Please solve this Q from CL - FLT

[zango]

Originally Posted by amit_in1976 @ Thu Oct 28, 2004 6:31 pm

Zango/Varsha,
The first statement of the question says that all the three customers have bought 1 utensil each. So if the calculation is for 2 or more of type A, this means that two customers or all customers buy utensils of type A.

The solution given by Zango is the one mentioned in CL FLT. However, I feel that solution given by Ranjan seems more mathematical.

For the second one, Ranjan I had initially thought about the same that if we say four digits, then it is 1000 but then in many problems I have seen...0000 is also considered a case. Maybe I am confused!

Thanks for the help anyways.

Regards

amit,

the soln Ranjan suggested seems to be the mathematical interpretation of my logic - i generally attack probability problems in this fashion (Ronjan - comments please )

[jha16june]

Hi,
First of all solutions given by CL are correct.
For the first question:
Total number of ways in which 3 utensils can be bought are
6c3*4c0 + 6c2*4c1 + 6c1*4c2 + 6c0*4c3 = 120.
Where as the number of favourabel cases are:
6c2*4c1 = 60;
Hence the probability = 60/120 = 1/2.

For the Second question, the smallest 4 digit number will be 1000 and not 0000(which is same as 0 and so a single digit number)
So the correct answer will be FFFF - 1000 = EFFF.

Thanks.

Originally Posted by amit_in1976

Hi,
Following is a question from CL - FLT (mycase it is FLT-9 from last year's material).

A shop has two different types of utensils - 6 of type A and 4 of type B. There are three customers who visit this shop and each of them buys 1 utensil. What is the probability that more than two utensils of type A are purchased.

The answer is 1/2 and the explanation given is not convincing.

My solution would be 6C2*4C1+6C3/10C3 which comes to 2/3


Also, another question from the same FLT

What is the difference between the smallest 4 digit Hexadecimal no and largest 4 digit hexadecimal no.

My answer is FFFF-0000 = FFFF

The solution says FFFF-1000=EFFF

Please let me know where I am wrong?

[chammo]

[quote=jha16june]Hi,
First of all solutions given by CL are correct.
For the first question:
Total number of ways in which 3 utensils can be bought are
6c3*4c0 + 6c2*4c1 + 6c1*4c2 + 6c0*4c3 = 120.
Where as the number of favourabel cases are:
6c2*4c1 = 60;
Hence the probability = 60/120 = 1/2.

For the Second question, the smallest 4 digit number will be 1000 and not 0000(which is same as 0 and so a single digit number)
So the correct answer will be FFFF - 1000 = EFFF.

Thanks.

See if ur giving this soln then why hvnt u taken 6c3*4c0 instead of 6c2*4c1 as the question was asking the prob. of more than 2.

[catquery]

Directions for questions 1 and 2: A shopkeeper believes in the demand-supply law of conducting business. He starts every morning by selling Product X at at Rs. 500 for the first hour. if the number of customers for any hour is more than 10, he will increase the price by Rs. 10 over the previous hour. If less than 10, he will decrease the price by Rs 10 over the previous hour. If it is equal to 10, he will keep the price constant. If the C.P. of product X is Rs. 440, answer the following questions.

1. If the customers for the first 4 hours are 15, 10, 6, 12. Find the profit made by the shopkeeper.

a. Rs 2560 b. Rs. 2740 c. Rs. 2250 d. Rs. 2510

2. The shopkeeper never sells for a loss. If he shuts his shop after 10 hours due to this principle and there was exactly one hour when the number of customers was 10. The number of hours when the number of customers is more than 10 is

a. 0 b. 1 c. 2 d. 3

[thakarsagar]

Originally Posted by catquery

Directions for questions 1 and 2: A shopkeeper believes in the demand-supply law of conducting business. He starts every morning by selling Product X at at Rs. 500 for the first hour. if the number of customers for any hour is more than 10, he will increase the price by Rs. 10 over the previous hour. If less than 10, he will decrease the price by Rs 10 over the previous hour. If it is equal to 10, he will keep the price constant. If the C.P. of product X is Rs. 440, answer the following questions.

1. If the customers for the first 4 hours are 15, 10, 6, 12. Find the profit made by the shopkeeper.

a. Rs 2560 b. Rs. 2740 c. Rs. 2250 d. Rs. 2510

2. The shopkeeper never sells for a loss. If he shuts his shop after 10 hours due to this principle and there was exactly one hour when the number of customers was 10. The number of hours when the number of customers is more than 10 is

a. 0 b. 1 c. 2 d. 3

1) 2740
2) I did'nt get the question right. Are you asking for the minimum of the hours when the no of customers is > 10??
In that case it's 1

[catquery]

ur both the answers are correct but can u plz post the detailed solution of the second question as i could not understand that one.

Originally Posted by thakarsagar

1) 2740
2) I did'nt get the question right. Are you asking for the minimum of the hours when the no of customers is > 10??
In that case it's 1

[thakarsagar]

Originally Posted by catquery

ur both the answers are correct but can u plz post the detailed solution of the second question as i could not understand that one.

2) See , the only possible sequence at which he can sell is...(ie if we are required to find the min no of hours when the no of customers is > 10)

500, 490,480,470,460,450,440,440,450,440

It increases only once.

[catquery]

1. let x^a + x^b = 1 , x > 0 Consider three statements :

1 ab > 0
2 a(x-1) > 0
3 a(x-1) < 0

Which of the following is necessarily true ?

a. 1 only b. 1 and 2 c. 1 and 3 d. None of these

2. t_1, t_2, t_3........... are infinite terms of a series defined as follows :

t_1 = 1
t_n = X * t_n-1 for all n>= 2 and n being even
t_n = Y * t_n-1 for all n>= 2 and n being odd
where x and y are constants such that [x] < 1 and [y] < 1
What is the sum to infinite terms ?

a. 1+x/ 1-xy b. 1+xy/ 1-xy+x+y c. 1-xy/ 1+xy-x-y d. None of these

[dICONoCLAST]

well..regarding the frsy question..wat i will say is..:
makin it as simple as tings shud b..lets take
x=2,a=-1,b=-1
nd bingo..it satisfyin the given equation..nd conseqently..we have (c) the right option..
isnt it..
nd yar..2nd question..i gt no clue..
plzz..whoever helps out..do make it simple 4 me to und..
he he he

[anupam will return]

Originally Posted by catquery

1. let x^a + x^b = 1 , x > 0 Consider three statements :

1 ab > 0
2 a(x-1) > 0
3 a(x-1) < 0

Which of the following is necessarily true ?

a. 1 only b. 1 and 2 c. 1 and 3 d. None of these

2. t_1, t_2, t_3........... are infinite terms of a series defined as follows :

t_1 = 1
t_n = X * t_n-1 for all n>= 2 and n being even
t_n = Y * t_n-1 for all n>= 2 and n being odd
where x and y are constants such that [x] < 1 and [y] < 1
What is the sum to infinite terms ?

a. 1+x/ 1-xy b. 1+xy/ 1-xy+x+y c. 1-xy/ 1+xy-x-y d. None of these

1) I just tried out some random values.. found 1 and 3 to be correct. hence c

2) the series can be expressed as :

1 + x + xy + x^2*y + x^2*y^2 + .........
So we have two infinite GP series:
a) 1 + xy + x^2*y^2 + x^3*y^3 + ..... and
b) x{ 1 + xy + x^2*y^2 + x^3*y^3 + ......}
therefore a = 1/(1-xy) and b = x/(1-xy) Hence final answer is a+b = (1+x)/(1-xy) (option a)

cheers,