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joelu926 · 发表于 2006-5-30 14:41:00

1. What is the greatest prime factor of 4 ^17 - 2 ^ 28 ?

ans......7

2. In the xy-plane. link k has positive slop and x-intercept 4. If the area of the triangle

formed by link k and the two axes is 12. What of the y- intercept of link?

ans.......-6

3. IS the positive interger J divisible by a greater number of different prime numbers than

the positive interger k ?

(1) j is divisible by 30

(2) k=1000

ans....(C)

4.

How much time did it take a certain car to travel 400 kilometers?

(1) The car traveled the first 200 kilometers in 2.5 hours

(2) If the car's average speed had been 20 kiolmeters per hour

greater than it was, it would have traveled the 400 kilometers in 1 hours less time than

it did.

ans.....(B)

yaoyao99 · 发表于 2006-5-30 15:07:00

1.
4^17 = (2^2)^17 = 2^34
2^34 - 2^28 = 2^28 x (2^6 - 1) = 2^28 x 63 = 2^28 * 7 * 3^2

2.
intersections: (0,4) and (y, 0)
4 * y' / 2 = 12 => y' = 6
slope is positive => y is below the x axis => y = -6

3.
1) J = 2 * 3 * 5 => J has 3 different prime factors (inconclusive)
2) K = 2^3 * 5^3 => K has 2 different prime factors (inconclusive)
1 + 2 => J has more different prime factors

4.
1) Inconclusive, no idea about the car's speed for the next 200 kms
2) (actual speed + 20) * (actual time - 1 hour) = 400 kms = actual speed * actual time
Can solve for actual time

B

[此贴子已经被作者于2006-5-30 15:12:04编辑过]

joelu926 · 发表于 2006-5-30 15:14:00

thanks

挺簡單的嘛，看來是自己頭腦不太清楚。

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