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Econ
10-23-2004, 04:00 PM
(1) In a given river, the current is 6mph. A certain riverboat travels 18mph in still water. How far upstream (against the current) can the boat travel if a round trip is 10 hours?

(2) If x is a prime and (x)(N) is both the square of an integer and the cube of an integer then find the maximum value of 1/(Nx).

Both questions are copied word for word. I will post the answer within 24 hours.

awhig
10-23-2004, 04:14 PM
Q1 . 80 miles.

Q2. Do you mean (x)(N) as x ^ N . If so then I give answer as 1/12.

Econ
10-23-2004, 04:27 PM
Q1: Nice work
Q2: Sorry, I meant (x)*(N) and Nx is again (x)*(N) (multiplication)

awhig
10-23-2004, 04:41 PM
Q1: Nice work
Q2: Sorry, I meant (x)*(N) and Nx is again (x)*(N) (multiplication)
Ques 2. 1/64 should be the anwer.

gre_nidhi
10-23-2004, 07:23 PM
For ist one i agree with awhig....80 miles.

2) is it 1/128 ?????

Dingus
10-23-2004, 08:17 PM
1st: (18-6)*t = (18+6)(10-t)
solving for t --> 20/3
12*20/3 -->80
2nd: If in the question both the "integers" mentioned are different, the maximum value of 1/N*x = 1/64 (8^2 , 4^3). I agree with awhig.

Econ
10-23-2004, 08:43 PM
Yes.
(1) 80 (2) 1/64
Questions were taken from 800com.
The first one I missed it (I didn't get that for some time it travels with 24)...hope it does not happen on the real Test!

lmtuan
10-24-2004, 07:00 AM
These question are too easy!
question 1: 80
question 2:
a=2, N=32, a*N = 64 = (8)^2 = (4) ^3
Thus, 1/ (a*N) = 1/64

Dingus
10-24-2004, 10:53 AM
Yes.
(1) 80 (2) 1/64
Questions were taken from 800com.
The first one I missed it (I didn't get that for some time it travels with 24)...hope it does not happen on the real Test!

That will not happen Econ! I know you are going to score that fabulous 800 in your test on Friday. My prayers and wishes are with you. :) They definitely are not easy straightforward questions. Also, the more mistakes one makes before the test day, the more insight one gets into one's weaknesses. That way, on the test day, you know what exactly to expect and avoid.
Cheers and all the best!
Dingus

(My test is also on that day. :crazy: )