Mathematics

1)
1-2-5-10-13-26-28-58
(1 , 2) (5 , 10) (13 , 26) ,......
(1 , 2) (2+3 , 10) (10+3 , 26) , the next term should be (26+3 , 58)
i.e. (29 , 58)
28 does not belong in the following series , it should be 29 ,
ANSWER : (C)


2) 3 sides : (3x-8), (3x-6) and (5x-16),
Case 1 :
3x-8 = 3x-6 , no solution.
Case 2 :
3x-8 = 5x-16
x = 4
3 sides are 3*4-8 = 4 , 3*4-6 = 6 and 5*4-16 = 4
Case 3 :
3x-6 = 5x-16
x = 5

3 sides are 3*5-8 = 7 , 3*5-6 = 9 and 5*5-16 = 9
There are 2 possible values for x.


3)a+b<0, ab<0 and a<b
By ab<0 and a<b,
we have b > 0 , a < 0
Combine a+b<0 with b > 0 , a < 0 :
- a > b ......(2)

or
a < - b ......(3)
Combine a<b and (2) we have :
a < b < - a ......(4)

combine (4) with (3) and we know that b>0 so - b < b :
a < - b < b < - a
No choice is true. Please check your question.
For example , for a+b<0, ab<0 and a<b ,

Let a = -2 , b = 1 , then

a+b = -2 + 1 < 0 , ab =(-2)(1) < 0 and -2 < 1 is suitable.
The result a < - b < b < - a
i.e. - 2 < - 1 < 1 < - (-2) is true.

1.D

2.3x-8not equal to 3x-6 so it is not those isos. sides,because of this 3x-8=5x-16and 3x-6 also =5x-16 so x can be 4/5

3.D

2010-04-29 19:05:26 補充：
a must be negative no. and if b is negative no. after a time b they will not be smaller than 0 so b must be positive number .at this moment the answer is very obvious ,