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
capacity = X
X-(2/5X+7) = X/4
3X/5-7 = X/4
7X/20 = 7
X = 20 #
quart意為1/4
: 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)
Machine X rate = w/5
Machine Y rate = w/t
w／w/5+w/t = 2
1／1/5+1/t = 2
5t/t+5 = 2
5t = 2t+10
3t = 10
t = 10/3 = 3 1/3 #
: 3. At a school, out of 120 seniors, 80 srniors take Calculus and 64 seniors
: take Biochemistry.
: Column A Column B
: The number of seniors: The number of seniors
: who take both Calculus 24
: and Biochemistry. ANS: D 我算80+64-120=24 C
因題目沒說此120人只修這2門課，所以Ans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
10^50-74 = 99………926
└共48個9┘
把此答之所有阿拉伯數字相加 = 48x9+2+6 = 440 #
: 5. In the xy-plane, point A (22,-2) and B (10,-2) lies on a circle with cente
: O. If the measure of angle AOB is 120 degrees, then what is the area of th
: circle?
: (A) 12π
: (B) 24π
: (C) 36π
: (D) 48π
: (E) 60π ANS:(D)
此題有圖解輔助說明更易懂，此處無法圖解，僅用算式解題。
2：√3 = r：6
r = 12/√3
πr^2 = π(12/√3)^2 = 144/3 π = 48π #
: 6. For any positive integer n, the sum of the first n positive integers equal
: [(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)
答 = 100+102+104+…+298
= 2(50+51+52+…+149)
= 2x 50+149/2 x100
= 19900 #
Between 99 and 300不包含99和300，除非寫between 99 and 300, inclusive. 此敍述就表
示包含99和300
: 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 machine
: together produce 5/4w appliances in 3 days, how many days would it takes
: 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
此題是GMAT題目。
5/4w／w/t+w/t-2 = 3
5/4／1/t+1/t-2 = 3
5/4／2t-2/t(t-2)
5t(t-2)／8t-8 = 3
5t(t-2) = 24t-24
5t^2 -34t+24 = 0
(5t-4)(t-6) = 0
t = 6, 5/4(不合)
6x2 = 12 #
: 8. In town X, 64 percent of the population are employed, and 48 percent of th
: 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)
此題是GMAT題目。
設total population = X
employed population = 0.64X
employed males = 0.48X
employed females = 0.64X-0.48X = 0.16X
0.16X/0.64X x100% = 1/4x100% = 25% #
注意最後問What percent of the employed people…
: 9. In a company, 50% of the male employees and 40% of the female employees ar
: at least 35 years old. If 42% of all the employees are at least35 years ol
: , 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
0.5m+0.4f = 0.42(m+f)
0.08m = 0.02f
4m = f
f/m+f = f／f/4+f = 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 = 2^2x3^2x7
252^5 = 2^10x3^10x7^5
6 = 2x3
6^z = 2^zx3^z
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)
題意：從8:00到9:00，分針要花幾分鐘才能趕上時針？
假設鐘之圓周 = 2πr，從8:00到9:00，時針走的距離 = 2πr/12
時針之速度 = 2πr/12 x 1/60
分針之速度 = 時針速度的12倍 = 2πr/60
分針要趕上時針所要走的距離 = 4/6圓周+時針速度x時間
= 4/6(2πr)+ 2πr/12 x 1/60 x t
此距離也 = 分針速度x時間 = 2πr/60xt
所以2πr/60 t = 4/6(2πr)+ 2πr/12x1/60 t
t/60 = 4/6 + 1/12x60 t
t/60(1-1/12) = 4/6，t/60x11/12 = 4/6，t/10x11/12 = 4/1，t = 480/11 #
: 12. A positive integer n is said to be "prime-saturated" if the product of al
: 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)
96 = 2^5 x3
the product of all the different positive prime factors of 96 = 2x3 = 6
the square root of 96 = √96
6 <√96 #
: 13. A photographer will arrange 6 people of 6 different heights for photograp
: 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？
↑Yes!
（以上內容由美加 黃冠文老師提供）
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