The Official CAT 2007 Quant Thread

[Cymba]

Originally Posted by STALWART

From the digits 1,2,3........9 , a nine digit number is formed without any repitition . what is the probability that the number will be divisible by 11 ?

For a no. to be divisible by 11, the diff b/w the sums of no. in odd n even places must either be 0 or a multiple of 11.

Now, since its a nine digit no. without repitation, hence the sum of the digits is 45.

Let sum of digits in odd places be x
then, sum of digits in even places be 45-x

So, |x-(45-x)|= 11n or 0

This is not true for any value. Hence, prob is zero.

[STALWART]

Originally Posted by Cymba

For a no. to be divisible by 11, the diff b/w the sums of no. in odd n even places must either be 0 or a multiple of 11.

Now, since its a nine digit no. without repitation, hence the sum of the digits is 45.

Let sum of digits in odd places be x
then, sum of digits in even places be 45-x

So, |x-(45-x)|= 11n or 0

This is not true for any value. Hence, prob is zero.

What about 28 and 17 ...... ?? (28-17 = 11) and (28+17 = 45)

... Sayonara

[arunk8186]

Originally Posted by STALWART

From the digits 1,2,3........9 , a nine digit number is formed without any repitition . what is the probability that the number will be divisible by 11 ?

.... Sayonara

Difference bet the sum of digits at odd places (this be x) and even places (this is 45-x) has to be 11n (n = -1, 0, 1)

|x-(45-x)| = 11n; solving, x= 17, 28 and (45-x) =28, 17 respectively.

No. of digits in odd places = 5(sum=x); No. of digits in even places = 4(sum = 45-x)

Case 1:

x = 17 and (45-x) = 28

Possibilities for x=17 are numbers formed wit the digits 1,2,3,4,7(5! numbers totally) or

1,2,3,5,6(another 5! numbers) ( No other numbers outside this combination satisfies the condition of x = 17

Courtesy: Elimination )

(NOTE: all these 5! + 5! = 240 no.s are distinct permutations)

So Possibilities for (45-x) = 28 with the remaining 4 digits after the odd places are filled wit one of the above

240 numbers is = 4! Ways

Total numbers in this case 1 = 240*4! = 5760.

Case 2:

x = 28 and (45-x) = 17

Possibilities for (45-x)=17, are numbers formed wit the digits {9,5,1,2},{9,4,3,1},

{8,6,1,2},{8,5,3,1},{8,4,2,3},{7,6,3,1},{7,5,4,1}, {7,5,2,3},{6,5,2,4} a total of 9*4!

=216 numbers...

So Possibilities for x=28 with the remaining 5 digits after the even places are filled wit one of the 216

numbers is = 5! Ways

Total numbers in this case 2 = 216*5! = 25920.

Total 9 digit numbers possible = 9! = 362880

Total favorable cases( no.s divisible by 11) = 5760+25920 = 31680

Probability that the selected number is divisible by 11= 31680 / 362880 = .0873

Not the elegant of solutions... but still Stalwart Bhai is this right?

Cheers

[Cymba]

Here are some qs from last yr XAT ppr

1) For how many integers n^(n/(20-n)) is the square of an integer?

a) 0 b) 1 c) 2 d) 3 e) 4

2) ABC is a triangle with (angle)ABC=30 and (angle)CAB=15. If M is the midpoint of AB then (angle)ACM=

a) 15 b) 30 c) 45 d) 60 e) None of these

[Hi2All]

Hello friends...
A man spending half of his salary for house hold expenses, 1/4th for rent, 1/5th for travel expenses, a man deposits the rest in a bank. If his monthly deposits in the bank amount 50. What is his monthly salary?

How to approach this problem???

[junoonmba]

Please sove these two........

3f(x+2)+4f(1/x+2)=4x f(4)=?

and

a<b<c
a+b+c=6,ab+bc+ca=9

Max a and min a ?

[anshaar]

sorry buddy....I dint get ur question

[Kent]

Put x=0.5 once and then x=2, then solve for f(4) from the 2 equations.
Do a,b,c have anymore constraints ?

[gautamgomzi]

Q. Brass is an alloy of copper and zinc. Bronze is an alloy containing 80%copper, 4%zinc and 16% tin. A fused mass of brass & bronze is found to contain 74% copper, 16%zinc and 10% tin. The ratio of copper to zinc in Brass is ??Ans. 64% and 36%Q. Concentrations of three wines A, B and C are 10%, 20% and 30% respectively. They are mixed in the ratio 2:3 resulting in a 23% concentrated solution. Find x.Ans. x = 5Hey Guys pls help me out with these ques..Thnx...Gautam

[IIM maniac]

Originally Posted by gautamgomzi

Q. Brass is an alloy of copper and zinc. Bronze is an alloy containing 80%copper, 4%zinc and 16% tin. A fused mass of brass & bronze is found to contain 74% copper, 16%zinc and 10% tin. The ratio of copper to zinc in Brass is ??Ans. 64% and 36%Q. Concentrations of three wines A, B and C are 10%, 20% and 30% respectively. They are mixed in the ratio 2:3 resulting in a 23% concentrated solution. Find x.Ans. x = 5Hey Guys pls help me out with these ques..Thnx...Gautam

Hi,
I dont know if my apraoch is correct or not, but here is what my answers
comes for 1st question :
Bronze contains copper : Zinc : Tin = 80:4:16
Brass does not contains Tin (This i have assumed from question)
The fusion contains copper : Zinc : Tin = 74 : 16 : 10
Now for copper in Brass:
74% copper in fusion is the avg of % copper in Bronze & brass, so
(80 + x) / 2 = 74,
144 - 80 = 64
So copper is 64 % and remaining is Zinc i.e. 36%
I hope i am correct, if i am wrong then suggestion are welcome