Help needed

[rakeshrajagopal]

Hi All,

I have few more questions to which I am not able to find a solution.

1. A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the 1st row is standing in fron t of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of teh people are possible?

Choice of Answers - 5,6,9,24,36

2. On saturday morning malachi will begin a camping vacation and he will return home at the end of teh first day on which it rains. If on the first three days of the vacation the probability of rain on each day is .2, what is the probability that malachi will return home at the end of the day on the following monday?

Choice of Answers - .008, .0128, .488, .512, .640

3. The population of city x is 50% of the population of city y. The population of city x is what % of teh total population of city x & city y?

Choice of answers - 25%, 33 1/3%, 40%, 50%, 66 2/3%

4. The points R,T,U lie on a circle that has radius 4. If the length of arc RTU is 4pi/3, what is the length of line segment RU?

Choice of answers - 4/3, 8/3, 3,4,6.

5. A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average(arithmetic mean) of teh other 20 numbers in the list, then n is what fraction of the sum of the numbers in the list?

Choice of answers - 1/20, 1/6, 1/5, 4/21, 5/21.

6. For any integer k greater than 1, the symbol k^* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5^*/4^*?

Choice of answers - 5, 5/4,4/5,1/4,1/5.

7. One gram of a certain health food contains 7% of teh minimum daily requirement of vitamin E and 3% of the minimum daily requirement of vitamin A. If E&A are to be obtained from no other source, approximately how many grams of the health food must be eaten daily to provide at least the minimum daily requirement of both vitamins?

Choice of answers - 3,7,10,14,33.

Cheers

Rakesh

[outreach]

3. The population of city x is 50% of the population of city y. The population of city x is what % of teh total population of city x & city y?

Choice of answers - 25%, 33 1/3%, 40%, 50%, 66 2/3%

x=1/2y
x+y=3/2y

now the Q is x is what percent of x+y

i.e
3/2y=100%
1/2y=?

?=33 1/3%

[outreach]

2. On saturday morning malachi will begin a camping vacation and he will return home at the end of teh first day on which it rains. If on the first three days of the vacation the probability of rain on each day is .2, what is the probability that malachi will return home at the end of the day on the following monday?

Choice of Answers - .008, .0128, .488, .512, .640


making an assumption that malachi returns only when it rains

probability of raining=.2
probability of not raining=1-.2=.8


does not rain on first day=0.8
does not rain on 2 day=0.8
rains on 3 day=0.2

0.8*.8*.2
0.128



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1. A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the 1st row is standing in fron t of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of teh people are possible?

Choice of Answers - 5,6,9,24,36


1 2 3 4 5 6 be the six people with increasing heights.

1 will always stand in left corner of row 1
6 will always stand in right corner of row 2.

now we have 4 people ( 2 3 4 5) to arrange in 4 seats. 2 in the front and 2 in the back.

select 2 people from 4 people who will sit in the first row = 4C2 ways = 6.
but a case when both 4 and 5 are in the first row. is not acceptable. we need to have atleast one of 4 or 5 in the second row. hence subtract 1.
hence, answer = 6 - 1 =5

[outreach]

4. The points R,T,U lie on a circle that has radius 4. If the length of arc RTU is 4pi/3, what is the length of line segment RU?

Choice of answers - 4/3, 8/3, 3,4,6


lenght of arc =2*pi*r*(angle/360)
given length of arc=4pi/3

4pi/3=2*pi*r*(angle/360)
angle=60

centre of circle be O
OR and OU lenth same as both r radius
hence triangle ORU is equilateral triangle

length of RU is 4

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6. For any integer k greater than 1, the symbol k^* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5^*/4^*?

Choice of answers - 5, 5/4,4/5,1/4,1/5.

1/5

[rakeshrajagopal]

2. On saturday morning malachi will begin a camping vacation and he will return home at the end of teh first day on which it rains. If on the first three days of the vacation the probability of rain on each day is .2, what is the probability that malachi will return home at the end of the day on the following monday?

Choice of Answers - .008, .0128, .488, .512, .640


making an assumption that malachi returns only when it rains

probability of raining=.2
probability of not raining=1-.2=.8


does not rain on first day=0.8
does not rain on 2 day=0.8
rains on 3 day=0.2

0.8*.8*.2
0.128



------


1. A photographer will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the 1st row is standing in fron t of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of teh people are possible?

Choice of Answers - 5,6,9,24,36


1 2 3 4 5 6 be the six people with increasing heights.

1 will always stand in left corner of row 1
6 will always stand in right corner of row 2.

now we have 4 people ( 2 3 4 5) to arrange in 4 seats. 2 in the front and 2 in the back.

select 2 people from 4 people who will sit in the first row = 4C2 ways = 6.
but a case when both 4 and 5 are in the first row. is not acceptable. we need to have atleast one of 4 or 5 in the second row. hence subtract 1.
hence, answer = 6 - 1 =5

Isn't 4C2 = 4x3 = 12 rather than 6. Kindly explain

[rakeshrajagopal]

4. The points R,T,U lie on a circle that has radius 4. If the length of arc RTU is 4pi/3, what is the length of line segment RU?

Choice of answers - 4/3, 8/3, 3,4,6


lenght of arc =2*pi*r*(angle/360)
given length of arc=4pi/3

4pi/3=2*pi*r*(angle/360)
angle=60

centre of circle be O
OR and OU lenth same as both r radius
hence triangle ORU is equilateral triangle

length of RU is 4

--------------
6. For any integer k greater than 1, the symbol k^* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5^*/4^*?

Choice of answers - 5, 5/4,4/5,1/4,1/5.

1/5

Kindly explain how you arrived at 1/5 as the solution.