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Re: There are y different travelers who each have a choice of vacationing at one of n different destinations.

Assume some easy numbers and test the answers. Set Y=3 and n=2 So 3 travelers each have 2 choices. This equals 2^3=8 ways they can be allocated. Since there are only 2 ways all 3 of them can stay at the same spot, the probability is 2/8 = 1/4 Which of the answers gives 1/4 when the substitution is m...


Re: In a city where all streets run east-to-west, all avenues run north-to-south, and all intersections are right angles

5 steps down and 2 to the right are required to make the trip. The 5 steps down can be allocated to the 3 avenues 7!/5!2! = 21 ways Since 2 steps down are allocated to avenue 1 in the question, this leaves 3 steps to be allocated to the other 2 avenues, which can be done 4!/3! = 4 ways Answer [spoil...


Re: A company plans to assign identification numbers to its employees. Each number is to consist of four different digit

Since 0 can't be the first digit there are 9 choices for the first digit . For the second digit there are also 9 choices since 0 can be used. Third digit then 8 choices. And fourth digit 7 choices. So the total is 9*9*8*7. Rather than multiplying this out, we can see that the 9*9 will leave a 1 as t...


Re: In the game of Dubblefud, red chips, blue chips and green chips are each worth \(2, 4\) and \(5\) points respectivel

Set the numbers of blue and green chips equal to X and the number of red chips equal to Y.

So 2^Y * 4^X*5^X = 16000, or

2^Y * 2^2X * 5^X = 2^4 * 2^3 * 5^3, or

2^(Y+2X)*5^X = 2^7 *5^3. So

X=3 and (Y+2*3)=7, so

Y=1=number of red chips


Re: Bikesville is 200 miles from Restsville. Jasmine can complete the entire trip in 8 hours, and Monte takes two hours

One speed is 200/8=25, the other is 200/(8+2)= 20 Closing speed is the sum of the two or 45 Distance traveled between them is 200, so Time=distance/rate = 200/45 = 4.44 hours. Answer is not among the answer choices. I don't view 4.4 as being approximately 4, even if 4 is the best choice among them.


Re: A woman has seven cookies - four chocolate chip and three oatmeal. She gives one cookie to each of her six children

Distributing 6 cookies can be done in the following ways: 3 chocolate, 3 oatmeal 4 chocolate, 2 oatmeal Pairing Deborah and Kim (D and K) together, let's examine each way above: D&K can each have a chocolate cookie, in which case there are 4 choices of children for the remaining chocolate cookie. Th...


Re: If Jake loses \(8\) pounds, he will weigh twice as much as his sister. Together they now weigh \(278\) pounds. What

Source: GMAT Paper Tests If Jake loses \(8\) pounds, he will weigh twice as much as his sister. Together they now weigh \(278\) pounds. What is Jake's present weight, in pounds? A. \(131\) B. \(135\) C. \(139\) D. \(147\) E. \(188\) The OA is E This is the same thing as saying that if you subtract ...


Re: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times,

The question is asking for the probability of a set of outcomes which occur in a specific order. Since each toss is independent of the other and each face has a 1/2 chance of appearing the probability is [spoiler]1/32, E[/spoiler] If the question had asked for probability of 3 heads and 2 tails occu...


Re: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta,

The pattern of labeling numbers is a repeating pattern of 5 letters. So we need to determine how many cycles plus any fraction of a cycle are contained within the number. We are free to choose which gamma and which delta. Let's choose the smallest, 2 and 3. So, the number for which a label is desire...


Re: If x < y and y < 10, what is the greatest possible integer value of x + y?

Easy to make the assumption that since the question is seeking an integer value that the individual values must also be integers, but that is not stated as a limitation. So the goal is to maximize both X and Y to maximize their sum. Clearly each can be >9 and every amount below 10 that Y is must be ...


Re: If Enid and Topanga each roll a single ten-sided die (which has sides numbered 1 through 10), what is the probabilit

Don't forget ties.

The odds of a tie are one rolls a number and the other has 1/10 chance of matching, so

1/10 chance of tie

This leaves 9/10 chance to roll different numbers.

Half the time a given person will roll higher than the other, so

1/2*9/10 = [spoiler]9/20, B[/spoiler]


Re: On each of the first three days of the month, Danny ate twice the number of apples he had eaten the day before. The

Let X equal the number of apples eaten on the first day. So the second day he ate 2X apples and the third day 4X. Let the number of apples he ate on the 4th day equal Y. The ratio of the number of apples eaten on the third day to the number eaten on the 4th day is then: 4X/Y = 3/5 Y is then equal to...