刚做完prep1。结局惨烈。几个数学题。求战友们解答。

xtxtxtli

1. for all positive integers m,
m（包了一个方框）=3m， if m is odd;
m(包了一个方框）=1/2m, if m is even
which is equivalent to 带方框的9*带方框的7？

我算的是81， 答案是27

2.if n is a positive integer and the product of all the integers from 1 to n,  is a multiple of 990, what is the least possible value of n?

答案:11

3. of the 60 animals on a certain farm, 2/3 are either pigs or cows. how many of the animals are cows?
1) the farm has more than twice as many cows as it has pigs.
2) the farm has more than 12 pigs.

答案选c

4. an integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?
1) the tens digit of n is a factor of the units digit of n.
2) the tens digit of n is 2.

选A。

5. is z equal to the median of the three positive integers x,y, and z?
1) x<y+z
2) y=z


一模数学46分。错了13题。请教距离51分还有多远呢？
对各位朋友的帮助，不胜感激！！

sdcar2010

If you can see the attached picture, you would have a better time to solve the problem 1 LZ posted.

According to the stimulus, [9] = 3*9 =27. [6] = (1/2) * 6 = 3.  So [9]*[6] = 27 * 3 = 81.  So far so good.  But if you choose (a) as the correct answer, you were wrong because (a) is [81] = 3*81 = 243!

On the other hand, (d) [27] = 3*27 = 81, is the right answer!

-- by 会员 sdcar2010 (2011/1/5 22:39:41)

佩服SDCAR的古道热肠，不厌其烦地解释，今天看到题干终于明白了，谢谢你的指点。

-- by 会员 mijianture (2011/3/25 14:01:21)

The pleasure is all mine.

mijianture

If you can see the attached picture, you would have a better time to solve the problem 1 LZ posted.

According to the stimulus, [9] = 3*9 =27. [6] = (1/2) * 6 = 3.  So [9]*[6] = 27 * 3 = 81.  So far so good.  But if you choose (a) as the correct answer, you were wrong because (a) is [81] = 3*81 = 243!

On the other hand, (d) [27] = 3*27 = 81, is the right answer!

-- by 会员 sdcar2010 (2011/1/5 22:39:41)

佩服SDCAR的古道热肠，不厌其烦地解释，今天看到题干终于明白了，谢谢你的指点。

sdcar2010

LS is right. My bad.

gmat2000

4. an integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?
1) the tens digit of n is a factor of the units digit of n.
2) the tens digit of n is 2.

1) Let's say the units digit of n is a.  Then the tens digit of n is a factor of a.  Therefore, n = 10*m*a + a = a*(10m +1).  Then n has a factor of a and a is bigger than 1 since n is greater than 20.  n is a composite for sure. Sufficient.
2) Insufficient.  21, 22, 23 ....

-- by 会员 sdcar2010 (2011/1/5 11:56:31)

do not understand n = 10*m*a + a, should it be like n = AB = 10xA + AC =A(10+C).. ?

sdcar2010

If n! = somthing * 11, is n at least as big as 11?

Shine61

2.if n is a positive integer and the product of all the integers from 1 to n,  is a multiple of 990, what is the least possible value of n?

n! = n*(n-1)*. . . *2*1= m*990 = m*11*9*5*2

So n! contains the factors of 11, 9, 5, and 2.  Then n is at least as big as 11!

-- by 会员 sdcar2010 (2011/1/5 11:42:35)

还是不太明白。

gesteven

大侠回复太全了，佩服佩服。

Rebeca

N人！服了！！

sdcar2010

If you can see the attached picture, you would have a better time to solve the problem 1 LZ posted.

According to the stimulus, [9] = 3*9 =27. [6] = (1/2) * 6 = 3.  So [9]*[6] = 27 * 3 = 81.  So far so good.  But if you choose (a) as the correct answer, you were wrong because (a) is [81] = 3*81 = 243!

On the other hand, (d) [27] = 3*27 = 81, is the right answer!