 97>√97
96: 2,3 2*3<√96
95: 5,19 5*19>√95 d
: 13. A photographer will arrange 6 people of 6 different heights for photograph
: by placing them in two rows of three so that each person in the first row
: is standing in front of someone in the second row. The heights of the
: people within each row must increase from left to right, and each person
: in the second row must be taller than the person standing in front of him
: or her. How many such arrangement of 6 people are possible?
: (A) 5
: (B) 6
: (C) 9
: (D) 24
: (E) 36 ANS:(A) 這題沒有公式，純粹土法煉鋼找出五種方式嗎？
只能用古法練鋼吧,用公式跟一堆條件算會更麻煩Orz
假設高度分別是 1 2 3 4 5 6 ,要排成兩排,由左往右漸增,後要比前高
因此一開始1跟6就已經固定了,一個前左一個後右,
6
1
再來2跟5也只能有2個位子選,2一定要在1後或1右,5一定要在6前或6左
6 2 6 56 256
125 1 5 12 1 共4種,再放進3跟4
456 246 456 356 256
123 135 123or124 134 共5種~
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※ 編輯: wearytolove 來自: 140.112.150.172 (01/13 20:41)
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