[求助]GMATPREP幾道數學題

scholarliu

烦请各位高手帮我解答以下几道题目，感激不尽阿

1.      X, Y为integers,问X(Y+1)是否为even number?

(1)   X, Y各为prime number

(2)   Y>7

Ans: C

2.      500 is the multiple of 100 that is closest to X and 400 is the multiple of 100 that is closest to Y, which multiple of 100 is closest to X+Y？

(1)   X<500

(2)   Y<400

Ans：E

3.      If d is positive integer, f is the product of the first 30 positive integers, what is the value of d?

(1)   10^d is a factor of f

(2)   D>6

Ans ：C

t5oct2005

1. (1) [x,y] = [2,2] & [3,2] though fulfill requirement but results contradict each other

(2) x,y are not specified to be odd or even

together, prime>7 is always odd thus make y+1 always even, therefore x(y+1) is made always even.

2.500 is the multiple of 100 that is closest to X => 450<X<550

400 is the multiple of 100 that is closest to Y => 350<Y<450

so 800<X+Y<1000, one of 800, 900, 1000 will be multiple of 100 is closest to X+Y

(1) X<500,=> 800<X+Y<950, either 800 or 900 will be multiple of 100 is closest to X+Y

(2) Y<400 => same as above

together => 800<X+Y<900, either 800 or 900 will be multiple of 100 is closest to X+Y as we cannot confine X+Y to any smaller intervals (if within 50, we may probably solve this question)

3. need hard work to calculate 30! ? no!

we have 5,10,15,20,25,30 and some 2s to see how many zeros there are in the tail of the result

5x2, 15x2 contributes 1 zero each

10, 20, 30 => 3 zeros

25x4 => be careful, it contributes 2 zeros

so totally there are 1x2+3+2=7 zeros in the tails of 30!

for (1) d can be 1,2,3,4,5,6,7 (2) d can be any integer >6

together, d can only be 7 to fulfill both requirements.

scholarliu

哇...厉害厉害……

不过2.中, 为啥500 is the multiple of 100 that is closest to X => 450<X<550而

400 is the multiple of 100 that is closest to Y => 350<Y<450????

我看不懂为啥X和Y的范围会这样耶

t5oct2005

for x=449, 400 instead of 500 is the multiple of 100 which is closest to x

similarly, for x=551, 600 instead o 500 is the multiple of 100 which is closest to x

therefore x can only reside in (450,550).

scholarliu

Oh...I got it. Thanks a lot

scholarliu

再请问以下问题该如何解决呢?

1.      On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

(1)   On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.

(2)   The number of women on the sight-seeing tour was less than 30.

答案是C,可是我觉得是E耶…..

2.      The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

答案是40% increase…..晕,我连题目都搞不太清楚,天阿!!!

3.      问X是否介于0和1之间?

(1)   X介于-(1/2)和3/2之间

(2)   3/4 is 1/4 more than X

答案是B,可是我觉得第二选项只能求出X<1,但无法得知X>0阿??

4.      某间大学中, there are twice as many English majors as history majors and three times as many English majors as math majors. 求 the ratio of the number of history majors to the number of math majors?

答案是3 to 2. 可是我怎么算都是2 to 3???

t5oct2005

your questions are interesting.

1. given w:c=5:2

(1) c:m=5:11, you agree it is insufficient

(2) W<30, you also agree it alone is insufficient

together, w:c:m = 25:10:22 (see any difference? all have to be integers!) thus w=25 and m=22.

2.rate = A^2/B, the question asks how shall A change to cope with a 100% increase of B to make the rate constant

(xA)^2/(2B) = A^2/B => x^2=2 => x=1.414 => A has to increase to 1.414A, equivalent to say an increase of appr. 40%

3. (1) is out.

(2) 3/4 = X+(1/4)X or 3/4 = X+1/4, I don't know. any way, you can work out X.

4. E=2H & E=3M => M:H=2:3 or H:M=3:2

[此贴子已经被作者于2005-11-1 23:08:28编辑过]

scholarliu

看完解答,发觉我真的是…..该去撞墙啰….头脑不清成这副德行…唉

可是我还是有点疑问

3. 条件二的3/4 is 1/4 more than X,我以为是3/4-X会大于等于1/4的意思耶??

4.  there are twice as many English majors as history majors and three times as many English majors as math majors.这段话的意思不是说2E=H, 3E= M吗???

t5oct2005

3. 条件二的3/4 is 1/4 more than X,我以为是3/4-X会大于等于1/4的意思耶??

则个我也不太清楚，不知道你的想法该怎么用英语表达；3/4 is 1/4 larger than X等同于什么呢？是3/4 = X+1/4? 那3/4 is larger than X+1/4 才应该表达为3/4>X+1/4吧？

4.  there are twice as many English majors as history majors and three times as many English majors as math majors.这段话的意思不是说2E=H, 3E= M吗???

我从kaplan2005数学某章里得到的：half as many A as B => B/2 = A

比较 I have twice as many apples as you have. 是不是说我拥有的苹果是你拥有的两倍？

而 I have twice as many apples as pears. 也应该是说苹果是梨的两倍

scholarliu

喔喔....你应该是对的啦...我错啰