## Oct 20, 2008

1. Since 1=5, the answer for 5 should be 1. Alternatively, the answer can be 12345.
2. This question is easy to solve. Dave does more than James, and that means: 1/12-1/15=1/602, and the 15 here represents 1/60 as a whole. Thus, the answer is 15÷1/60=900.
3. Here's the solution: (2a + a + 3b = 3a + 3b = 3 (a + b) = 3*10 = 30). The answer is 30.
4. 3 = 1 +2

10/10 = 1

1 + 1 = 2

2 + 10 = 12

12*2 = 24

5. (1 + 1/9) *9 = 10, or alternatively, √[(1+9)*(1+9)]=10

6. 8-1-3x/2=0
3x=(0+1+8)×2
3x=18

x=6

7. Let f(x) = 4x³-2x²-3x+1=0

Then, f(1) = 4(1)³-2(1)²-3(1)+1=0

Now, use (x-1) to dissolve 4x³-2x²-3x+1 into (x-1)( 4x³-2x²-3x+1)>

(x-1)( 4x³-2x²-3x+1) = 0

(x-1)[x-(-2±√20)/8 ]=0

Hence, x=1 or x=(√5-1) /4 or x=-(√5+1)/4

Alternatively,

4x^3-2x^2-3x+1=0
4x^3-4x-（x^2-x）-x^2+1=0
4x(x-1)(x+1)-x(x-1)-(x-1)(x+1)=0
(x-1)(4x^2+4x-x-x-1)=0
(x-1)(4x^2+2x-1)=0

Hence, x=1 or x=(√5-1) /4 or x=-(√5+1)/4

8. Hence, (10-2X)*(6-2X)*X=4(5-x)(3-x)x=4(x-5)(x-3)x

9. The answer for this question is 30. Let me explain. The square can be formed up into one square, four, nine and sixteen small squares. One big square has 16 small squares. Within this big square, 9 of them form up 4-square square, 4 of them form up 9-square square, and lastly 1 forms up 16-square square shape. Thus, 16 + 9 + 4 + 1 = 30.

10. There're numerous ways to get the answer. See my calculations below:

* 9 x9 + 19 = 100
* (9+1) x (9+1) = 100
* 9*9 + 19 = 100
* 9 + 1 = 10, and 9-9 = 0, from the answers you obtained, you can combine them to get 100

11. This answer can be obtained in two ways. See my calculations below:

* (1+4)*3+6=24
* 6/(1-3/4)

12. 5-6/2 + 9 = 11, or (-5 + 6) * 2 + 9 = 11

13. 9/9 + 99 = 100

14. (5-1/5)*5 = 24 or 5*5 -1^5 = 25 - 1 = 25 (5 -1/5) * 5 = 24

15. 8 ÷ (3-8 ÷3) = 24

16. There're numerous ways to get the answer. See my calculations below:

* 5x 5-5 +5 ÷5 = 25-5+1 = 21
* 5*5-(5-5/5) = 21
* 5/5 + (5*5-5) = 21

Hmmm…how many scores are you at? More than 40…Wow, “Bravo”, “excelente”, “yoku dekimashita”, “handal”…brilliant, Hooray!!! Congratulation! You're now almost an expert to solve the mathematical questions!

Anonymous said...

You answer to number six is wrong if following order of operations.
You have 8-1-3x/2=0
So you move the constants to the other side:
-3x/2=1-8
Then divide by negative one on both sides:
3x/2=8-1 or 3x/2=7
Then multiply both sides by two:
3x=14
Finally divide by three to isolate x:
x=14/3