请教PREP数学题

xianinginsz · 发表于 2010-10-22 08:55:29

1.
DS：x，y都是正整数，x=8y+12，x和y的最大common divisor是什么？
（1）x=12u，u是整数
（2）y=12z，z是整数

2.
DS：in the fraction x/y, where x and y are positive integers, what is the value of y?
(1) the least common dominator of x/y and 1/3 is 6
(2) x=1

3.
DS：if 500 is the multiple of 100 that is closest to x and 400 is the multiple of 100 that is closest to y, what multiple of 100 is closest to x+y?
(1)x<500
(2)y<400

4. PS: 有一组21个宇航员，其中12个有过飞行经验，现在要从中选一个3人小组，使得组员中正好一人有过飞行经验，问有多少种选法？
a.432 b.594 c.864 d.1330 e.7980

xianinginsz · 发表于 2010-10-22 09:52:26

希望数学NN帮忙解答

xianinginsz · 发表于 2010-10-22 11:25:19

自己找的答案
1.This is a VERY difficult problem. The vast, vast majority of people will not be able to tackle this problem in 2 minutes and will need to make an educated guess and move on.

Statement (1) tells us that 12 is a divisor of x. What does it tell us about y?
12u = 8y + 12
(multiple of 12) = 8y + (multiple of 12)
8y must be a multiple of 12.

Therefore, y must be a multiple of 3 and 3 is a divisor of y. 3 might be the greatest common divisor of x and y. But y might have other divisors too (e.g., 6 or 12). Insufficient.

Statement (2) tells us that 12 is a divisor of y.
What does it tell us about x?
x = 8(12z) + 12
x = (multiple of 12) + (multiple of 12)
x must be a multiple of 12.
12 is a divisor of x.

So 12 is a common divisor of x and y. But is it the greatest common divisor?

RULE: If one number is b units away from another number, and b is a factor of both numbers, the greatest common factor of the two numbers is b. (If you want to really understand this, then think about why. Otherwise, just remember the rule.)

x (one number) is 12 units away from 8y (another number). 12 is a factor of x and 8y. Therefore, 12 is the GCF of x and 8y. The GCF of x and y can’t be bigger than the GCF of x and 8y. Thus, we can be assured that 12 is the GCF of x and y. Statement (2) alone is SUFFICIENT.

xianinginsz · 发表于 2010-10-22 11:27:44

2.
Statement 2)Says nothing about y, insufficient.

Statement 1)
rephrase: the LCM of y and 3 is (2)(3). Draw an LCM chart. 3 has one (3), so y MUST have one (2). additionally, y may also have an additional (3), without changing the LCM. Therefore, y can be (2) OR (2)(3). Insufficient.

Together)
y = (2) or (2)(3)
x = 1, does not affect the denominator.
Still insufficient. E.

xianinginsz · 发表于 2010-10-22 11:29:24

3.
Per the stem:
Range of X: 449<X<550
Range of Y: 349<X<450

By 1: Say X=499
Now if Y = 449 then nearest multiple of 100 to X+Y will be: 900

Say X=449 Now if Y = 350 then nearest multiple of 100 to X+Y will be: 800

Similarly you can prove that it is E

xianinginsz · 发表于 2010-10-22 11:30:23

4.
Total no of ways to select 1 person with experience - 12.
Total no of ways to select remaining 2 persons - 9C2.

hence total ways - 12 x 9C2 = 432.

differece between permutation and combination.

if one has to choose 2 people from 9 people,ask- does the ORDER matter? That is - is AB different from BA. You'll have to see context. Let's say there is a team with 2 players in it. Tehn you only have 1 combination of the team, say, Jack and Daniels. You can' t say I have 2 teams: jack, Daniels and Daniels, Jack. Here the ORDER doeesn't matter. BUT, if they race each other, ORDER matter: Ex jack can come first and Daniels second, and vice-versa[ assuming no tie].

zhongyaya · 发表于 2010-10-23 18:52:18

RULE: If one number is b units away from another number, and b is a factor of both numbers, the greatest common factor of the two numbers is b. (If you want to really understand this, then think about why. Otherwise, just remember the rule.)

楼上给的解释相当棒~但是第一题的rule我不太懂~后面的筒子们能不能给解释下？谢谢啦

zhongyaya · 发表于 2010-10-23 18:54:17

RULE: If one number is b units away from another number, and b is a factor of both numbers, the greatest common factor of the two numbers is b. (If you want to really understand this, then think about why. Otherwise, just remember the rule.)

楼上给的解释相当棒~但是第一题的rule我不太懂~后面的筒子们能不能给解释下？谢谢啦

zhongyaya · 发表于 2010-11-1 13:12:36

顶~

请教PREP数学题

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