请教GMATPREP问题

1. a thin piece of wire 40 meters long is cut into two pieces. one piece is used to form a circle with radius r, and the other is used to form a aquare. no wire is left over. which of the following represents the total area, in saure meters, of the circular and the aquare regions in terms of r?

pai r²  ;  

pai r^{2  _{+ 10;}}  

pai r² + 1/4 pai2 r²

pai r² + (40-2 pai r)²

pai r² + (10- 1/2 pai r )²

^{答案是E，我认为是D}

2. a furniture dealer pruchased a desk for $150 and then set the selling price equal to the pruchase price plus a markup that was 40 percent of the selling price. if the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?

$40; $60; $80; $90; $100

the answer is 100; i think is $60?

3. the number 75 can be written as the sum of the squares of 3 different positive integers. what is the sum of these 3 integers?

17; 16; 15; 14; 13

the answer is 13

想知道这个题的思路，应该如何去想？

4. is x-y+1 greater than x+y-1

1) x>0

2) y<o

the answer is B, my answer is C?

5. an integer greater than 1 that is not prime is called compositie. 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.

the answer is A, why?

thank you

是E呀，剩下的绳子长40-2pai*r，围成正方形，边长当然要除4，再平方才是面积呀。MM要避免马虎引起的错误啊。

要注意是卖出价格的60％，而不是购买价格的60％

所以应该是(150+profit)*40%=profit

没想出什么好办法。我只能采用穷举法往里套。最大的数最多为8，因为9^2>75,将1-8往里套，看哪个满足。

X-Y+1-(X+Y-1)=2-2Y,如果使这个数大于0的话，Y<1,所以B就足够了

设tens digit of n is X,untis digit表示为kX

则n=10X+kX=X(10+k)

而n>20,说明X>2,所以n至少可分解为X(非1正整数）和10+k两个因子

所以A就足够了

admire Hitlzc......

Hitlzc MM解释的真清楚，非常感谢

3. the number 75 can be written as the sum of the squares of 3 different positive integers. what is the sum of these 3 integers?
17; 16; 15; 14; 13
the answer is 13

我觉得2楼说的“最大的数最多为8，因为9^2>75”很对，在2楼得基础上接下来可以这样试：

1(1),2(4),3(9),4(16),5(25),6(36),7(49),8(64)

观察平方末尾的数字为：1，4，9，6，5

要得到75，必须有5（25），然后必须保证平方末尾是1，9同时出现；要不就是4，6同时出现，这样就缩小了猜得范围了

接下来75-25=50,那么一眼就能看出来1＋49＝50了，结果就是1+7+5=13了