[問題]11/28要考試了,有幾題GMATPrep test1的問題

[conliao]

考試在即,麻煩高手幫幫忙解答一下,感恩~~

1. If n is a multiple of 5 and n=(p^2)*q, where p and q are prime numbers, which of the following must be a multiple of 25?
a) p^2 b) q^2 c) p*q d) (P^2)*(q^2) e) (p^3)*q

Ans: d

2. A certain office suply store stocks 2 sizes of selfstick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
a) 6 b) 8 c) 16 d) 24 e) 32

Ans: c

3. A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?
a) 10700 b) 10800 c) 10900 d) 11000 e) 11100

Ans: d

[fsab00037748]

1. n is a multiple of 5 and n=(p^2)*q, p and q are prime numbers
表示p=5或q=5
A.P^2 不一定是25的倍數, 因為有可能是q=5
B.q^2不一定是25的倍數, 因為有可能是p=5
C.p*q不會是25的倍數
D.p^2*q^2一定是25的倍數,不管是q=5或是p=5都可使之成立
E.p^3*q, 因為有可能是q=5



2. 2*4+ C(4,3) * 2 =16 思路如下:

有2種size (假設大和小好了),4種顏色

3 notepads of the same size and the same color就有2x4種包法
也就是 大B 大G 大Y 大P 4種, 小B 小 G 小Y 小P 4種, 共8種

3 notepads of the same size and of 3 different colors
也就是說從大size中四種顏色隨便挑3種出來, 小size中四種顏色隨便挑3種出來
C(4,3) * 2



3. 我不知道怎麼算,也很想知道, 還請知道的人解答了^^ 3q3q

[conliao]

感謝感謝~~
盡在不言中...

[celivia]

1. n is a multiple of 5 and n=(p^2)*q, p and q are prime numbers
表示p=5或q=5
A.P^2 不一定是25的倍數, 因為有可能是q=5
B.q^2不一定是25的倍數, 因為有可能是p=5
C.p*q不會是25的倍數
D.p^2*q^2一定是25的倍數,不管是q=5或是p=5都可使之成立
E.p^3*q, 因為有可能是q=5



2. 2*4+ C(4,3) * 2 =16 思路如下:

有2種size (假設大和小好了),4種顏色

3 notepads of the same size and the same color就有2x4種包法
也就是 大B 大G 大Y 大P 4種, 小B 小 G 小Y 小P 4種, 共8種

3 notepads of the same size and of 3 different colors
也就是說從大size中四種顏色隨便挑3種出來, 小size中四種顏色隨便挑3種出來
C(4,3) * 2



3. 我不知道怎麼算,也很想知道, 還請知道的人解答了^^ 3q3q

我是看答案湊出算式,思路我也不是很清楚
13200/11=12000 (平均人口)
設最少人的人口為(12000-X)
少掉的X人則平均分攤在其餘10個區
每個區則為(12000+X/10)人
由題目條件最多與最少人差10%
[(12000+x/10)-(12000-x)]/(12000-X) = 10%
可算出x=1000,則最少人的區為11000