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Ten PS questions for discussion today

Problem Solving — algebra and arithmetic
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by neilcao » Sat Jan 29, 2011 1:33 am
Q1.（4.32）*10^(-4) hundred thousandth?

Q2. If S(N)=1+2+3...+N, find S(2N)-S(N)?

Q3. Liquid A contains 25% of water，B 55%，when add A and B, the total volume is 300L，water is 35%, find B's volume?

Q4. Out of 64 people，5 speaks German，6 speaks English，10 speaks Frence，everyone speaks at least one language, one of them speaks 3. How many speaks only 2 languages?

Q5. In List K, there are 24 integers. Every number's unit digit is 5, 1/3 tensdigits is 0, 1/3 tensdigits is 1, find the tens digits of the sum of 24 integers.

Q6. Set A includes numbers that are all negative factors of 16, Set B includes numbers that all negative factors of 8. X belongs to set A, Y belongs to set B. Find the least values of x-y?


Q7. A number 0.54321, the pattern repeats (0.543215432154321), find the 987th number ?


Q8. x is the sum for even number between 1 and n，x=79*80, find n=?


Q9. r*=1-1/r, r*-(r-1)*=?


Q10. area of ABCD is 3 times more than ABE，find AE : AD


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by hja379 » Sat Jan 29, 2011 4:48 am
Just curious. What is the source for these questions.
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by VivianKerr » Wed Feb 02, 2011 10:24 pm
Hi Neil!

This is a lot of questions! You may find you get more responses if you create a new post for each question and format them a bit more clearly. :)

For Q7: I love these types of questions! They look intimidating but are actually quite easy. I'm assuming by 987th number, you mean the 987th digit after the decimal? We see that the 5th number will always be "1" so every multiply of 5 will be "1" as well. 985 is a multiply of 5. Counting two more places, the 987th number will be 4.
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by sjian89 » Tue Mar 01, 2011 2:42 pm
Here are my answers. Please confirm. THANKS!

1. 0
2. S(n)
3. 1/3
4. 42, if you mean 5, 6, and 10 only took German, English and French, respectively.
5. 80
6. -15
7. 4
8. 157 or 159
9. -r^-1 + (r-1)^-1
10. 2:3
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