ladesigner1

Determine a positive integer's expression for: "The sum of half the given number and twice the value of the number's reciprocal is?" I have "Sum = x/2 + 2/x" because the 2/x comes from 2(1/x) when I let x=positive integer. I would like to confirm this and compare it to (1/x)^2 because I wonder how word problems are phrased when a "square" is involved. Does "twice" ALWAYS mean 2x?

There is a total of 120 marbles in a box, each of which is red, green, blue, or white. If one marble is drawn from the box at random, the probability that it will be white is 1/4 and the probability that it will be green is 1/3. What is the probability that the marble will be either red or blue? Answer is 5/12, but how?

A certain state legislature consists of 124 members, each of whom is either a Democrat or a Republican. If there are 18 more Republicans than Democrats, how many Republicans are in the legislature? Answer is 71, but how?

In a certain fund, 40 percent of the money is invested in stocks, and of that portion, 20 percent is invested in preferred stocks. If the fund has $576 invested in preferred stocks, what is the total amount of the fund? Answer is $7,200, but how?

So, the following sentence is correct? Only one of the President's nominees was confirmed. Please advise. Thanks.

The Schaum's Authors explain that "we must separate the two cases" regarding the Zero Digit from the rest of the even-numbered digits. The explaination gets lengthy in the Schaum's College Mathematics book, and it does seem to fit with the answer indicated from the initial posting by zenith2000. Unfortunately, I don't think I can do justice to the piecewise solution that details 2/3-page of a densely-worded explaination from the book. Best just to look directly at entire example from the book.

A 3-member rowing team is to be selected from 4 men and 5 women. How many different 3-member teams be formed subject to the requirement that each team have at least 1 woman and at least 1 man in it? ANSWER is 70, but how?

Nothing like finding a full explaination in a book! I just picked up Schaum's Outlines of College Mathematics (Ayres/Schmidt) and found the full explaination to this problem on page 132 - #20.3 ©. It is a Permutation-type problem (I stand corrected from an earlier posting) with a detailed discussion on how to solve problems like these. Multiplicatin Principle applied: First, we form all numbers ending in 0; there are 6*5*1 of them. Next, we form all numbers ending in 2, 4 or 6; there are 5*5*3 of them. (The 3 comes from the three even digits: 2,4,6) Thus, in all, there are 6*5*1 + 5*5*3 = 105 numbers. Hope this is a start to where you can find the answer...

Mostly every solved Combination-type question I've seen involves either the "Multiplication Principle" or a subtraction/difference method. My only reference for this is via Schaum's Outlines of Statistics (Spiegel) and the FREE material from The Delta Course's Counting Methods Guide (PDF). I have never seen vknittala's approach applied before, but that doesn't mean it can't work. I am wondering: Rather than a Permutation-type problem (where ordered arrangement is considered), how about thinking about this question as a Combination-type problem? I thought about 7 objects taken 4 at a time... (7 digits combined with the 4 even numbers: 0, 2, 4, and 6) Then, 7C4 = 35. Multiplication Principle (more comfortable when I see this in solutions) then applied to the 35 combinations that consider the three-digit combinations to yield... 35*3 = 105 Does this method/answer fly?

There are 3 representatives from 5 different companies at a meeting. If they shake hands such that no representative shakes hand with his colleague, find the number of handshakes. Is it 5*4*3 ?